CN110264401A - Continuous type image magnification method, device and storage medium based on radial basis function - Google Patents
Continuous type image magnification method, device and storage medium based on radial basis function Download PDFInfo
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Abstract
The present invention relates to digital image processing techniques fields, disclose a kind of continuous type image magnification method based on radial basis function, this method comprises: selected one needs the image of enhanced processing as original image, and the mode that the original image is converted to discrete value is indicated and is stored；Interpolation processing is carried out to the original image based on radial basis function, obtains the interpolation image of original image；Spatial extent processing is carried out to the interpolation image based on the radial basis function, enlargement ratio is obtained, and sliding-model control is carried out to the interpolation image, constitutes enlarged drawing.The present invention also proposes a kind of continuous type image amplifying device and a kind of computer readable storage medium based on radial basis function.Operational efficiency of the present invention is higher, supports the amplification of dimensional images.
Description
Technical Field
The present invention relates to the field of digital image processing technologies, and in particular, to a method and an apparatus for continuous image magnification based on radial basis functions, and a computer-readable storage medium.
Background
Image amplification processing technology plays an important role in practical application, such as in medical systems, public security systems, aerospace systems and some image processing software, in order to be suitable for special occasions and obtain better visual effects, an effective method is often needed to change the size of the existing image and ensure that the changed image has better quality.
Image interpolation is the main method of image magnification. The traditional image interpolation algorithm focuses on the smoothing of an image so as to obtain a better visual effect, but the method also degrades the high-frequency part of the image while keeping the image smooth, so that the interpolation effect is poor, the phenomena of blurring, sawtooth, staircase and the like appear at the edge part of the image, and the detail part is not clear enough and cannot meet the expectation of image processing.
Now, in the field of digital image processing, many problems have been solved to some extent. However, with the increasing demands on the efficiency and effectiveness of digital image processing, the existing methods must be improved.
Disclosure of Invention
The invention provides a continuous image amplification method and device based on a radial basis function and a computer readable storage medium, and mainly aims to provide an image amplification scheme which is high in operation efficiency and supports high-dimensional image amplification.
In order to achieve the above object, the present invention provides a continuous image magnifying method based on radial basis functions, including:
selecting an image needing to be amplified as an original image, and converting the original image into a discrete value mode for representing and storing;
performing interpolation processing on the original image based on the radial basis function to obtain an interpolation image of the original image;
and performing space extension processing on the interpolation image based on the radial basis function to obtain a magnification ratio, and performing discretization processing on the interpolation image to form an amplified image.
Optionally, the radial basis function is a Multi-Quadric function.
Optionally, the interpolating the original image by using the radial basis function includes:
known to be defined as [0, M-1 ]]×[0，N-1]Set of data points ofFinding image functions
Wherein, M and N represent that the original image is M rows and N columns, R is the definition domain interval of the data point set, and R is3Representing a domain data dimension, λjIn order to interpolate the conditional weights of the image,in order to be a radial basis function,
the interpolation condition is satisfied:
wherein,
for the image function f*(x, y) selecting S x S integer points around the point to be interpolated as interpolation reference points for each non-integer point in the (x, y), wherein S is specified by a user;
solving formula 1 to obtain f*(x, y) defines a function value for each point on the domain, thereby obtaining an interpolated image of the original image.
Optionally, the performing spatial extension processing on the interpolated image to obtain a magnification factor, and performing discretization processing on the interpolated image to form an enlarged image includes:
the magnification of the interpolation image in the x direction is set as a, the magnification in the y direction is set as b, and the curve z is set as f*(x, y) is extended in x direction by a times in equal proportion and in y direction by b times in equal proportion, and a curved surface w is obtained as g*(u, v) wherein, a > 1, b > 1, g*(u, v) has the domain definition of R2To define the domain dimension, the specific solving process is as follows:
curved surface z ═ f*(x, y) at any point (x)0，y0，z0) On a curved surface w ═ g*The corresponding point on (u, v) is (u)0，v0，w0) The corresponding relationship is expressed as follows:
when any one pixel (u1, v1) in the enlarged image g (u, v) is set, the curved surface w is g*(u1, v1, w1) at point (u, v) on curved surface z ═ f*Corresponding point (x) on (x, y)1，y1，z1) The correspondence of (a) is as follows:
using said f*(x, y), finding g*(u, v), take g*(u, v) all integer points in the defined domain constitute the magnified image g (u, v), where image g (u, v) is [ aM []Line, [ bN]Column, then the value range of u, v is: u is more than or equal to 0 and less than or equal to [ aM%]-1，0≤v≤[bN]-1。
Optionally, the method further comprises:
and calculating Euclidean distances of gray matrixes of the original image and the amplified image, and judging the similarity of the original image and the amplified image.
