WO2025149464A1 - Alternative prediction methods for the lifting wavelet transform in subdivision mesh surfaces - Google Patents

Abstract

Some embodiments of a method may include: obtaining an input signal corresponding to a mesh; splitting the input signal into a plurality of odd-indexed samples and a plurality of even-indexed samples, wherein the plurality of odd-indexed samples of the input signal correspond to vertices in the mesh at a lower resolution level, and wherein the plurality of even-indexed samples of the input signal correspond to vertices in the mesh at a higher resolution level; determining at least one sample of a predicted signal using at least three of the plurality of odd-indexed samples; and subtracting the predicted signal from the plurality of even-indexed samples to generate a wavelet coefficient signal.

Description

ALTERNATIVE PREDICTION METHODS FOR THE LIFTING WAVELET TRANSFORM IN SUBDIVISION MESH SURFACES

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims benefit of European Patent Application No. EP24305075, entitled “ALTERNATIVE PREDICTION METHODS FOR THE LIFTING WAVELET TRANSFORM IN SUBDIVISION MESH SURFACES” and filed January 11, 2024, which is hereby incorporated by reference in its entirety.

BACKGROUND

[0002] Visual volumetric video-based coding (V3C) is described in ISO/IEC 23090-5:2021 , Information technology — Coded representation of immersive media — Part 5: Visual volumetric video-based coding (V3C) and video-based point cloud compression (V-PCC). Video-based dynamic mesh coding (V-DMC) is a framework for compressing dynamic meshes that is being developed by extending V3C. The V-DMC framework may involve different attributes specified for a dynamic mesh sequence. In V-DMC, the underlying static mesh codec may decode mesh attributes per face or per vertex. These attributes may provide additional information about the static mesh e.g., color, texture coordinates, normals, reflectance information, transparency information, and/or user-defined attributes.

[0003] For V-DMC, a framework is developed by extending V3C. V3C is described at ISO/IEC 23090- 5:2021, Information technology — Coded representation of immersive media — Part 5: Visual volumetric video-based coding (V3C) and video-based point cloud compression (V-PCC).

SUMMARY

[0004] A first example method in accordance with some embodiments may include: obtaining an input signal corresponding to a mesh; splitting the input signal into a plurality of odd-indexed samples and a plurality of even-indexed samples, wherein the plurality of odd-indexed samples of the input signal correspond to vertices in the mesh at a lower resolution level, and wherein the plurality of even-indexed samples of the input signal correspond to vertices in the mesh at a higher resolution level; determining at least one sample of a predicted signal using at least three of the plurality of odd-indexed samples; and subtracting the predicted signal from the plurality of even-indexed samples to generate a wavelet coefficient signal. [0005] Some embodiments of the first example method may further include subtracting the wavelet coefficient signal from the plurality of odd-indexed samples.

[0006] For some embodiments of the first example method, determining the at least one sample of the predicted signal may include determining at least one weighted value based on four samples of the plurality of odd-indexed samples, wherein the four samples are nearest neighbors of the at least one sample of the predicted signal.

[0007] For some embodiments of the first example method, the nearest neighbors are vertices of triangles adjacent to the at least one sample of the predicted signal.

[0008] For some embodiments of the first example method, determining the at least one weighted value based on the four samples of the plurality of odd-indexed samples includes determining an unequal weighting of the four samples.

[0009] For some embodiments of the first example method, determining the at least one weighted value is based on relative distances of the four samples to the at least one sample of the predicted signal.

[0010] For some embodiments of the first example method, determining the at least one sample of the predicted signal includes determining at least one weighted value based on three samples of the plurality of odd-indexed samples, wherein the three samples are nearest neighbors of the at least one sample of the predicted signal.

[0011] For some embodiments of the first example method, the nearest neighbors are vertices of triangles adjacent to the at least one sample of the predicted signal.

[0012] For some embodiments of the first example method, determining the at least one weighted value based on the three samples of the plurality of odd-indexed samples includes determining an unequal weighting of the three samples.

[0013] For some embodiments of the first example method, determining the at least one weighted value is based on relative distances of the three samples to the at least one sample of the predicted signal.

[0014] For some embodiments of the first example method, the at least one sample of the predicted signal may include a boundary point of the mesh.

[0015] A first example apparatus in accordance with some embodiments may include: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform any one of the methods listed above. [0016] A second example method in accordance with some embodiments may include: obtaining a wavelet-transformed coarse input signal corresponding to a mesh, wherein the wavelet-transformed coarse input signal includes a first plurality of samples; obtaining a wavelet coefficients input signal corresponding to the mesh; determining at least one sample of a predicted signal using at least three of the first plurality of samples of the mesh signal; adding the predicted signal to the wavelet coefficients input signal to generate a second plurality of samples; and merging the first plurality of samples with the second plurality of samples to generate an output signal corresponding to the mesh.

[0017] For some embodiments of the second example method, the first plurality of samples corresponds to even-indexed samples of the output signal, and the second plurality of samples corresponds to odd- indexed samples of the output signal.

[0018] Some embodiments of the second example method may further include subtracting the wavelet coefficients input signal from the wavelet-transformed coarse input signal.

[0019] For some embodiments of the second example method, determining the at least one sample of the predicted signal may include determining at least one weighted value based on four samples of the first plurality of samples, wherein the four samples are nearest neighbors of the at least one sample of the predicted signal.

[0020] For some embodiments of the second example method, the nearest neighbors are vertices of triangles adjacent to the at least one sample of the predicted signal.

[0021] For some embodiments of the second example method, determining the at least one weighted value based on the four samples of the first plurality of samples includes determining an unequal weighting of the four samples.

[0022] For some embodiments of the second example method, determining the at least one weighted value is based on relative distances of the four samples to the at least one sample of the predicted signal.

[0023] For some embodiments of the second example method, determining the at least one sample ofthe predicted signal includes determining at least one weighted value based on three samples ofthe first plurality of samples, wherein the three samples are nearest neighbors of the at least one sample of the predicted signal.

[0024] For some embodiments of the second example method, the nearest neighbors are vertices of triangles adjacent to the at least one sample of the predicted signal. [0025] For some embodiments of the second example method, determining the at least one weighted value based on the three samples of the first plurality of samples includes determining an unequal weighting of the three samples.

[0026] For some embodiments of the second example method, determining the at least one weighted value is based on relative distances of the three samples to the at least one sample of the predicted signal.

[0027] For some embodiments of the second example method, the at least one sample of the predicted signal includes a boundary point of the mesh.

[0028] A second example apparatus in accordance with some embodiments may include: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform any one of the methods listed above.

[0029] A third example method in accordance with some embodiments may include: obtaining an input signal corresponding to a mesh; splitting the input signal into a first plurality of samples and a second plurality of samples, determining at least one sample of a predicted signal using at least three of the first plurality of samples; and subtracting the predicted signal from the second plurality of samples to generate a wavelet coefficient signal.

[0030] For some embodiments of the second example method, the first plurality of samples of the input signal correspond to vertices in the mesh at a lower resolution level, and the second plurality of samples of the input signal correspond to vertices in the mesh at a higher resolution level.

[0031] For some embodiments of the second example method, the first plurality of samples of the input signal correspond to odd-indexed samples of the input signal, and the second plurality of samples of the input signal correspond to even-indexed samples of the input signal.

[0032] For some embodiments of the second example method, the first plurality of samples of the input signal correspond to vertices in the mesh at a higher resolution level, and the second plurality of samples of the input signal correspond to vertices in the mesh at a lower resolution level.

[0033] For some embodiments of the second example method, the first plurality of samples of the input signal correspond to even-indexed samples of the input signal, and the second plurality of samples of the input signal correspond to odd-indexed samples of the input signal.

[0034] A third example apparatus in accordance with some embodiments may include: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform any one of the methods listed above. [0035] An example method of performing a wavelet transform on an input signal corresponding to a mesh in accordance with some embodiments may include: obtaining the input signal; splitting the input signal into lower-resolution samples and higher-resolution samples; generating a prediction signal, wherein the prediction signal includes prediction samples corresponding to the higher-resolution samples, and wherein each of the prediction samples is generated based on at least three of the lower-resolution samples; and subtracting the prediction signal from the higher-resolution samples to generate a wavelet coefficient signal.

[0036] A fourth example apparatus in accordance with some embodiments may include: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform any one of the methods listed above.

[0037] An example method of performing a wavelet transform on an input signal corresponding to a mesh in accordance with some embodiments may include: splitting the input signal into lower-resolution samples and higher-resolution samples; generating a prediction signal based on at least three lower-resolution samples for each sample of the prediction signal; and subtracting the prediction signal from the higher- resolution samples to generate a wavelet coefficient signal.

[0038] A fifth example apparatus in accordance with some embodiments may include: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform any one of the methods listed above.

[0039] A sixth example apparatus in accordance with some embodiments may include at least one processor configured to perform any one of the methods listed above.

[0040] A seventh example apparatus in accordance with some embodiments may include a computer- readable medium storing instructions for causing one or more processors to perform any one of the methods listed above.

[0041] An eighth example apparatus in accordance with some embodiments may include at least one processor and at least one non-transitory computer-readable medium storing instructions for causing the at least one processor to perform any one of the methods listed above.

[0042] An example signal in accordance with some embodiments may include a signal conveying a wavelet coefficient signal generated according to a method listed above.

BRIEF DESCRIPTION OF THE DRAWINGS

[0043] FIG. 1A is a system diagram illustrating an example communications system according to some embodiments. [0044] FIG. 1 B is a system diagram illustrating an example wireless transmit/receive unit (WTRU) that may be used within the communications system illustrated in FIG. 1A according to some embodiments.

[0045] FIG. 1 C is a system diagram illustrating an example set of interfaces for a system according to some embodiments.

[0046] FIG. 2A is a functional block diagram of block-based video encoder, such as an encoder used for Versatile Video Coding (WC), according to some embodiments.

[0047] FIG. 2B is a functional block diagram of a block-based video decoder, such as a decoder used for WC, according to some embodiments.

[0048] FIG. 3A is a schematic side view illustrating an example waveguide display that may be used with extended reality (XR) applications according to some embodiments.

[0049] FIG. 3B is a schematic side view illustrating an example alternative display type that may be used with extended reality applications according to some embodiments.

[0050] FIG. 3C is a schematic side view illustrating an example alternative display type that may be used with extended reality applications according to some embodiments.

[0051] FIG. 4A is a schematic illustration showing an example base mesh according to some embodiments.

[0052] FIG. 4B is a schematic illustration showing an example mesh after 1 subdivision iteration according to some embodiments.

[0053] FIG. 4C is a schematic illustration showing an example mesh after 2 subdivision iterations according to some embodiments.

[0054] FIG. 4D is a schematic illustration showing an example mesh after 3 subdivision iterations according to some embodiments.

[0055] FIG. 4E is a schematic illustration showing an example mesh after 4 subdivision iterations according to some embodiments.

[0056] FIG. 4F is a schematic illustration showing an example mesh after 5 subdivision iterations according to some embodiments.

[0057] FIG. 5 is a schematic illustration showing an example wavelet coefficient computation in linear polyhedral subdivision according to some embodiments. [0058] FIG. 6A is a schematic illustration showing an example regular connectivity of a triangular mesh according to some embodiments.

[0059] FIG. 6B is a schematic illustration showing an example irregular connectivity of a triangular mesh according to some embodiments.

[0060] FIG. 6C is a schematic illustration showing an example semi-regular connectivity of a triangular mesh according to some embodiments.

[0061] FIG. 7A is a process diagram illustrating an example forward lifting wavelet transform according to some embodiments.

[0062] FIG. 7B is a process diagram illustrating an example forward lifting wavelet transform according to some embodiments.

[0063] FIG. 7C is a process diagram illustrating an example inverse lifting wavelet transform according to some embodiments.

[0064] FIG. 7D is a process diagram illustrating an example inverse lifting wavelet transform according to some embodiments.

[0065] FIG. 8A is a schematic illustration showing an example manifold mesh according to some embodiments.

[0066] FIG. 8B is a schematic illustration showing an example non-manifold mesh according to some embodiments.

[0067] FIG. 8C is a schematic illustration showing an example non-manifold mesh according to some embodiments.

[0068] FIG. 9A is a schematic illustration showing an example closed mesh with no boundaries according to some embodiments.

[0069] FIG. 9B is a schematic illustration showing an example open mesh with a boundary according to some embodiments.

[0070] FIG. 10A is a schematic illustration showing an example mesh containing a new vertex not on a mesh boundary according to some embodiments.

[0071] FIG. 10B is a schematic illustration showing an example mesh containing a new vertex on a mesh boundary according to some embodiments. [0072] FIG. 11 is a process diagram illustrating an example V-DMC intra-frame encoder according to some embodiments.

[0073] FIG. 12 is a process diagram illustrating an example V-DMC intra-frame decoder according to some embodiments.