In addition, to achieve the above object, the present invention further provides a radial basis function based continuous image magnifying device, including a memory and a processor, where the memory stores a radial basis function based continuous image magnifying program executable on the processor, and the radial basis function based continuous image magnifying program implements the following steps when executed by the processor:
selecting an image needing to be amplified as an original image, and converting the original image into a discrete value mode for representing and storing;
performing interpolation processing on the original image based on a radial basis function Multi-Quadric to obtain an interpolation image of the original image;
and carrying out space extension processing on the interpolation image based on the radial basis function Multi-Quadric to obtain the magnification, and carrying out discretization processing on the interpolation image to form an amplified image.
Optionally, the interpolating the original image by using the radial basis function Multi-Quadric includes:
known to be defined as [0, M-1 ]]×[0，N-1]Set of data points ofFinding image functions
Wherein, M and N represent that the original image is M rows and N columns, R is the definition domain interval of the data point set, and R is3Representing a domain data dimension, λjIn order to interpolate the conditional weights of the image,in order to be a radial basis function,
the interpolation condition is satisfied:
wherein,
for the image function f*(x, y) selecting S x S integer points around the point to be interpolated as interpolation reference points for each non-integer point in the (x, y), wherein S is specified by a user;
solving formula 1 to obtain f*(x, y) defines a function value for each point on the domain, thereby obtaining an interpolated image of the original image.
Optionally, the performing spatial extension processing on the interpolated image to obtain a magnification factor, and performing discretization processing on the interpolated image to form an enlarged image includes:
the magnification of the interpolation image in the x direction is set as a, the magnification in the y direction is set as b, and the curve z is set as f*(x, y) is extended in x direction by a times in equal proportion and in y direction by b times in equal proportion, and a curved surface w is obtained as g*(u, v) wherein a > 1, b > 1, g*(u, v) has the domain definition of R2To define the domain dimension, the specific solving process is as follows:
curved surface z ═ f*(x, y) at any point (x)0，y0，z0) On a curved surface w ═ g*The corresponding point on (u, v) is (u)0，v0，w0) The corresponding relationship is expressed as follows:
when any one pixel (u1, v1) in the enlarged image g (u, v) is set, the curved surface w is g*(u1, v1, w1) at point (u, v) on curved surface z ═ f*Corresponding point (x) on (x, y)1，y1，z1) The correspondence of (a) is as follows:
using said f*(x, y), finding g*(u, v), take g*(u, v) all integer points in the defined domain constitute the magnified image g (u, v), where image g (u, v) is [ aM []Line, [ bN]Column, then the value range of u, v is: u is more than or equal to 0 and less than or equal to [ aM%]-1，0≤v≤[bN]-1。
Optionally, when executed by the processor, the radial basis function-based continuous image magnification program further implements the following steps:
and calculating Euclidean distances of gray matrixes of the original image and the amplified image, and judging the similarity of the original image and the amplified image.
In addition, to achieve the above object, the present invention also provides a computer readable storage medium having stored thereon a radial basis function-based continuous image magnification program, which is executable by one or more processors to implement the steps of the radial basis function-based continuous image magnification method as described above.
According to the continuous image amplification method and device based on the radial basis function and the computer-readable storage medium, the radial basis function is used for amplifying the image and converting the image into the curved surface reconstruction problem, the interpolation format is constructed aiming at the lost information, and then the computer is used for automatically selecting the interpolation node and solving the interpolation equation, so that the processed image can be obtained. The function prototype based on the Multi-Quadric is simple, so that the operation efficiency is high, and high-dimensional image amplification is supported.
Drawings
FIG. 1 is a schematic flowchart of a continuous image magnifying method based on radial basis functions according to an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating an internal structure of a radial basis function-based continuous image magnifying device according to an embodiment of the present invention;
fig. 3 is a block diagram illustrating a radial basis function based continuous image magnifying procedure of a radial basis function based continuous image magnifying device according to an embodiment of the present invention.
The implementation, functional features and advantages of the objects of the present invention will be further explained with reference to the accompanying drawings.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The terms "first," "second," "third," "fourth," and the like in the description and in the claims of the present application and in the drawings described above, if any, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It will be appreciated that the data so used may be interchanged under appropriate circumstances such that the embodiments described herein may be practiced otherwise than as specifically illustrated or described herein. Furthermore, the descriptions of "first," "second," etc. are for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicit ly indicating a number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature.
Further, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The invention provides a continuous image amplification method based on a radial basis function.
Referring to fig. 1, a schematic flow chart of a continuous image magnifying method based on radial basis functions according to an embodiment of the present invention is shown. The method may be performed by an apparatus, which may be implemented by software and/or hardware.
In this embodiment, the radial basis function-based continuous image magnification method includes:
s1, selecting an image to be enlarged as an original image, and converting the original image into discrete values for display and storage.
In a preferred embodiment of the present invention, assuming that the coordinates of the original image are (x, y), there are M rows and N columns, the original image is denoted as f (x, y), the original image can be enlarged, and the coordinates of the enlarged image are (u, v), then the enlargement of the original image is realized:
namely, it is
Wherein a is the magnification in the x direction, b is the magnification in the y direction, a > 1, b > 1. When a > 1 magnifies in the x direction, b > 1 magnifies in the y direction, and when a is b, the images before and after the magnification have the same aspect ratio.
In actual calculations, images need to be represented and stored in discrete values. For ease of programming and presentation, and uniformity of format, the preferred embodiment of the present invention represents the original image as follows: assuming that the width of each pixel is 1, f (x, y) represents the value of the pixel (x, y) on the upper right two-dimensional coordinate system with the lower left in the original image as the origin, where x, y are positive integers or 0. In this way, the original image is represented in discrete-valued digital text.
Subsequent interpolation of f (x, y) yields f*(x, y) are continued over their domain of definition, a correspondence is established such that for each point on the magnified image g (u, v), there is f*A point on (x, y) corresponds to this, forming a continuous enlargement of the image.
And S2, carrying out interpolation processing on the original image based on the radial basis function to obtain an interpolation image of the original image.
A radial basis function is a real-valued function whose value depends only on the distance from the origin, i.e., Φ (x) ═ Φ (| x |), or may also be the distance to any point c, which is called the center point, i.e., Φ (x, c) ═ Φ (| x-c |). Any function Φ that satisfies the property Φ (x) ═ Φ (| | x |), can be called a radial basis function. Common radial basis functions are: the gauss distribution function of the Kriging method, the Multi-Quadric function of Hardy, and the thin plate spline of Duchon. The invention selects a Multi-Quadric function as a radial basis function.
The Multi-Quadric function is abbreviated as MQ, and the formula is as follows:
the interpolation processing of the original image by using the radial basis function Multi-Quadric comprises the following steps:
1. known to be defined as [0, M-1 ]]×[0，N-1]Set of data points ofFinding a function
Wherein, M and N represent that the original image is M rows and N columns, R is the definition domain interval of the data point set, and R is3Representing a domain data dimension, λjIn order to interpolate the conditional weights of the image,is a radial basis function of the radial direction,
the interpolation condition is satisfied:
wherein,
it is clear that the interpolation problem described above is for an arbitrary set of data pointsWhen in useSolutions which are mutually different exist pairwise and the only necessary condition is that: symmetric matrices are all non-singular, so that it can be guaranteed that the interpolation problem has a solution and a unique solution:
when the shape parameters in the Multi-Quadric interpolation function are small, the solution of the Multi-Quadric function is almost a piecewise linear function, and the smoothness is good.
2. And selecting a radial basis function Multi-Quadric point to be interpolated and an interpolation reference point.
For image f*It is feasible to construct an interpolation format solution for each non-integer point of (x, y) with only a small number of its surrounding integer points. The radial basis function interpolation has some shielding property, and the influence of data points with a longer distance is very small. The interpolation reference point is selected by adopting a method similar to bicubic interpolation, except that the bicubic interpolation takes 4 × 4 to 16 integer points around the point to be interpolated as the interpolation reference point, and S integer points around the point to be interpolated are taken as the interpolation reference point in the preferred embodiment of the invention, and S can be specified by a user. If the point to be interpolated is too close to one or both edges of the image to directly obtain its surrounding S points, the S points are adjusted to have the smallest sum of the distances from all points to the point to be interpolated and just not to cross the boundary.
3. Based on this, f can be obtained from solving equation 1*(x, y) defines a function value for each point on the domain, thereby obtaining an interpolated image of the original image.
S3, performing space extension processing on the interpolation image based on the radial basis function Multi-Quadric to obtain the magnification, and performing discretization processing on the interpolation image to form an enlarged image.
Let the magnification in the x direction be a, the magnification in the y direction be b, where a > 1, b > 1, and f for a curved surface z*(x, y) is extended in x direction by a times in equal proportion and in y direction by b times in equal proportion, and a curved surface w is obtained as g*(u, v) wherein g*(u, v) domain of definitionR2The representation defines a domain data dimension.