[0074] FIG. 13 is a schematic illustration showing example different size adjacent triangles of a new mesh vertex according to some embodiments.

[0075] FIG. 14 is a schematic illustration showing an example different size adjacent triangles of a new mesh vertex according to some embodiments.

[0076] FIG. 15 is a schematic illustration showing an example adjacent triangle of a new vertex on a mesh boundary according to some embodiments.

[0077] FIG. 16 is a flowchart illustrating an example process for preforming a wavelet transform according to some embodiments.

[0078] FIG. 17 is a flowchart illustrating an example process for preforming an inverse wavelet transform according to some embodiments.

[0079] The entities, connections, arrangements, and the like that are depicted in— and described in connection with— the various figures are presented by way of example and not by way of limitation. As such, any and all statements or other indications as to what a particular figure “depicts,” what a particular element or entity in a particular figure “is” or “has,” and any and all similar statements— that may in isolation and out of context be read as absolute and therefore limiting— may only properly be read as being constructively preceded by a clause such as “In at least one embodiment, ... " For brevity and clarity of presentation, this implied leading clause is not repeated ad nauseum in the detailed description.

DETAILED DESCRIPTION

[0080] FIG. 1A is a diagram illustrating an example communications system 100 in which one or more disclosed embodiments may be implemented. The communications system 100 may be a multiple access system that provides content, such as voice, data, video, messaging, broadcast, etc., to multiple wireless users. The communications system 100 may enable multiple wireless users to access such content through the sharing of system resources, including wireless bandwidth. For example, the communications systems 100 may employ one or more channel access methods, such as code division multiple access (CDMA), time division multiple access (TDMA), frequency division multiple access (FDMA), orthogonal FDMA (OFDMA), single-carrier FDMA (SC-FDMA), zero-tail unique-word DFT-Spread OFDM (ZT UW DTS-s OFDM), unique word OFDM (UW-OFDM), resource block-filtered OFDM, filter bank multicarrier (FBMC), and the like.

[0081] As shown in FIG. 1A, the communications system 100 may include wireless transmit/receive units (WTRUs) 102a, 102b, 102c, 102d, a RAN 104/113, a CN 106, a public switched telephone network (PSTN) 108, the Internet 110, and other networks 112, though it will be appreciated that the disclosed embodiments contemplate any number of WTRUs, base stations, networks, and/or network elements. Each of the WTRUs 102a, 102b, 102c, 102d may be any type of device configured to operate and/or communicate in a wireless environment. By way of example, the WTRUs 102a, 102b, 102c, 102d, any of which may be referred to as a “station” and/or a “STA”, may be configured to transmit and/or receive wireless signals and may include a user equipment (UE), a mobile station, a fixed or mobile subscriber unit, a subscription-based unit, a pager, a cellular telephone, a personal digital assistant (PDA), a smartphone, a laptop, a netbook, a personal computer, a wireless sensor, a hotspot or Mi-Fi device, an Internet of Things (loT) device, a watch or other wearable, a head-mounted display (HMD), a vehicle, a drone, a medical device and applications (e.g., remote surgery), an industrial device and applications (e.g., a robot and/or other wireless devices operating in an industrial and/or an automated processing chain contexts), a consumer electronics device, a device operating on commercial and/or industrial wireless networks, and the like. Any of the WTRUs 102a, 102b, 102c and 102d may be interchangeably referred to as a UE.

[0082] The communications systems 100 may also include a base station 114a and/or a base station 114b. Each of the base stations 114a, 114b may be any type of device configured to wirelessly interface with at least one of the WTRUs 102a, 102b, 102c, 102d to facilitate access to one or more communication networks, such as the CN 106, the Internet 110, and/or the other networks 112. By way of example, the base stations 114a, 114b may be a base transceiver station (BTS), a Node-B, an eNode B, a Home Node B, a Home eNode B, a gNB, a NR NodeB, a site controller, an access point (AP), a wireless router, and the like. While the base stations 114a, 114b are each depicted as a single element, it will be appreciated that the base stations 114a, 114b may include any number of interconnected base stations and/or network elements.

[0083] The base station 114a may be part of the RAN 104/113, which may also include other base stations and/or network elements (not shown), such as a base station controller (BSC), a radio network controller (RNC), relay nodes, etc. The base station 114a and/or the base station 114b may be configured to transmit and/or receive wireless signals on one or more carrier frequencies, which may be referred to as a cell (not shown). These frequencies may be in licensed spectrum, unlicensed spectrum, or a combination of licensed and unlicensed spectrum. A cell may provide coverage for a wireless service to a specific geographical area that may be relatively fixed or that may change over time. The cell may further be divided into cell sectors. For example, the cell associated with the base station 114a may be divided into three sectors. Thus, in one embodiment, the base station 114a may include three transceivers, i.e., one for each sector of the cell. In an embodiment, the base station 114a may employ multiple-input multiple output (MIMO) technology and may utilize multiple transceivers for each sector of the cell. For example, beamforming may be used to transmit and/or receive signals in desired spatial directions.

[0084] The base stations 114a, 114b may communicate with one or more of the WTRUs 102a, 102b, 102c, 102d over an air interface 116, which may be any suitable wireless communication link (e.g., radio frequency (RF), microwave, centimeter wave, micrometer wave, infrared (IR), ultraviolet (UV), visible light, etc.). The air interface 116 may be established using any suitable radio access technology (RAT).

[0085] More specifically, as noted above, the communications system 100 may be a multiple access system and may employ one or more channel access schemes, such as CDMA, TDMA, FDMA, OFDMA, SC-FDMA, and the like. For example, the base station 114a in the RAN 104/113 and the WTRUs 102a, 102b, 102c may implement a radio technology such as Universal Mobile Telecommunications System (UMTS) Terrestrial Radio Access (UTRA), which may establish the air interface 116 using wideband CDMA (WCDMA). WCDMA may include communication protocols such as High-Speed Packet Access (HSPA) and/or Evolved HSPA (HSPA+). HSPA may include High-Speed Downlink (DL) Packet Access (HSDPA) and/or High-Speed UL Packet Access (HSUPA).

[0086] In an embodiment, the base station 114a and the WTRUs 102a, 102b, 102c may implement a radio technology such as Evolved UMTS Terrestrial Radio Access (E-UTRA), which may establish the air interface 116 using Long Term Evolution (LTE) and/or LTE-Advanced (LTE-A) and/or LTE-Advanced Pro (LTE-A Pro).

[0087] In an embodiment, the base station 114a and the WTRUs 102a, 102b, 102c may implement a radio technology such as NR Radio Access , which may establish the air interface 116 using New Radio (NR).

[0088] In an embodiment, the base station 114a and the WTRUs 102a, 102b, 102c may implement multiple radio access technologies. For example, the base station 114a and the WTRUs 102a, 102b, 102c may implement LTE radio access and NR radio access together, for instance using dual connectivity (DC) principles. Thus, the air interface utilized by WTRUs 102a, 102b, 102c may be characterized by multiple types of radio access technologies and/or transmissions sent to/from multiple types of base stations (e.g., a eNB and a gNB). [0089] In other embodiments, the base station 114a and the WTRUs 102a, 102b, 102c may implement radio technologies such as IEEE 802.11 (i.e., Wireless Fidelity (WiFi), IEEE 802.16 (i.e., Worldwide Interoperability for Microwave Access (WiMAX)), CDMA2000, CDMA2000 1X, CDMA2000 EV-DO, Interim Standard 2000 (IS-2000), Interim Standard 95 (IS-95), Interim Standard 856 (IS-856), Global System for Mobile communications (GSM), Enhanced Data rates for GSM Evolution (EDGE), GSM EDGE (GERAN), and the like.

[0090] The base station 114b in FIG. 1A may be a wireless router, Home Node B, Home eNode B, or access point, for example, and may utilize any suitable RAT for facilitating wireless connectivity in a localized area, such as a place of business, a home, a vehicle, a campus, an industrial facility, an air corridor (e.g., for use by drones), a roadway, and the like. In one embodiment, the base station 114b and the WTRUs 102c, 102d may implement a radio technology such as IEEE 802.11 to establish a wireless local area network (WLAN). In an embodiment, the base station 114b and the WTRUs 102c, 102d may implement a radio technology such as IEEE 802.15 to establish a wireless personal area network (WPAN). In yet another embodiment, the base station 114b and the WTRUs 102c, 102d may utilize a cellular-based RAT (e.g., WCDMA, CDMA2000, GSM, LTE, LTE-A, LTE-A Pro, NR etc.) to establish a picocell or femtocell. As shown in FIG. 1A, the base station 114b may have a direct connection to the Internet 110. Thus, the base station 114b may not be required to access the Internet 110 via the CN 106.

[0091] The RAN 104/113 may be in communication with the CN 106, which may be any type of network configured to provide voice, data, applications, and/or voice over internet protocol (VoIP) services to one or more of the WTRUs 102a, 102b, 102c, 102d. The data may have varying quality of service (QoS) requirements, such as differing throughput requirements, latency requirements, error tolerance requirements, reliability requirements, data throughput requirements, mobility requirements, and the like. The CN 106 may provide call control, billing services, mobile location-based services, pre-paid calling, Internet connectivity, video distribution, etc., and/or perform high-level security functions, such as user authentication. Although not shown in FIG. 1A, it will be appreciated that the RAN 104/113 and/or the CN 106 may be in direct or indirect communication with other RANs that employ the same RAT as the RAN 104/113 or a different RAT. For example, in addition to being connected to the RAN 104/113, which may be utilizing a NR radio technology, the CN 106 may also be in communication with another RAN (not shown) employing a GSM, UMTS, CDMA 2000, WiMAX, E-UTRA, or WiFi radio technology.

[0092] The CN 106 may also serve as a gateway for the WTRUs 102a, 102b, 102c, 102d to access the PSTN 108, the Internet 110, and/or the other networks 112. The PSTN 108 may include circuit-switched telephone networks that provide plain old telephone service (POTS). The Internet 110 may include a global system of interconnected computer networks and devices that use common communication protocols, such as the transmission control protocol (TCP), user datagram protocol (UDP) and/or the internet protocol (IP) in the TCP/IP internet protocol suite. The networks 112 may include wired and/or wireless communications networks owned and/or operated by other service providers. For example, the networks 112 may include another CN connected to one or more RANs, which may employ the same RAT as the RAN 104/113 or a different RAT.

[0093] Some or all ofthe WTRUs 102a, 102b, 102c, 102d in the communications system 100 may include multi-mode capabilities (e.g., the WTRUs 102a, 102b, 102c, 102d may include multiple transceivers for communicating with different wireless networks over different wireless links). For example, the WTRU 102c shown in FIG. 1A may be configured to communicate with the base station 114a, which may employ a cellular-based radio technology, and with the base station 114b, which may employ an IEEE 802 radio technology.

[0094] FIG. 1 B is a system diagram illustrating an example WTRU 102. As shown in FIG. 1 B, the WTRU 102 may include a processor 118, a transceiver 120, a transmit/receive element 122, a speaker/microphone 124, a keypad 126, a display/touchpad 128, non-removable memory 130, removable memory 132, a power source 134, a global positioning system (GPS) chipset 136, and/or other peripherals 138, among others. It will be appreciated that the WTRU 102 may include any sub-combination of the foregoing elements while remaining consistent with an embodiment.

[0095] The processor 118 may be a general purpose processor, a special purpose processor, a conventional processor, a digital signal processor (DSP), a plurality of microprocessors, one or more microprocessors in association with a DSP core, a controller, a microcontroller, Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs) circuits, any other type of integrated circuit (IC), a state machine, and the like. The processor 118 may perform signal coding, data processing, power control, input/output processing, and/or any other functionality that enables the WTRU 102 to operate in a wireless environment. The processor 118 may be coupled to the transceiver 120, which may be coupled to the transmit/receive element 122. While FIG. 1 B depicts the processor 118 and the transceiver 120 as separate components, it will be appreciated that the processor 118 and the transceiver 120 may be integrated together in an electronic package or chip.

[0096] The transmit/receive element 122 may be configured to transmit signals to, or receive signals from, a base station (e.g., the base station 114a) over the air interface 116. For example, in one embodiment, the transmit/receive element 122 may be an antenna configured to transmit and/or receive RF signals. In an embodiment, the transmit/receive element 122 may be an emitter/detector configured to transmit and/or receive I R, UV, or visible light signals, for example. In yet another embodiment, the transmit/receive element 122 may be configured to transmit and/or receive both RF and light signals. It will be appreciated that the transmit/receive element 122 may be configured to transmit and/or receive any combination of wireless signals.

[0097] Although the transmit/receive element 122 is depicted in FIG. 1 B as a single element, the WTRU 102 may include any number of transmit/receive elements 122. More specifically, the WTRU 102 may employ MIMO technology. Thus, in one embodiment, the WTRU 102 may include two or more transmit/receive elements 122 (e.g., multiple antennas) for transmitting and receiving wireless signals over the air interface 116.

[0098] The transceiver 120 may be configured to modulate the signals that are to be transmitted by the transmit/receive element 122 and to demodulate the signals that are received by the transmit/receive element 122. As noted above, the WTRU 102 may have multi-mode capabilities. Thus, the transceiver 120 may include multiple transceivers for enabling the WTRU 102 to communicate via multiple RATs, such as NR and IEEE 802.11, for example.

[0099] The processor 118 of the WTRU 102 may be coupled to, and may receive user input data from, the speaker/microphone 124, the keypad 126, and/or the display/touchpad 128 (e.g., a liquid crystal display (LCD) display unit or organic light-emitting diode (OLED) display unit). The processor 118 may also output user data to the speaker/microphone 124, the keypad 126, and/or the display/touchpad 128. In addition, the processor 118 may access information from, and store data in, any type of suitable memory, such as the non-removable memory 130 and/or the removable memory 132. The non-removable memory 130 may include random-access memory (RAM), read-only memory (ROM), a hard disk, or any other type of memory storage device. The removable memory 132 may include a subscriber identity module (SIM) card, a memory stick, a secure digital (SD) memory card, and the like. In other embodiments, the processor 118 may access information from, and store data in, memory that is not physically located on the WTRU 102, such as on a server or a home computer (not shown).

[0100] The processor 118 may receive power from the power source 134, and may be configured to distribute and/or control the power to the other components in the WTRU 102. The power source 134 may be any suitable device for powering the WTRU 102. For example, the power source 134 may include one or more dry cell batteries (e.g., nickel-cadmium (NiCd), nickel-zinc (NiZn), nickel metal hydride (NiMH), lithium- ion (Li-ion), etc.), solar cells, fuel cells, and the like.

[0101] The processor 118 may also be coupled to the GPS chipset 136, which may be configured to provide location information (e.g., longitude and latitude) regarding the current location of the WTRU 102. In addition to, or in lieu of, the information from the GPS chipset 136, the WTRU 102 may receive location information over the air interface 116 from a base station (e.g., base stations 114a, 114b) and/or determine its location based on the timing of the signals being received from two or more nearby base stations. It will be appreciated that the WTRU 102 may acquire location information by way of any suitable locationdetermination method while remaining consistent with an embodiment.

[0102] The processor 118 may further be coupled to other peripherals 138, which may include one or more software and/or hardware modules that provide additional features, functionality and/or wired or wireless connectivity. For example, the peripherals 138 may include an accelerometer, an e-compass, a satellite transceiver, a digital camera (for photographs and/or video), a universal serial bus (USB) port, a vibration device, a television transceiver, a hands free headset, a Bluetooth® module, a frequency modulated (FM) radio unit, a digital music player, a media player, a video game player module, an Internet browser, a Virtual Reality and/or Augmented Reality (VR/AR) device, an activity tracker, and the like. The peripherals 138 may include one or more sensors, the sensors may be one or more of a gyroscope, an accelerometer, a hall effect sensor, a magnetometer, an orientation sensor, a proximity sensor, a temperature sensor, a time sensor; a geolocation sensor; an altimeter, a light sensor, a touch sensor, a magnetometer, a barometer, a gesture sensor, a biometric sensor, and/or a humidity sensor.

[0103] The WTRU 102 may include a full duplex radio for which transmission and reception of some or all of the signals (e.g., associated with particular subframes for both the UL (e.g., for transmission) and downlink (e.g., for reception) may be concurrent and/or simultaneous. The full duplex radio may include an interference management unit to reduce and or substantially eliminate self-interference via either hardware (e.g., a choke) or signal processing via a processor (e.g., a separate processor (not shown) or via processor 118). In an embodiment, the WTRU 102 may include a half-duplex radio for which transmission and reception of some or all of the signals (e.g., associated with particular subframes for either the UL (e.g., for transmission) or the downlink (e.g., for reception)).

[0104] Although the WTRU is described in FIGs. 1 A-1 B as a wireless terminal, it is contemplated that in certain representative embodiments that such a terminal may use (e.g., temporarily or permanently) wired communication interfaces with the communication network.

[0105] In representative embodiments, the other network 112 may be a WLAN.

[0106] In view of FIGs. 1 A-1 B, and the corresponding description, one or more, or all, of the functions described herein may be performed by one or more emulation devices (not shown). The emulation devices may be one or more devices configured to emulate one or more, or all, of the functions described herein. For example, the emulation devices may be used to test other devices and/or to simulate network and/or WTRU functions.

[0107] The emulation devices may be designed to implement one or more tests of other devices in a lab environment and/or in an operator network environment. For example, the one or more emulation devices may perform the one or more, or all, functions while being fully or partially implemented and/or deployed as part of a wired and/or wireless communication network in order to test other devices within the communication network. The one or more emulation devices may perform the one or more, or all, functions while being temporarily implemented/deployed as part of a wired and/or wireless communication network. The emulation device may be directly coupled to another device for purposes of testing and/or may performing testing using over-the-air wireless communications.

[0108] The one or more emulation devices may perform the one or more, including all, functions while not being implemented/deployed as part of a wired and/or wireless communication network. For example, the emulation devices may be utilized in a testing scenario in a testing laboratory and/or a non-deployed (e.g. , testing) wired and/or wireless communication network in order to implement testing of one or more components. The one or more emulation devices may be test equipment. Direct RF coupling and/or wireless communications via RF circuitry (e.g., which may include one or more antennas) may be used by the emulation devices to transmit and/or receive data.

[0109] FIG. 1 C is a system diagram illustrating an example set of interfaces for a system according to some embodiments. An extended reality display device, together with its control electronics, may be implemented for some embodiments. System 150 can be embodied as a device including the various components described below and is configured to perform one or more of the aspects described in this document. Examples of such devices, include, but are not limited to, various electronic devices such as personal computers, laptop computers, smartphones, tablet computers, digital multimedia set top boxes, digital television receivers, personal video recording systems, connected home appliances, and servers. Elements of system 150, singly or in combination, can be embodied in a single integrated circuit (IC), multiple ICs, and/or discrete components. For example, in at least one embodiment, the processing and encoder/decoder elements of system 150 are distributed across multiple ICs and/or discrete components. In various embodiments, the system 150 is communicatively coupled to one or more other systems, or other electronic devices, via, for example, a communications bus or through dedicated input and/or output ports. In various embodiments, the system 150 is configured to implement one or more of the aspects described in this document. [0110] The system 150 includes at least one processor 152 configured to execute instructions loaded therein for implementing, for example, the various aspects described in this document. Processor 152 may include embedded memory, input output interface, and various other circuitries as known in the art. The system 150 includes at least one memory 154 (e.g., a volatile memory device, and/or a non-volatile memory device). System 150 may include a storage device 158, which can include non-volatile memory and/or volatile memory, including, but not limited to, Electrically Erasable Programmable Read-Only Memory (EEPROM), Read-Only Memory (ROM), Programmable Read-Only Memory (PROM), Random Access Memory (RAM), Dynamic Random Access Memory (DRAM), Static Random Access Memory (SRAM), flash, magnetic disk drive, and/or optical disk drive. The storage device 158 can include an internal storage device, an attached storage device (including detachable and non-detachable storage devices), and/or a network accessible storage device, as non-limiting examples.

[0111] System 150 includes an encoder/decoder module 156 configured, for example, to process data to provide an encoded video or decoded video, and the encoder/decoder module 156 can include its own processor and memory. The encoder/decoder module 156 represents module(s) that can be included in a device to perform the encoding and/or decoding functions. As is known, a device can include one or both of the encoding and decoding modules. Additionally, encoder/decoder module 156 can be implemented as a separate element of system 150 or can be incorporated within processor 152 as a combination of hardware and software as known to those skilled in the art.

[0112] Program code to be loaded onto processor 152 or encoder/decoder 156 to perform the various aspects described in this document can be stored in storage device 158 and subsequently loaded onto memory 154 for execution by processor 152. In accordance with various embodiments, one or more of processor 152, memory 154, storage device 158, and encoder/decoder module 156 can store one or more of various items during the performance of the processes described in this document. Such stored items can include, but are not limited to, the input video, the decoded video or portions of the decoded video, the bitstream, matrices, variables, and intermediate or final results from the processing of equations, formulas, operations, and operational logic.

[0113] In some embodiments, memory inside of the processor 152 and/or the encoder/decoder module 156 is used to store instructions and to provide working memory for processing that is needed during encoding or decoding. In other embodiments, however, a memory external to the processing device (for example, the processing device can be either the processor 152 or the encoder/decoder module 152) is used for one or more of these functions. The external memory can be the memory 154 and/or the storage device 158, for example, a dynamic volatile memory and/or a non-volatile flash memory. In several embodiments, an external non-volatile flash memory is used to store the operating system of, for example, a television. In at least one embodiment, a fast external dynamic volatile memory such as a RAM is used as working memory for video coding and decoding operations, such as for MPEG-2 (MPEG refers to the Moving Picture Experts Group, MPEG-2 is also referred to as ISO/IEC 13818, and 13818-1 is also known as H.222, and 13818-2 is also known as H.262), HEVC (HEVC refers to High Efficiency Video Coding, also known as H.265 and MPEG-H Part 2), or WC (Versatile Video Coding, a new standard being developed by JVET, the Joint Video Experts Team).

[0114] The input to the elements of system 150 can be provided through various input devices as indicated in block 172. Such input devices include, but are not limited to, (i) a radio frequency (RF) portion that receives an RF signal transmitted, for example, over the air by a broadcaster, (ii) a Component (COMP) input terminal (or a set of COMP input terminals), (iii) a Universal Serial Bus (USB) input terminal, and/or (iv) a High Definition Multimedia Interface (HDMI) input terminal. Other examples, not shown in FIG. 1C, include composite video.

[0115] In various embodiments, the input devices of block 172 have associated respective input processing elements as known in the art. For example, the RF portion can be associated with elements suitable for (i) selecting a desired frequency (also referred to as selecting a signal, or band-limiting a signal to a band of frequencies), (ii) downconverting the selected signal, (iii) band-limiting again to a narrower band of frequencies to select (for example) a signal frequency band which can be referred to as a channel in certain embodiments, (iv) demodulating the downconverted and band-limited signal, (v) performing error correction, and (vi) demultiplexing to select the desired stream of data packets. The RF portion of various embodiments includes one or more elements to perform these functions, for example, frequency selectors, signal selectors, band-limiters, channel selectors, filters, downconverters, demodulators, error correctors, and demultiplexers. The RF portion can include a tuner that performs various of these functions, including, for example, downconverting the received signal to a lower frequency (for example, an intermediate frequency or a near-baseband frequency) or to baseband. In one set-top box embodiment, the RF portion and its associated input processing element receives an RF signal transmitted over a wired (for example, cable) medium, and performs frequency selection by filtering, downconverting, and filtering again to a desired frequency band. Various embodiments rearrange the order of the above-described (and other) elements, remove some of these elements, and/or add other elements performing similar or different functions. Adding elements can include inserting elements in between existing elements, such as, for example, inserting amplifiers and an analog-to-digital converter. In various embodiments, the RF portion includes an antenna. [0116] Additionally, the USB and/or HDMI terminals can include respective interface processors for connecting system 150 to other electronic devices across USB and/or HDMI connections. It is to be understood that various aspects of input processing, for example, Reed-Solomon error correction, can be implemented, for example, within a separate input processing IC or within processor 152 as necessary. Similarly, aspects of USB or HDMI interface processing can be implemented within separate interface ICs or within processor 152 as necessary. The demodulated, error corrected, and demultiplexed stream is provided to various processing elements, including, for example, processor 152, and encoder/decoder 156 operating in combination with the memory and storage elements to process the datastream as necessary for presentation on an output device.

[0117] Various elements of system 150 can be provided within an integrated housing, Within the integrated housing, the various elements can be interconnected and transmit data therebetween using suitable connection arrangement 174, for example, an internal bus as known in the art, including the Inter- IC (I2C) bus, wiring, and printed circuit boards.

[0118] The system 150 includes communication interface 160 that enables communication with other devices via communication channel 162. The communication interface 160 can include, but is not limited to, a transceiver configured to transmit and to receive data over communication channel 162. The communication interface 160 can include, but is not limited to, a modem or network card and the communication channel 162 can be implemented, for example, within a wired and/or a wireless medium.

[0119] Data is streamed, or otherwise provided, to the system 150, in various embodiments, using a wireless network such as a Wi-Fi network, for example IEEE 802.11 (IEEE refers to the Institute of Electrical and Electronics Engineers). The Wi-Fi signal of these embodiments is received over the communications channel 162 and the communications interface 160 which are adapted for Wi-Fi communications. The communications channel 162 of these embodiments is typically connected to an access point or router that provides access to external networks including the Internet for allowing streaming applications and other over-the-top communications. Other embodiments provide streamed data to the system 150 using a set-top box that delivers the data over the HDMI connection of the input block 172. Still other embodiments provide streamed data to the system 150 using the RF connection of the input block 172. As indicated above, various embodiments provide data in a non-streaming manner. Additionally, various embodiments use wireless networks other than Wi-Fi, for example a cellular network or a Bluetooth network.

[0120] The system 150 can provide an output signal to various output devices, including a display 176, speakers 178, and other peripheral devices 180. The display 176 of various embodiments includes one or more of, for example, a touchscreen display, an organic light-emitting diode (OLED) display, a curved display, and/or a foldable display. The display 176 can be for a television, a tablet, a laptop, a cell phone (mobile phone), or other device. The display 176 can also be integrated with other components (for example, as in a smart phone), or separate (for example, an external monitor for a laptop). The other peripheral devices 180 include, in various examples of embodiments, one or more of a stand-alone digital video disc (or digital versatile disc) (DVR, for both terms), a disk player, a stereo system, and/or a lighting system. Various embodiments use one or more peripheral devices 180 that provide a function based on the output of the system 150. For example, a disk player performs the function of playing the output of the system 150.

[0121] In various embodiments, control signals are communicated between the system 150 and the display 176, speakers 178, or other peripheral devices 180 using signaling such as AV.Link, Consumer Electronics Control (CEC), or other communications protocols that enable device-to-device control with or without user intervention. The output devices can be communicatively coupled to system 150 via dedicated connections through respective interfaces 164, 166, and 168. Alternatively, the output devices can be connected to system 150 using the communications channel 162 via the communications interface 160. The display 176 and speakers 178 can be integrated in a single unit with the other components of system 150 in an electronic device such as, for example, a television. In various embodiments, the display interface 164 includes a display driver, such as, for example, a timing controller (T Con) chip.

[0122] The display 176 and speaker 178 can alternatively be separate from one or more of the other components, for example, if the RF portion of input 172 is part of a separate set-top box. In various embodiments in which the display 176 and speakers 178 are external components, the output signal can be provided via dedicated output connections, including, for example, HDMI ports, USB ports, or COMP outputs.

[0123] The system 150 may include one or more sensor devices 168. Examples of sensor devices that may be used include one or more GPS sensors, gyroscopic sensors, accelerometers, light sensors, cameras, depth cameras, microphones, and/or magnetometers. Such sensors may be used to determine information such as user’s position and orientation. Where the system 150 is used as the control module for an extended reality display (such as control modules 124, 132), the user’s position and orientation may be used in determining how to render image data such that the user perceives the correct portion of a virtual object or virtual scene from the correct point of view. In the case of head-mounted display devices, the position and orientation of the device itself may be used to determine the position and orientation of the user for the purpose of rendering virtual content. In the case of other display devices, such as a phone, a tablet, a computer monitor, or a television, other inputs may be used to determine the position and orientation of the user for the purpose of rendering content. For example, a user may select and/or adjust a desired viewpoint and/or viewing direction with the use of a touch screen, keypad or keyboard, trackball, joystick, or other input. Where the display device has sensors such as accelerometers and/or gyroscopes, the viewpoint and orientation used for the purpose of rendering content may be selected and/or adjusted based on motion of the display device.

[0124] The embodiments can be carried out by computer software implemented by the processor 152 or by hardware, or by a combination of hardware and software. As a non-limiting example, the embodiments can be implemented by one or more integrated circuits. The memory 154 can be of any type appropriate to the technical environment and can be implemented using any appropriate data storage technology, such as optical memory devices, magnetic memory devices, semiconductor-based memory devices, fixed memory, and removable memory, as non-limiting examples. The processor 152 can be of any type appropriate to the technical environment, and can encompass one or more of microprocessors, general purpose computers, special purpose computers, and processors based on a multi-core architecture, as non-limiting examples.

Block-Based Video Coding

[0125] Like HEVC, the WC is built upon the block-based hybrid video coding framework. FIG. 2A gives the block diagram of a block-based hybrid video encoding system 200. Variations of this encoder 200 are contemplated, but the encoder 200 is described below for purposes of clarity without describing all expected variations.

[0126] Before being encoded, a video sequence may go through pre-encoding processing 204, for example, applying a color transform to an input color picture (e g., conversion from RGB 4:4:4 to YCbCr 4:2:0), or performing a remapping of the input picture components in order to get a signal distribution more resilient to compression (for instance using a histogram equalization of one of the color components). Metadata can be associated with the pre-processing and attached to the bitstream.

[0127] The input video signal 202 including a picture to be encoded is partitioned 206 and processed block by block in units of, for example, CUs. Different CUs may have different sizes. In VTM-1 .0, a CU can be up to 128x128 pixels. However, different from the HEVC which partitions blocks only based on quad-trees, in the VTM-1 .0, a coding tree unit (CTU) is split into CUs to adapt to varying local characteristics based on quad/binary/ternary-tree. Additionally, the concept of multiple partition unit type in the HEVC is removed, such that the separation of CU, prediction unit (PU) and transform unit (TU) does not exist in the WC-1 .0 anymore; instead, each CU is always used as the basic unit for both prediction and transform without further partitions. In the multi-type tree structure, a CTU is firstly partitioned by a quad-tree structure. Then, each quad-tree leaf node can be further partitioned by a binary and ternary tree structure. Different splitting types may be used, such as quaternary partitioning, vertical binary partitioning, horizontal binary partitioning, vertical ternary partitioning, and horizontal ternary partitioning. [0128] In the encoder of FIG. 2A, spatial prediction 208 and/or temporal prediction 210 may be performed. Spatial prediction (or “intra prediction”) uses pixels from the samples of already coded neighboring blocks (which are called reference samples) in the same video picture/slice to predict the current video block. Spatial prediction reduces spatial redundancy inherent in the video signal. Temporal prediction (also referred to as “inter prediction” or “motion compensated prediction”) uses reconstructed pixels from the already coded video pictures to predict the current video block. Temporal prediction reduces temporal redundancy inherent in the video signal. A temporal prediction signal for a given CU may be signaled by one or more motion vectors (MVs) which indicate the amount and the direction of motion between the current CU and its temporal reference. Also, if multiple reference pictures are supported, a reference picture index may additionally be sent, which is used to identify from which reference picture in the reference picture store 212 the temporal prediction signal comes.

[0129] The mode decision block 214 in the encoder chooses the best prediction mode, for example based on a rate-distortion optimization method. This selection may be made after spatial and/or temporal prediction is performed. The intra/inter decision may be indicated by, for example, a prediction mode flag. The prediction block is subtracted from the current video block 216 to generate a prediction residual. The prediction residual is de-correlated using transform 218 and quantized 220. (For some blocks, the encoder may bypass both transform and quantization, in which case the residual may be coded directly without the application of the transform or quantization processes.) The quantized residual coefficients are inverse quantized 222 and inverse transformed 224 to form the reconstructed residual, which is then added back to the prediction block 226 to form the reconstructed signal of the CU. Further in-loop filtering, such as deblocking/SAO (Sample Adaptive Offset) filtering, may be applied 228 on the reconstructed CU to reduce encoding artifacts before it is put in the reference picture store 212 and used to code future video blocks. To form the output video bitstream 230, coding mode (inter or intra), prediction mode information, motion information, and quantized residual coefficients are all sent to the entropy coding unit (108) to be further compressed and packed to form the bit-stream.

[0130] FIG. 2B gives a block diagram of a block-based video decoder 250. In the decoder 250, a bitstream is decoded by the decoder elements as described below. Video decoder 250 generally performs a decoding pass reciprocal to the encoding pass as described in FIG. 2A. The encoder 200 also generally performs video decoding as part of encoding video data.

[0131] In particular, the input of the decoder includes a video bitstream 252, which can be generated by video encoder 200. The video bit-stream 252 is first unpacked and entropy decoded at entropy decoding unit 254 to obtain transform coefficients, motion vectors, and other coded information. Picture partition information indicates how the picture is partitioned. The decoder may therefore divide 256 the picture according to the decoded picture partitioning information. The coding mode and prediction information are sent to either the spatial prediction unit 258 (if intra coded) or the temporal prediction unit 260 (if inter coded) to form the prediction block. The residual transform coefficients are sent to inverse quantization unit 262 and inverse transform unit 264 to reconstruct the residual block. The prediction block and the residual block are then added together at 266 to generate the reconstructed block. The reconstructed block may further go through in-loop filtering 268 before it is stored in reference picture store 270 for use in predicting future video blocks.

[0132] The decoded picture 272 may further go through post-decoding processing 274, for example, an inverse color transform (e.g. conversion from YCbCr 4:2:0 to RGB 4:4:4) or an inverse remapping performing the inverse of the remapping process performed in the pre-encoding processing 204. The post-decoding processing can use metadata derived in the pre-encoding processing and signaled in the bitstream. The decoded, processed video may be sent to a display device 276. The display device 276 may be a separate device from the decoder 250, or the decoder 250 and the display device 276 may be components of the same device.

[0133] Various methods and other aspects described in this disclosure can be used to modify modules of a video encoder 200 or decoder 250. Moreover, the systems and methods disclosed herein are not limited to WC or HEVC, and can be applied, for example, to other standards and recommendations, whether preexisting or future-developed, and extensions of any such standards and recommendations (including WC and HEVC). Unless indicated otherwise, or technically precluded, the aspects described in this disclosure can be used individually or in combination.

[0134] FIG. 3A is a schematic side view illustrating an example waveguide display that may be used with extended reality (XR) applications according to some embodiments. An image is projected by an image generator 302. The image generator 302 may use one or more of various techniques for projecting an image. For example, the image generator 302 may be a laser beam scanning (LBS) projector, a liquid crystal display (LCD), a light-emitting diode (LED) display (including an organic LED (OLED) or micro LED (piLED) display), a digital light processor (DLP), a liquid crystal on silicon (LCoS) display, or other type of image generator or light engine.

[0135] Light representing an image 312 generated by the image generator 302 is coupled into a waveguide 304 by a diffractive in-coupler 306. The in-coupler 306 diffracts the light representing the image 312 into one or more diffractive orders. For example, light ray 308, which is one of the light rays representing a portion of the bottom of the image, is diffracted by the in-coupler 306, and one of the diffracted orders 310 (e.g. the second order) is at an angle that is capable of being propagated through the waveguide 304 by total internal reflection. The image generator 302 displays images as directed by a control module 324, which operates to render image data, video data, point cloud data, or other displayable data.

[0136] At least a portion of the light 310 that has been coupled into the waveguide 304 by the diffractive in-coupler 306 is coupled out of the waveguide by a diffractive out-coupler 314. At least some of the light coupled out of the waveguide 304 replicates the incident angle of light coupled into the waveguide. For example, in the illustration, out-coupled light rays 316a, 316b, and 316c replicate the angle of the in-coupled light ray 308. Because light exiting the out-coupler replicates the directions of light that entered the in-coupler, the waveguide substantially replicates the original image 312. A user’s eye 318 can focus on the replicated image.

[0137] In the example of FIG. 3A, the out-coupler 314 out-couples only a portion of the light with each reflection allowing a single input beam (such as beam 308) to generate multiple parallel output beams (such as beams 316a, 316b, and 316c). In this way, at least some of the light originating from each portion of the image is likely to reach the user’s eye even if the eye is not perfectly aligned with the center of the out- coupler. For example, if the eye 318 were to move downward, beam 316c may enter the eye even if beams 316a and 316b do not, so the user can still perceive the bottom of the image 312 despite the shift in position. The out-coupler 314 thus operates in part as an exit pupil expander in the vertical direction. The waveguide may also include one or more additional exit pupil expanders (not shown in FIG. 3A) to expand the exit pupil in the horizontal direction.

[0138] In some embodiments, the waveguide 304 is at least partly transparent with respect to light originating outside the waveguide display. For example, at least some of the light 320 from real-world objects (such as object 322) traverses the waveguide 304, allowing the user to see the real-world objects while using the waveguide display. As light 320 from real-world objects also goes through the diffraction grating 314, there will be multiple diffraction orders and hence multiple images. To minimize the visibility of multiple images, it is desirable for the diffraction order zero (no deviation by 314) to have a great diffraction efficiency for light 320 and order zero, while higher diffraction orders are lower in energy. Thus, in addition to expanding and out-coupling the virtual image, the out-coupler 314 is preferably configured to let through the zero order of the real image. In such embodiments, images displayed by the waveguide display may appear to be superimposed on the real world.

[0139] FIG. 3B is a schematic side view illustrating an example alternative display type that may be used with extended reality applications according to some embodiments. In an XR head-mounted display device 330, a control module 332 controls a display 334, which may be an LCD, to display an image. The headmounted display includes a partly-reflective surface 336 that reflects (and in some embodiments, both reflects and focuses) the image displayed on the LCD to make the image visible to the user. The partly-reflective surface 336 also allows the passage of at least some exterior light, permitting the user to see their surroundings.

[0140] FIG. 3C is a schematic side view illustrating an example alternative display type that may be used with extended reality applications according to some embodiments. In an XR head-mounted display device 340, a control module 342 controls a display 344, which may be an LCD, to display an image. The image is focused by one or more lenses of display optics 346 to make the image visible to the user. In the example of FIG. 3C, exterior light does not reach the user’s eyes directly. However, in some such embodiments, an exterior camera 348 may be used to capture images of the exterior environment and display such images on the display 344 together with any virtual content that may also be displayed.

[0141] The embodiments described herein are not limited to any particular type or structure of XR display device.

[0142] V-DMC uses a subdivision (or tessellation) process, which begins with a coarse BASE MESH, and then progressively adds vertices to get more geometric detail. The subdivision process is applied over multiple iterations, which may be thought of as hierarchically adding levels of detail. Each subdivision adds a new child vertex at the midpoint of the edge connecting its parents, and then displacement information is coded to ‘move’ that vertex to its true position. The displacement values are transformed using a Lifting Wavelet Transform, and a key step of this transform is the “PREDICT” step which predicts each component displacement value (x, y, and z displacement components are treated separately) from the displacement used to code the parent vertices. The existing PREDICT step is a simple averaging of the displacement values of the parents. The current application discusses a modification to the PREDICT step of the Lifting Wavelet Transform in order to utilize contributions from additional neighbor vertices. The application provides details for howto handle central edges vs. mesh boundary edges, and the application also provides a fallback case for the ‘non-manifold’ mesh regions. Some embodiments weight the contributions from the parents and the additional neighbor vertices (e.g., based on topology or actual distances between the vertices).

[0143] The current MPEG V-DMC (Video-based Dynamic Mesh Coding) Test Model (TM) is based on the reference Mammou, K., et al, [V-CG] Apple's Dynamic Mesh Coding CfP Response, MPEG Input Document m59281 (v4), ISO/IEC JTC 1 /SC 29/WG 7 (2022) (“Mammou”). In V-DMC, the coding of the mesh geometry, which is the x, y, z positions of the mesh vertices, is based on a variation of the subdivision wavelets scheme (See Lounsbery, M., Multiresolution Analysis for Surfaces of Arbitrary Topological Type, U. OF WASHINGTON (1994) (Ph. D Thesis for Dept, of Comp. Sci. and Engin.) (‘Lounsbery 1”) and Lounsbery, M., et al., Multiresolution Analysis for Surfaces of Arbitrary Topological Type, 16:1 ACM TRANSACTIONS ON G APHICS 34-73 (1997) ‘Lounsbery 2”)). V-DMC implements the coding using a Lifting Wavelet Transform (Sweldens, W., The Lifting Scheme: A Construction of Second Generation Wavelets, 29:2 SIAM J. MATHEMATICAL ANALYSIS 511-546 (1998) (“Sweldens”)). The subdivision wavelets scheme is based on surface subdivision.

[0144] Surface subdivision begins with a 3D mesh called a base mesh, which may be obtained by a mesh simplification (or decimation) process, such as the process described in Garland, M. and Heckbert, P. S., Surface Simplification using Quadric Error, SIGGRAPH’97 (1997) (“Garland'). from a higher-resolution mesh. The base mesh contains a relatively small number of vertices and faces. The mesh is progressively refined using a subdivision process that iteratively adds new vertices and faces to the mesh by subdividing the existing faces into smaller sub-faces. The new vertices are then displaced to new positions according to some pre-defined rules, to progressively refine the mesh shape, as shown in the example in FIGs. 4A to 4F.

[0145] FIG. 4A is a schematic illustration showing an example base mesh according to some embodiments. FIG. 4B is a schematic illustration showing an example mesh after 1 subdivision iteration according to some embodiments. FIG. 4C is a schematic illustration showing an example mesh after 2 subdivision iterations according to some embodiments. FIG. 4D is a schematic illustration showing an example mesh after 3 subdivision iterations according to some embodiments. FIG. 4E is a schematic illustration showing an example mesh after 4 subdivision iterations according to some embodiments. FIG. 4F is a schematic illustration showing an example mesh after 5 subdivision iterations according to some embodiments.

[0146] A number of different surface subdivision schemes exist, e.g., see Benton. In V-DMC, the default choice is a midpoint subdivision scheme, which inserts at each iteration a new vertex at the midpoint of each existing edge.

[0147] FIGs. 4A-4F illustrate a subdivision process. FIG. 4A shows a base mesh 402, which is to be refined. FIGs. 4B to 4F show the resulting mesh models 404, 406, 408, 410, 412 after a different number of subdivision iterations. The model 412 in FIG. 4F has been rendered with interpolated shading to demonstrate its smoothness, while the meshes 402, 404, 406, 408, 410 in FIGs. 4A-4E are shown in their faceted form to illustrate the addition of new vertices and sub-faces at each subdivision iteration.

[0148] The simplest form of subdivision wavelets as described in Lounsberry 1 and Lounsberry 2, which has linear time complexity for analysis and synthesis, may be implemented by a piecewise linear subdivision that is basically equivalent to the Lifting Wavelet Transform (Sweldens). In this form, the lowest-resolution approximation of the mesh shape is represented by the base mesh, and the wavelet coefficients between any two successive resolution (subdivision) levels represent the differences between the “child” vertex x, y, z positions at the higher resolution level and the prediction of these child positions from the positions of their “parents” at the lower resolution level.

[0149] FIG. 5 is a schematic illustration showing an example wavelet coefficient computation in linear polyhedral subdivision according to some embodiments. For example, in FIG. 5, the wavelet coefficient w (502) associated with the displaced vertex v (504) (where v is a higher-resolution level vertex that was originally added at the midpoint m (506) of a lower-resolution level edge pq (508)) may be computed as shown in Eq. 1 : w = v — - (p + ) = v — m (1)

[0150] In Eq. 1 , the resulting wavelet coefficient w is the difference between the final position of v and its prediction m . The base mesh, and therefore the mesh geometry, may be progressively refined by successively adding more wavelet coefficients to inserted vertices at higher resolution (subdivision) levels.

[0151] FIG. 5 illustrates wavelet coefficient computation in linear polyhedral subdivision of a mesh 500. Two of the example base mesh vertices are labeled p and q. An example new vertex is labeled m (506) and is inserted at the edge midpoints of the base mesh. The example final position vertex is labeled v (504), and the vertex represents the final position of the vertex v (504) that was originally inserted (predicted) at the midpoint m (506).

[0152] The subdivision wavelets framework relies on the fact that the connectivity of the base mesh may be refined in a predictable manner (by using a set of standard subdivision rules known to both the encoder and decoder) to obtain the final higher-resolution mesh. However, most mesh models, as understood, do not have a predictable regular or semi-regular connectivity.

[0153] FIG. 6A is a schematic illustration showing an example regular connectivity of a triangular mesh according to some embodiments. FIG. 6B is a schematic illustration showing an example irregular connectivity of a triangular mesh according to some embodiments. FIG. 6C is a schematic illustration showing an example semi-regular connectivity of a triangular mesh according to some embodiments.

[0154] In V-DMC, the original input mesh is first downsampled (e.g., by using the method in Garland) to obtain a base mesh, and then a midpoint subdivision scheme is applied to iteratively upsample the base mesh again to reach approximately the same resolution (number of vertices and faces) as the original mesh. Although, in the current V-DMC TM, the number of vertices and faces in the upsampled mesh is usually much larger than in the original mesh. The differences between the upsampled mesh vertex (x, y, z) positions at the highest subdivision (resolution) level and the original mesh vertex positions (where the point correspondences between the original and subdivided meshes are found by nearest-point searching) are then represented as a set of displacement vectors (or “displacements”). These displacement vectors indicate how to deform the subdivided mesh surface to approximate more closely the original mesh surface. The displacement vectors are transformed by applying a linear Lifting Wavelet Transform Sweldens), and the resulting wavelet coefficients are encoded for transmission to the decoder.

[0155] FIGs 6A-6C show examples of different connectivity types for a triangular mesh: FIG. 6A shows an example 600 of regular connectivity, in which all the vertices have the same number of incident edges. FIG. 6B shows an example 630 of irregular connectivity, in which the vertices may have different numbers of incident edges. FIG. 6C shows an example 660 of semi-regular connectivity, in which most vertices have a regular connectivity, while some have irregular connectivity.

[0156] FIG. 7A is a process diagram illustrating an example forward lifting wavelet transform according to some embodiments. FIG. 7B is a process diagram illustrating an example forward lifting wavelet transform according to some embodiments. FIG. 7C is a process diagram illustrating an example inverse lifting wavelet transform according to some embodiments. FIG. 7D is a process diagram illustrating an example inverse lifting wavelet transform according to some embodiments.

[0157] The (Forward) Lifting Wavelet Transform 700 that is currently used in V-DMC is depicted in FIG. 7A and consists of the following steps: an odd/even split 702, a prediction (P) 704, a computation 706 of wavelet coefficients, and an update (U) block 708.

[0158] FIG. 7B shows an example transform 720 using higher resolution level samples as odd-indexed samples with the following steps: an odd/even split 722, a prediction (P) 724, a computation 726 of wavelet coefficients, and an update (U) block 728.

[0159] FIG. 7C shows an example inverse transform 740 using higher resolution level samples as even- indexed samples with the following steps: an update (U) block 742, a prediction (P) 744, a computation 746 of even samples, and an odd/even merge 748.

[0160] FIG. 7D shows an example inverse transform 760 using higher resolution level samples as odd- indexed samples with the following steps: an update (U) block 762, a prediction (P) 764, a computation 766 of even samples, and an odd/even merge 768.

[0161] The input to the odd/even split block 702 is a signal (in this case, the x, and z components of the displacement vectors, which are treated separately) that is split into even-indexed and odd-indexed samples, such that each group contains half the samples of the original signal. This splitting step is sometimes called a “Lazy Wavelet Transform”. In the context of a mesh, the odd-indexed and even-indexed samples correspond to vertices at different resolution levels. The odd-indexed samples normally correspond to vertices at a lower resolution level (analogous to the result of a low-pass filter in a traditional wavelet transform), and the even-indexed samples correspond to vertices at a higher resolution level. For some embodiments, odd-indexed samples may correspond to higher resolution level samples and even-indexed samples may correspond to lower-resolution level samples. Such a scenario is shown in FIGs. 7B and 7D, while the converse is shown in FIGs. 7A and 7C.

[0162] The prediction (P) 704 step computes a prediction (approximation) for the even samples based on the odd samples (also may be the other way around). The prediction is computed as shown in Eq. 2: in which v₁₂ represents a new vertex that is added in the middle of the edge (v_1; v₂), and Signal(v_}) and Signal(v₂) are the values of the signals (displacement values, in this case) at the vertices and v₂, respectively. The predicted value for the displacement at vertex v₁₂ is the average of the signal (displacement) values on the vertices v_r and v₂.

[0163] To compute 706 wavelet coefficients, the prediction result is subtracted from the even samples, and the resulting residual values are the wavelet coefficients. This calculation may be formulated as shown in Eq. 3: w_i2 = Signal (v₁₂ ) - Pre d(v₁₂) (3) in which Signal (v₁₂ ) represents the actual value of the signal (displacement) on the vertex v₁₂, and w₁₂ represents the value of the wavelet coefficient (which also has x, z components) associated with the newly added vertex v₁₂.

[0164] The Update (U) 708 step adds the wavelet coefficients to the odd signal samples (which represent the coarser signal “approximation”). This addition recovers some of the energy lost during signal splitting and prepares the signal for the next prediction step (if there is one). In V-DMC, the update is currently computed as shown in Eq. 4: in which w E vindicates the wavelet coefficients for the neighboring vertices of vertex v. The V-DMC TM also has an option to skip the Update step altogether.

[0165] FIG. 7A shows the Forward Lifting Wavelet Transform 700 used in V-DMC and shown in Mammou.

[0166] FIG. 7C shows the Inverse Wavelet Transform 740, which is used at the decoder to reconstruct the input signal (displacements) from the coarse approximation and the wavelet coefficients, proceeds in the reverse direction to the Forward Wavelet Transform. The Inverse Wavelet Transform is also performed at the encoder to reconstruct the mesh geometry so that texture transfer may be applied before texture compression. See FIG. 11.

[0167] This application describes a modification to the “Predict” step (Eq. 2) of the Lifting Wavelet Transform. Currently this prediction is based on a linear interpolation (averaging) between the signals on the two parent vertices on the edge where the new child vertex is inserted.

[0168] For some embodiments, the value of the signal at the child vertex is predicted by using the signal values of its parents on the same edge and the signal values on the other vertices of the triangles adjacent to this edge.

[0169] FIG. 8A is a schematic illustration showing an example manifold mesh according to some embodiments. FIG. 8B is a schematic illustration showing an example non-manifold mesh according to some embodiments. FIG. 8C is a schematic illustration showing an example non-manifold mesh according to some embodiments.

[0170] For a manifold triangle mesh 800 with boundaries, see FIG. 8A. For a manifold triangle mesh with boundaries, the edges on the boundary each have only one adjacent triangle, while the edges away from the boundary each have two adjacent triangles. This application focuses on manifold triangle meshes with and without boundaries. FIGs. 8B and 8C are non-manifold meshes 830, 860. For a manifold mesh, each edge that is not on a boundary is shared by only two faces and not more, and one ring of connected faces must be around each vertex, not a broken ring, as in FIG. 8B. Boundary edges are shared by only one face.

[0171] FIG. 9A is a schematic illustration showing an example closed mesh with no boundaries according to some embodiments. FIG. 9B is a schematic illustration showing an example open mesh with a boundary according to some embodiments. FIG. 9A shows an example of a closed mesh 900, which has no boundaries. In FIG. 9A, each edge has two adjacent triangles. FIG. 9B shows an example of an open mesh 950 with a boundary 952.

[0172] FIG. 10A is a schematic illustration showing an example mesh containing a new vertex not on a mesh boundary according to some embodiments. FIG. 10B is a schematic illustration showing an example mesh containing a new vertex on a mesh boundary according to some embodiments.

[0173] For some embodiments, neighboring vertices are taken into account for prediction of the signal on a newly inserted vertex, examples of which are shown in FIGs. 10A and 10B. Taking into account more than just the direct neighbors of the new vertex may produce a more accurate prediction of the signal value on the new vertex. This increased accuracy may occur because the value of this signal may be affected by the values on all the vertices of the adjacent triangles, not only the values of its direct parents that are found on the same edge as the new vertex.

[0174] FIG. 10A shows an example of a manifold triangle mesh 1000 in which the edge 1002 containing the newly inserted vertex 1004 is not on a mesh boundary. Point c (1004) is a newly inserted vertex. Points a (1006) and b (1008) are the direct parent nodes. Points d (1010) and e (1012) are additional neighbors that may be used in addition to points a (1006) and b (1008) to predict the location of point e (1004), which may be expressed as a signal value of the newly inserted vertex.

[0175] FIG. 10B shows an example of a manifold triangle mesh 1050 in which the new vertex is on a mesh boundary. Points a (1052) and b (1054) are the direct parent nodes. Point d (1058) is an additional neighbor that may be used in addition to points a (1052) and b (1054) to predict the location of point c (1056).

[0176] For some scenarios, some parts of a mesh may be manifold and some parts of the mesh may be non-manifold. For some embodiments, the manifold condition may be checked, which may be a check of the number of adjacent triangles, on each edge. This check may be performed before predicting the signal (location) of a newly inserted vertex on that edge.

[0177] If the mesh in the corresponding area is manifold, then additional neighbors may be used in the prediction. If the mesh in the corresponding area is non-manifold, then a midpoint prediction may be used, as shown in Eq. 2.

[0178] FIG. 11 is a process diagram illustrating an example V-DMC intra-frame encoder according to some embodiments. See Mammou for general details regarding the V-DMC intra-frame encoder 1100. For some embodiments, the idea of using additional neighbors for predicting the signal (location) of a newly inserted vertex may be applied inside the Wavelet Transform block 1102 and the Inverse Wavelet Transform block 1104. Both blocks 1102, 1104 are shown in FIG. 11 . Such changes to these blocks would work within the operation of the V-DMC intra-frame encoder 1100.

[0179] FIG. 12 is a process diagram illustrating an example V-DMC intra-frame decoder according to some embodiments. See Mammou for general details regarding the V-DMC intra-frame decoder 1200. For some embodiments, the idea of using additional neighbors for predicting the signal (location) of a newly inserted vertex may be applied inside the Inverse Wavelet Transform block 1202, which is shown in FIG. 12. Such changes to this block 1202 would work within the operation of the V-DMC intra-frame decoder 1200.

[0180] The sections below describe some variations of the prediction methods for the Lifting Wavelet Transform, which take into account the neighboring vertices shown in FIGs. 10A and 10B. Regardless of how the signal value on the newly inserted vertex is predicted, the connectivity of the mesh is kept the same. The vertex remains on the edge where the vertex was inserted (for example, as illustrated in FIGs. 10A and 10B), such that the connectivity of the mesh in the neighborhood does not change. In other words, the new vertex position (x, y, z) is still at the midpoint of the corresponding edge, regardless of how the signal on this vertex (the displacement values, in the case of V-DMC) are predicted.

Average of the Neighbors

[0181] For some embodiments, the predicted signal at each new vertex may be calculated as an average of the signal values of the neighbors, as shown in FIG. 10A and in Eq. 5:

Sig a)+S ig (b)+Sig(dj+Sig(e)

Pred c = 4 (5) in which Si^(... ) is the signal value (e.g., displacement value in V-DMC) of the corresponding vertex. For

FIG. 10B, the corresponding prediction is shown in Eq. 6:

Average of the Neighbors with Weights

[0182] For some embodiments, weights may be applied to the signals of the different neighboring vertices, before computing the prediction. In some embodiments, the weights may be applied in a manner that may be reproduced at the decoder without relying on any additional data from the encoder. Doing so may avoid transmitting extra data to the decoder.

Weights for Approximately Equal-Sized Triangles

[0183] For some embodiments, the weights may be computed as the inverse of the “number of edges” between the vertex to be predicted and each neighbor. In the cases shown in FIGs. 10A and 10B, where the adjacent triangles are approximately equal in size and approximately equilateral, the “distance” between vertex a and c, and between c and b, is approximately half the length of an edge for each, This relationship occurs because point c is originally inserted at the midpoint of the edge connecting a and b. So, the weight for the signals on a and b would be: = 2 for this scenario. The “distance” between c and d, and c and e, would be one edge in each case, so the weight for the signals on d and e would be 1 . For the case shown in FIG. 10A, the prediction is shown in Eqs. 7 and 8:

Pred(c) = 0.5 * Sig d) + 0.5 * Sig(b) + 0.25 * Sig d') + 0.25 * Sig(e~) (8) [0184] For the case shown in FIG. 10B, the prediction is shown in Eq. 9:

Weights for Unequal-Sized Triangles

[0185] FIG. 13 is a schematic illustration showing example different size adjacent triangles of a new mesh vertex according to some embodiments. As illustrated in FIG. 13, for example, the adjacent triangles 1302, 1304 of an edge with a newly inserted vertex 1306 may have significantly different sizes. In this case, a default midpoint subdivision may be used. Alternatively, the scenario shown below in Eq. 10 may be used.

[0186] In a subdivision surface hierarchy, the mesh triangles and the associated vertex positions (plus the signals on these vertices) at one resolution level (or subdivision level, or level of detail (LoD)) are reconstructed before computing the predictions for the vertices at the next resolution level. As such, the actual distance between the new vertex (which was originally inserted at an edge midpoint) and each of its neighbors, as illustrated in FIG. 13, may be determined. In this case, the prediction on vertex c may be computed as shown in Eq. 10:

[0187] The distance, distQ, may be computed as a 3D Euclidean distance between the corresponding vertex (x,y, z) positions. For some embodiments, to save computation time and resources, the square root operation of a 3D Euclidean distance calculation may be skipped, and the squared Euclidean distance may be used instead.

[0188] FIG. 14 is a schematic illustration showing an example different size adjacent triangles of a new mesh vertex according to some embodiments. FIG. 14 shows an example 1400 of the distances 1402, 1404, 1406, 1408 between vertex position coordinates 1410, 1412, 1414, 1416, which may be used to compute the distances and weights in Eq. 10.

[0189] FIG. 15 is a schematic illustration showing an example adjacent triangle of a new vertex on a mesh boundary according to some embodiments. Similar to Eq. 10, a weighting method may be adapted for when the edge with the inserted vertex is on a mesh boundary, as shown in FIG. 15 and Eq. 11 :

[0190] FIG. 15 shows an example 1500 of the distances 1502, 1504, 1506 between vertex position coordinates 1508, 1510, 1512, which may be used to compute the weights in Eq. 11. [0191] For some embodiments, when the adjacent triangles for an edge have too great an angle between them (which may be measured and compared with a threshold), the above-mentioned methods may network well. In such a case, some embodiments may default to using a midpoint prediction, such as the one shown in Eq. 2.

[0192] As understood, this application provides a new way of computing/determining predictions for signals of newly inserted vertices on subdivision surfaces using a Lifting Wavelet Transform to compute subdivision wavelets. Although this application may be applied to the MPEG V-DMC standard, the ideas herein may be applied to other systems that use a Lifting Wavelet Transform with manifold triangle meshes.

[0193] As understood, this application describes a potentially better prediction with smaller prediction residuals, or wavelet coefficients, to encode and transmit to the decoder by taking into account more neighbors of the vertex whose signal is to be predicted.

[0194] For some embodiments, slightly more computation may be incurred than when computing a midpoint prediction, since additional checks may be performed. For example, a check for adjacent triangles of each edge, a check for triangle edge lengths, and/or a check of angle sizes of adjacent triangles may be done before doing a prediction. If these adjacent triangles are stored efficiently in memory, they may be accessed and processed efficiently.

[0195] FIG. 16 is a flowchart illustrating an example process for preforming a wavelet transform according to some embodiments. For some embodiments, an example process 1600 may include obtaining 1602 an input signal corresponding to a mesh. For some embodiments, the example process 1600 may further include splitting 1604 the input signal into a plurality of odd-indexed samples and a plurality of even-indexed samples, wherein the plurality of odd-indexed samples of the input signal correspond to vertices in the mesh at a lower resolution level, and wherein the plurality of even-indexed samples of the input signal correspond to vertices in the mesh at a higher resolution level. For some embodiments, the example process 1600 may further include determining 1606 at least one sample of a predicted signal using at least three of the plurality of odd- indexed samples. For some embodiments, the example process 1600 may further include subtracting 1608 the predicted signal from the plurality of even-indexed samples to generate a wavelet coefficient signal.

[0196] FIG. 17 is a flowchart illustrating an example process for preforming an inverse wavelet transform according to some embodiments. For some embodiments, an example process 1700 may include obtaining 1702 a wavelet-transformed coarse input signal corresponding to a mesh, wherein the wavelet-transformed coarse input signal includes a first plurality of samples. For some embodiments, the example process 1700 may further include obtaining 1704 a wavelet coefficients input signal corresponding to the mesh. For some embodiments, the example process 1700 may further include determining 1706 at least one sample of a predicted signal using at least three of the first plurality of samples of the mesh signal. For some embodiments, the example process 1700 may further include adding 1708 the predicted signal to the wavelet coefficients input signal to generate a second plurality of samples. For some embodiments, the example process 1700 may further include merging 1710 the first plurality of samples with the second plurality of samples to generate an output signal corresponding to the mesh.

[0197] While the methods and systems in accordance with some embodiments are generally discussed in context of extended reality (XR), some embodiments may be applied to any XR contexts such as, e.g., virtual reality (VR) / mixed reality (MR) I augmented reality (AR) contexts. Also, although the term “head mounted display (HMD)” is used herein in accordance with some embodiments, some embodiments may be applied to a wearable device (which may or may not be attached to the head) capable of, e.g., XR, VR, AR, and/or MR for some embodiments.

[0198] A first example method in accordance with some embodiments may include: obtaining an input signal corresponding to a mesh; splitting the input signal into a plurality of odd-indexed samples and a plurality of even-indexed samples, wherein the plurality of odd-indexed samples of the input signal correspond to vertices in the mesh at a lower resolution level, and wherein the plurality of even-indexed samples of the input signal correspond to vertices in the mesh at a higher resolution level; determining at least one sample of a predicted signal using at least three of the plurality of odd-indexed samples; and subtracting the predicted signal from the plurality of even-indexed samples to generate a wavelet coefficient signal.

[0199] Some embodiments of the first example method may further include subtracting the wavelet coefficient signal from the plurality of odd-indexed samples.

[0200] For some embodiments of the first example method, determining the at least one sample of the predicted signal may include determining at least one weighted value based on four samples of the plurality of odd-indexed samples, wherein the four samples are nearest neighbors of the at least one sample of the predicted signal.

[0201] For some embodiments of the first example method, the nearest neighbors are vertices of triangles adjacent to the at least one sample of the predicted signal.

[0202] For some embodiments of the first example method, determining the at least one weighted value based on the four samples of the plurality of odd-indexed samples includes determining an unequal weighting of the four samples. [0203] For some embodiments of the first example method, determining the at least one weighted value is based on relative distances of the four samples to the at least one sample of the predicted signal.

[0204] For some embodiments of the first example method, determining the at least one sample of the predicted signal includes determining at least one weighted value based on three samples of the plurality of odd-indexed samples, wherein the three samples are nearest neighbors of the at least one sample of the predicted signal.

[0205] For some embodiments of the first example method, the nearest neighbors are vertices of triangles adjacent to the at least one sample of the predicted signal.

[0206] For some embodiments of the first example method, determining the at least one weighted value based on the three samples of the plurality of odd-indexed samples includes determining an unequal weighting of the three samples.

[0207] For some embodiments of the first example method, determining the at least one weighted value is based on relative distances of the three samples to the at least one sample of the predicted signal.

[0208] For some embodiments of the first example method, the at least one sample of the predicted signal may include a boundary point of the mesh.

[0209] A first example apparatus in accordance with some embodiments may include: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform any one of the methods listed above.

[0210] A second example method in accordance with some embodiments may include: obtaining a wavelet-transformed coarse input signal corresponding to a mesh, wherein the wavelet-transformed coarse input signal includes a first plurality of samples; obtaining a wavelet coefficients input signal corresponding to the mesh; determining at least one sample of a predicted signal using at least three of the first plurality of samples of the mesh signal; adding the predicted signal to the wavelet coefficients input signal to generate a second plurality of samples; and merging the first plurality of samples with the second plurality of samples to generate an output signal corresponding to the mesh.

[0211] For some embodiments of the second example method, the first plurality of samples corresponds to even-indexed samples of the output signal, and the second plurality of samples corresponds to odd- indexed samples of the output signal.

[0212] Some embodiments of the second example method may further include subtracting the wavelet coefficients input signal from the wavelet-transformed coarse input signal. [0213] For some embodiments of the second example method, determining the at least one sample of the predicted signal may include determining at least one weighted value based on four samples of the first plurality of samples, wherein the four samples are nearest neighbors of the at least one sample of the predicted signal.

[0214] For some embodiments of the second example method, the nearest neighbors are vertices of triangles adjacent to the at least one sample of the predicted signal.

[0215] For some embodiments of the second example method, determining the at least one weighted value based on the four samples of the first plurality of samples includes determining an unequal weighting of the four samples.

[0216] For some embodiments of the second example method, determining the at least one weighted value is based on relative distances of the four samples to the at least one sample of the predicted signal.

[0217] For some embodiments of the second example method, determining the at least one sample ofthe predicted signal includes determining at least one weighted value based on three samples ofthe first plurality of samples, wherein the three samples are nearest neighbors of the at least one sample of the predicted signal.

[0218] For some embodiments of the second example method, the nearest neighbors are vertices of triangles adjacent to the at least one sample of the predicted signal.

[0219] For some embodiments of the second example method, determining the at least one weighted value based on the three samples of the first plurality of samples includes determining an unequal weighting of the three samples.

[0220] For some embodiments of the second example method, determining the at least one weighted value is based on relative distances of the three samples to the at least one sample of the predicted signal.

[0221] For some embodiments of the second example method, the at least one sample of the predicted signal includes a boundary point of the mesh.

[0222] A second example apparatus in accordance with some embodiments may include: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform any one of the methods listed above.

[0223] A third example method in accordance with some embodiments may include: obtaining an input signal corresponding to a mesh; splitting the input signal into a first plurality of samples and a second plurality of samples, determining at least one sample of a predicted signal using at least three of the first plurality of samples; and subtracting the predicted signal from the second plurality of samples to generate a wavelet coefficient signal.

[0224] For some embodiments of the second example method, the first plurality of samples of the input signal correspond to vertices in the mesh at a lower resolution level, and the second plurality of samples of the input signal correspond to vertices in the mesh at a higher resolution level.

[0225] For some embodiments of the second example method, the first plurality of samples of the input signal correspond to odd-indexed samples of the input signal, and the second plurality of samples of the input signal correspond to even-indexed samples of the input signal.

[0226] For some embodiments of the second example method, the first plurality of samples of the input signal correspond to vertices in the mesh at a higher resolution level, and the second plurality of samples of the input signal correspond to vertices in the mesh at a lower resolution level.

[0227] For some embodiments of the second example method, the first plurality of samples of the input signal correspond to even-indexed samples of the input signal, and the second plurality of samples of the input signal correspond to odd-indexed samples of the input signal.

[0228] A third example apparatus in accordance with some embodiments may include: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform any one of the methods listed above.

[0229] An example method of performing a wavelet transform on an input signal corresponding to a mesh in accordance with some embodiments may include: obtaining the input signal; splitting the input signal into lower-resolution samples and higher-resolution samples; generating a prediction signal, wherein the prediction signal includes prediction samples corresponding to the higher-resolution samples, and wherein each of the prediction samples is generated based on at least three of the lower-resolution samples; and subtracting the prediction signal from the higher-resolution samples to generate a wavelet coefficient signal.

[0230] A fourth example apparatus in accordance with some embodiments may include: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform any one of the methods listed above.

[0231] An example method of performing a wavelet transform on an input signal corresponding to a mesh in accordance with some embodiments may include: splitting the input signal into lower-resolution samples and higher-resolution samples; generating a prediction signal based on at least three lower-resolution samples for each sample of the prediction signal; and subtracting the prediction signal from the higher- resolution samples to generate a wavelet coefficient signal. [0232] A fifth example apparatus in accordance with some embodiments may include: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform any one of the methods listed above.

[0233] A sixth example apparatus in accordance with some embodiments may include at least one processor configured to perform any one of the methods listed above.

[0234] A seventh example apparatus in accordance with some embodiments may include a computer- readable medium storing instructions for causing one or more processors to perform any one of the methods listed above.

[0235] An eighth example apparatus in accordance with some embodiments may include at least one processor and at least one non-transitory computer-readable medium storing instructions for causing the at least one processor to perform any one of the methods listed above.

[0236] An example signal in accordance with some embodiments may include a signal conveying a wavelet coefficient signal generated according to a method listed above.

[0237] This disclosure describes a variety of aspects, including tools, features, embodiments, models, approaches, etc. Many of these aspects are described with specificity and, at least to show the individual characteristics, are often described in a manner that may sound limiting. However, this is for purposes of clarity in description, and does not limit the disclosure or scope of those aspects. Indeed, all of the different aspects can be combined and interchanged to provide further aspects. Moreover, the aspects can be combined and interchanged with aspects described in earlier filings as well.

[0238] The aspects described and contemplated in this disclosure can be implemented in many different forms. While some embodiments are illustrated specifically, other embodiments are contemplated, and the discussion of particular embodiments does not limit the breadth of the implementations. At least one of the aspects generally relates to video encoding and decoding, and at least one other aspect generally relates to transmitting a bitstream generated or encoded. These and other aspects can be implemented as a method, an apparatus, a computer readable storage medium having stored thereon instructions for encoding or decoding video data according to any of the methods described, and/or a computer readable storage medium having stored thereon a bitstream generated according to any of the methods described.

[0239] In the present disclosure, the terms “reconstructed” and “decoded” may be used interchangeably, the terms “pixel” and “sample” may be used interchangeably, the terms “image,” “picture” and “frame” may be used interchangeably. Usually, but not necessarily, the term “reconstructed” is used at the encoder side while “decoded” is used at the decoder side. [0240] The terms HDR (high dynamic range) and SDR (standard dynamic range) often convey specific values of dynamic range to those of ordinary skill in the art. However, additional embodiments are also intended in which a reference to HDR is understood to mean “higher dynamic range” and a reference to SDR is understood to mean “lower dynamic range.” Such additional embodiments are not constrained by any specific values of dynamic range that might often be associated with the terms “high dynamic range” and “standard dynamic range.”

[0241] Various methods are described herein, and each of the methods comprises one or more steps or actions for achieving the described method. Unless a specific order of steps or actions is required for proper operation of the method, the order and/or use of specific steps and/or actions may be modified or combined. Additionally, terms such as “first”, “second”, etc. may be used in various embodiments to modify an element, component, step, operation, etc., such as, for example, a “first decoding” and a “second decoding”. Use of such terms does not imply an ordering to the modified operations unless specifically required. So, in this example, the first decoding need not be performed before the second decoding, and may occur, for example, before, during, or in an overlapping time period with the second decoding.

[0242] Various numeric values may be used in the present disclosure, for example. The specific values are for example purposes and the aspects described are not limited to these specific values.

[0243] Embodiments described herein may be carried out by computer software implemented by a processor or other hardware, or by a combination of hardware and software. As a non-limiting example, the embodiments can be implemented by one or more integrated circuits. The processor can be of any type appropriate to the technical environment and can encompass one or more of microprocessors, general purpose computers, special purpose computers, and processors based on a multi-core architecture, as nonlimiting examples.

[0244] Various implementations involve decoding. “Decoding”, as used in this disclosure, can encompass all or part of the processes performed, for example, on a received encoded sequence in order to produce a final output suitable for display. In various embodiments, such processes include one or more of the processes typically performed by a decoder, for example, entropy decoding, inverse quantization, inverse transformation, and differential decoding. In various embodiments, such processes also, or alternatively, include processes performed by a decoder of various implementations described in this disclosure, for example, extracting a picture from a tiled (packed) picture, determining an upsampling filter to use and then upsampling a picture, and flipping a picture back to its intended orientation.

[0245] As further examples, in one embodiment “decoding” refers only to entropy decoding, in another embodiment “decoding” refers only to differential decoding, and in another embodiment “decoding” refers to a combination of entropy decoding and differential decoding. Whether the phrase “decoding process” is intended to refer specifically to a subset of operations or generally to the broader decoding process will be clear based on the context of the specific descriptions.

[0246] Various implementations involve encoding. In an analogous way to the above discussion about “decoding”, “encoding” as used in this disclosure can encompass all or part of the processes performed, for example, on an input video sequence in order to produce an encoded bitstream. In various embodiments, such processes include one or more of the processes typically performed by an encoder, for example, partitioning, differential encoding, transformation, quantization, and entropy encoding. In various embodiments, such processes also, or alternatively, include processes performed by an encoder of various implementations described in this disclosure.

[0247] As further examples, in one embodiment “encoding” refers only to entropy encoding, in another embodiment “encoding” refers only to differential encoding, and in another embodiment “encoding” refers to a combination of differential encoding and entropy encoding. Whether the phrase “encoding process” is intended to refer specifically to a subset of operations or generally to the broader encoding process will be clear based on the context of the specific descriptions.

[0248] When a figure is presented as a flow diagram, it should be understood that it also provides a block diagram of a corresponding apparatus. Similarly, when a figure is presented as a block diagram, it should be understood that it also provides a flow diagram of a corresponding method/process.

[0249] Various embodiments refer to rate distortion optimization. In particular, during the encoding process, the balance or trade-off between the rate and distortion is usually considered, often given the constraints of computational complexity. The rate distortion optimization is usually formulated as minimizing a rate distortion function, which is a weighted sum of the rate and of the distortion. There are different approaches to solve the rate distortion optimization problem. For example, the approaches may be based on an extensive testing of all encoding options, including all considered modes or coding parameters values, with a complete evaluation of their coding cost and related distortion of the reconstructed signal after coding and decoding. Faster approaches may also be used, to save encoding complexity, in particular with computation of an approximated distortion based on the prediction or the prediction residual signal, not the reconstructed one. A mix of these two approaches can also be used, such as by using an approximated distortion for only some of the possible encoding options, and a complete distortion for other encoding options. Other approaches only evaluate a subset of the possible encoding options. More generally, many approaches employ any of a variety of techniques to perform the optimization, but the optimization is not necessarily a complete evaluation of both the coding cost and related distortion. [0250] The implementations and aspects described herein can be implemented in, for example, a method or a process, an apparatus, a software program, a data stream, or a signal. Even if only discussed in the context of a single form of implementation (for example, discussed only as a method), the implementation of features discussed can also be implemented in other forms (for example, an apparatus or program). An apparatus can be implemented in, for example, appropriate hardware, software, and firmware. The methods can be implemented in, for example, a processor, which refers to processing devices in general, including, for example, a computer, a microprocessor, an integrated circuit, or a programmable logic device. Processors also include communication devices, such as, for example, computers, cell phones, portable/personal digital assistants (“PDAs”), and other devices that facilitate communication of information between end-users.

[0251] Reference to “one embodiment” or “an embodiment” or “one implementation” or “an implementation”, as well as other variations thereof, means that a particular feature, structure, characteristic, and so forth described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrase “in one embodiment” or “in an embodiment” or “in one implementation” or “in an implementation”, as well any other variations, appearing in various places throughout this disclosure are not necessarily all referring to the same embodiment.

[0252] Additionally, this disclosure may refer to “determining” various pieces of information. Determining the information can include one or more of, for example, estimating the information, calculating the information, predicting the information, or retrieving the information from memory.

[0253] Further, this disclosure may refer to “accessing” various pieces of information. Accessing the information can include one or more of, for example, receiving the information, retrieving the information (for example, from memory), storing the information, moving the information, copying the information, calculating the information, determining the information, predicting the information, or estimating the information.

[0254] Additionally, this disclosure may refer to “receiving” various pieces of information. Receiving is, as with “accessing”, intended to be a broad term. Receiving the information can include one or more of, for example, accessing the information, or retrieving the information (for example, from memory). Further, “receiving” is typically involved, in one way or another, during operations such as, for example, storing the information, processing the information, transmitting the information, moving the information, copying the information, erasing the information, calculating the information, determining the information, predicting the information, or estimating the information.

[0255] It is to be appreciated that the use of any of the following ”, “and/or”, and “at least one of”, for example, in the cases of “A/B”, “A and/or B” and “at least one of A and B”, is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of both options (A and B). As a further example, in the cases of “A, B, and/or C” and “at least one of A, B, and C”, such phrasing is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of the third listed option (C) only, or the selection of the first and the second listed options (A and B) only, or the selection of the first and third listed options (A and C) only, or the selection of the second and third listed options (B and C) only, or the selection of all three options (A and B and C). This may be extended for as many items as are listed.

[0256] Also, as used herein, the word “signal” refers to, among other things, indicating something to a corresponding decoder. For example, in certain embodiments the encoder signals a particular one of a plurality of parameters for region-based filter parameter selection for de-artifact filtering. In this way, in an embodiment the same parameter is used at both the encoder side and the decoder side. Thus, for example, an encoder can transmit (explicit signaling) a particular parameter to the decoder so that the decoder can use the same particular parameter. Conversely, if the decoder already has the particular parameter as well as others, then signaling can be used without transmitting (implicit signaling) to simply allow the decoder to know and select the particular parameter. By avoiding transmission of any actual functions, a bit savings is realized in various embodiments. It is to be appreciated that signaling can be accomplished in a variety of ways. For example, one or more syntax elements, flags, and so forth are used to signal information to a corresponding decoder in various embodiments. While the preceding relates to the verb form of the word “signal”, the word “signal” can also be used herein as a noun.

[0257] Implementations can produce a variety of signals formatted to carry information that can be, for example, stored or transmitted. The information can include, for example, instructions for performing a method, or data produced by one of the described implementations. For example, a signal can be formatted to carry the bitstream of a described embodiment. Such a signal can be formatted, for example, as an electromagnetic wave (for example, using a radio frequency portion of spectrum) or as a baseband signal. The formatting can include, for example, encoding a data stream and modulating a carrier with the encoded data stream. The information that the signal carries can be, for example, analog or digital information. The signal can be transmitted over a variety of different wired or wireless links, as is known. The signal can be stored on a processor-readable medium.

[0258] We describe a number of embodiments. Features of these embodiments can be provided alone or in any combination, across various claim categories and types. Further, embodiments can include one or more of the following features, devices, or aspects, alone or in any combination, across various claim categories and types:

• Adapting residues at an encoder according to any of the embodiments discussed. • A bitstream or signal that includes one or more of the described syntax elements, or variations thereof.

• A bitstream or signal that includes syntax conveying information generated according to any of the embodiments described.

• Inserting in the signaling syntax elements that enable the decoder to adapt residues in a manner corresponding to that used by an encoder.

• Creating and/or transmitting and/or receiving and/or decoding a bitstream or signal that includes one or more of the described syntax elements, or variations thereof.

• Creating and/or transmitting and/or receiving and/or decoding according to any of the embodiments described.

• A method, process, apparatus, medium storing instructions, medium storing data, or signal according to any of the embodiments described.

• A TV, set-top box, cell phone, tablet, or other electronic device that performs adaptation of filter parameters according to any of the embodiments described.

• A TV, set-top box, cell phone, tablet, or other electronic device that performs adaptation of filter parameters according to any of the embodiments described, and that displays (e.g. using a monitor, screen, or other type of display) a resulting image.

• A TV, set-top box, cell phone, tablet, or other electronic device that selects (e.g. using a tuner) a channel to receive a signal including an encoded image, and performs adaptation of filter parameters according to any of the embodiments described.

• A TV, set-top box, cell phone, tablet, or other electronic device that receives (e.g. using an antenna) a signal over the air that includes an encoded image, and performs adaptation of filter parameters according to any of the embodiments described.

[0259] Note that various hardware elements of one or more of the described embodiments are referred to as “modules” that carry out (i.e. , perform, execute, and the like) various functions that are described herein in connection with the respective modules. As used herein, a module includes hardware (e.g., one or more processors, one or more microprocessors, one or more microcontrollers, one or more microchips, one or more application-specific integrated circuits (ASICs), one or more field programmable gate arrays (FPGAs), one or more memory devices) deemed suitable by those of skill in the relevant art for a given implementation. Each described module may also include instructions executable for carrying out the one or more functions described as being carried out by the respective module, and it is noted that those instructions could take the form of or include hardware (i.e. , hardwired) instructions, firmware instructions, software instructions, and/or the like, and may be stored in any suitable non-transitory computer-readable medium or media, such as commonly referred to as RAM, ROM, etc.

[0260] Although features and elements are described above in particular combinations, one of ordinary skill in the art will appreciate that each feature or element can be used alone or in any combination with the other features and elements. In addition, the methods described herein may be implemented in a computer program, software, or firmware incorporated in a computer-readable medium for execution by a computer or processor. Examples of computer-readable storage media include, but are not limited to, a read only memory (ROM), a random access memory (RAM), a register, cache memory, semiconductor memory devices, magnetic media such as internal hard disks and removable disks, magneto-optical media, and optical media such as CD-ROM disks, and digital versatile disks (DVDs). A processor in association with software may be used to implement a radio frequency transceiver for use in a WTRU, DE, terminal, base station, RNC, or any host computer.

Claims

1. A method comprising: obtaining an input signal corresponding to a mesh; splitting the input signal into a plurality of odd-indexed samples and a plurality of even-indexed samples, wherein the plurality of odd-indexed samples of the input signal correspond to vertices in the mesh at a lower resolution level, and wherein the plurality of even-indexed samples of the input signal correspond to vertices in the mesh at a higher resolution level; determining at least one sample of a predicted signal using at least three of the plurality of odd- indexed samples; and subtracting the predicted signal from the plurality of even-indexed samples to generate a wavelet coefficient signal.

2. The method of claim 1, further comprising subtracting the wavelet coefficient signal from the plurality of odd-indexed samples.

3. The method of any one of claims 1 -2, wherein determining the at least one sample of the predicted signal comprises determining at least one weighted value based on four samples of the plurality of odd-indexed samples, and wherein the four samples are nearest neighbors of the at least one sample of the predicted signal.

4. The method of claim 3, wherein the nearest neighbors are vertices of triangles adjacent to the at least one sample of the predicted signal.

5. The method of any one of claims 3-4, wherein determining the at least one weighted value based on the four samples of the plurality of odd-indexed samples comprises determining an unequal weighting of the four samples.

6. The method of any one of claims 3-5, wherein determining the at least one weighted value is based on relative distances of the four samples to the at least one sample of the predicted signal.

7. The method of any one of claims 1 -6, wherein determining the at least one sample of the predicted signal comprises determining at least one weighted value based on three samples of the plurality of odd-indexed samples, and wherein the three samples are nearest neighbors of the at least one sample of the predicted signal.

8. The method of claim 7, wherein the nearest neighbors are vertices of triangles adjacent to the at least one sample of the predicted signal.

9. The method of any one of claims 7-8, wherein determining the at least one weighted value based on the three samples of the plurality of odd-indexed samples comprises determining an unequal weighting of the three samples.

10. The method of any one of claims 7-9, wherein determining the at least one weighted value is based on relative distances of the three samples to the at least one sample of the predicted signal.

11 . The method of any one of claims 1-10, wherein the at least one sample of the predicted signal comprises a boundary point of the mesh.

12. An apparatus comprising: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform the method of any one of claims 1 through 11 .

13. A method comprising: obtaining a wavelet-transformed coarse input signal corresponding to a mesh, wherein the wavelet-transformed coarse input signal comprises a first plurality of samples; obtaining a wavelet coefficients input signal corresponding to the mesh; determining at least one sample of a predicted signal using at least three of the first plurality of samples of the mesh signal; adding the predicted signal to the wavelet coefficients input signal to generate a second plurality of samples; and merging the first plurality of samples with the second plurality of samples to generate an output signal corresponding to the mesh.

14. The method of claim 13, wherein the first plurality of samples corresponds to even-indexed samples of the output signal, and wherein the second plurality of samples corresponds to odd-indexed samples of the output signal.

15. The method of any one of claims 13-14, further comprising subtracting the wavelet coefficients input signal from the wavelet-transformed coarse input signal.

16. The method of any one of claims 13-15, wherein determining the at least one sample of the predicted signal comprises determining at least one weighted value based on four samples of the first plurality of samples, and wherein the four samples are nearest neighbors of the at least one sample of the predicted signal.

17. The method of claim 16, wherein the nearest neighbors are vertices of triangles adjacent to the at least one sample of the predicted signal.

18. The method of any one of claims 16-17, wherein determining the at least one weighted value based on the four samples of the first plurality of samples comprises determining an unequal weighting of the four samples.

19. The method of any one of claims 16-18, wherein determining the at least one weighted value is based on relative distances of the four samples to the at least one sample of the predicted signal.

20. The method of any one of claims 13-19, wherein determining the at least one sample of the predicted signal comprises determining at least one weighted value based on three samples of the first plurality of samples, and wherein the three samples are nearest neighbors of the at least one sample of the predicted signal.

21. The method of claim 20, wherein the nearest neighbors are vertices of triangles adjacent to the at least one sample of the predicted signal.

22. The method of any one of claims 20-21 , wherein determining the at least one weighted value based on the three samples of the first plurality of samples comprises determining an unequal weighting of the three samples.

23. The method of any one of claims 20-22, wherein determining the at least one weighted value is based on relative distances of the three samples to the at least one sample of the predicted signal.

24. The method of any one of claims 13-23, wherein the at least one sample of the predicted signal comprises a boundary point of the mesh.

25. An apparatus comprising: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform the method of any one of claims 13 through 24.

26. A method comprising: obtaining an input signal corresponding to a mesh; splitting the input signal into a first plurality of samples and a second plurality of samples, determining at least one sample of a predicted signal using at least three of the first plurality of samples; and subtracting the predicted signal from the second plurality of samples to generate a wavelet coefficient signal.

27. The method of claim 26, wherein the first plurality of samples of the input signal correspond to vertices in the mesh at a lower resolution level, and wherein the second plurality of samples of the input signal correspond to vertices in the mesh at a higher resolution level.

28. The method of any one of claims 26-27, wherein the first plurality of samples of the input signal correspond to odd-indexed samples of the input signal, and wherein the second plurality of samples of the input signal correspond to even-indexed samples of the input signal.

29. The method of claim 26, wherein the first plurality of samples of the input signal correspond to vertices in the mesh at a higher resolution level, and wherein the second plurality of samples of the input signal correspond to vertices in the mesh at a lower resolution level.

30. The method of any one of claims 26 and 29, wherein the first plurality of samples of the input signal correspond to even-indexed samples of the input signal, and wherein the second plurality of samples of the input signal correspond to odd-indexed samples of the input signal.

31. An apparatus comprising: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform the method of any one of claims 26 through 30.

32. A method of performing a wavelet transform on an input signal corresponding to a mesh, comprising: obtaining the input signal; splitting the input signal into lower-resolution samples and higher-resolution samples; generating a prediction signal, wherein the prediction signal comprises prediction samples corresponding to the higher- resolution samples, and wherein each of the prediction samples is generated based on at least three of the lower- resolution samples; and subtracting the prediction signal from the higher-resolution samples to generate a wavelet coefficient signal.

33. An apparatus comprising: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform the method of claim 32.

34. A method of performing a wavelet transform on an input signal corresponding to a mesh, comprising: splitting the input signal into lower-resolution samples and higher-resolution samples; generating a prediction signal based on at least three lower-resolution samples for each sample of the prediction signal; and subtracting the prediction signal from the higher-resolution samples to generate a wavelet coefficient signal.

35. An apparatus comprising: a processor; and a non-transitory computer-readable medium storing instructions operative, when executed by the processor, to cause the apparatus to perform the method of claim 34.

36. An apparatus comprising at least one processor configured to perform the method of any one of claims

1-11 , 13-24, 26-30, 32, and 34.

37. An apparatus comprising a computer-readable medium storing instructions for causing one or more processors to perform the method of any one of claims 1-11, 13-24, 26-30, 32, and 34.

38. An apparatus comprising at least one processor and at least one non-transitory computer-readable medium storing instructions for causing the at least one processor to perform the method of any one of claims 1-11, 13-24, 26-30, 32, and 34.

39. A signal conveying a wavelet coefficient signal generated according to the method of any one of claims

1-11, 26-30, 32, and 34.