The specific solving process is as follows:
let curved surface z be f*(x, y) at any point (x)0，y0，z0) Which is g on the curved surface*The corresponding point on (u, v) is (u)0，v0，w0) The corresponding relationship is expressed as follows:
similarly, if any one pixel (u1, v1) in the enlarged image g (u, v), the curved surface w is g*(u1, v1, w1) at a point (u, v) where the curved surface z is f*The corresponding point on (x, y) is (x)1，y1，z1) The correspondence is as follows:
using the last step f*(x, y), g is obtained*(u, v), take g*(u, v) all integer points in the defined domain constitute the magnified image g (u, v). Since this image is [ aM]Line, [ bN]If u, v can be obtained as follows: u is more than or equal to 0 and less than or equal to [ aM%]-1，0≤v≤[bN]-1。
And S4, calculating Euclidean distance of gray matrixes of the original image and the amplified image, and judging the similarity of the original image and the amplified image.
The distance between the images reflects the similarity of the images, and the smaller the distance, the higher the similarity. An M x N image is considered as a point in M x N dimensional european image space with e1, e 2...... eMN as a set of basis for the space, where ekN +1 corresponds to an ideal point source located at (k, l). So that an image x is (x)1，x2，...，xMN) (wherein xkN +1Is the gray value of pixel (k, l) corresponds to a point in image space.
Pass meterAnd calculating the Euclidean distance between the two images so as to judge the image amplification effect. Metric coefficient matrix G ═ Gij)MN×MNThe distance of the two images in image space is determined:
g if the long phases of all basis vectors are equalijTotally dependent on eiAnd ejAngle of (theta)ijAt this time, the distance measure of the two images is as follows:
a threshold value is set by calculating the euclidean distance between two images, and it is determined whether the calculated euclidean distance is greater than or equal to the set threshold value at step S5. When the euclidean distance is greater than the set threshold, it indicates that the image is continuously enlarged, and the larger the value, the better the image enlargement effect and the clearer the visual effect are, and the enlarged image may be output in step S6.
And when the Euclidean distance is smaller than the set threshold, repeating the steps from S2 to S4, continuously changing the parameter range, and continuously amplifying the image until the calculation result is equal to or larger than the set threshold, so that the continuous amplification of the image is realized.
The embodiment of the invention provides a continuous image amplification method based on a radial basis function Multi-quad, which is characterized in that an original image is subjected to interpolation calculation, spatial extension and discretization processing based on the radial basis function Multi-quad to obtain an amplified image, and finally, the similarity calculation between the original image and the amplified image is carried out by utilizing a gray matrix Euclidean distance to judge the image amplification effect, and the preferred embodiment of the invention has the following advantages:
the radial basis function Multi-Quadric function prototype is simple, a univariate function can be used for more powerfully describing a multivariate function, the operation efficiency is high for processing large-scale scattered data, and high-dimensional image amplification can be supported;
the radial basis function Multi-Quadric is adopted to amplify the image and convert the image into the curved surface reconstruction problem, an interpolation format can be constructed for the lost information, and then the amplified image is obtained, and the image amplification quality is better compared with that of the traditional interpolation method;
and comparing and calculating the original image and the amplified image by adopting the gray Euclidean distance, checking the amplification effect of the image, and verifying the feasibility of the method.
The invention also provides a continuous image amplification device based on the radial basis function. Referring to fig. 2, a schematic diagram of an internal structure of a radial basis function-based continuous image magnifying device according to an embodiment of the present invention is shown.
In the present embodiment, the continuous image magnifying device 1 based on the radial basis function may be a PC (personal computer), or may be a terminal device such as a smart phone, a tablet computer, or a portable computer. The radial basis function based continuous type image enlargement apparatus 1 includes at least a memory 11, a processor 12, a communication bus 13, and a network interface 14.
The memory 11 includes at least one type of readable storage medium, which includes a flash memory, a hard disk, a multimedia card, a card type memory (e.g., SD or DX memory, etc.), a magnetic memory, a magnetic disk, an optical disk, and the like. The memory 11 may in some embodiments be an internal storage unit of the radial basis function based continuous type image magnification device 1, such as a hard disk of the radial basis function based continuous type image magnification device 1. The memory 11 may also be an external storage device of the continuous image magnifying device 1 based on the radial basis function in other embodiments, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), and the like, which are equipped on the continuous image magnifying device 1 based on the radial basis function. Further, the memory 11 may also include both an internal storage unit and an external storage device of the radial basis function-based continuous type image amplifying apparatus 1. The memory 11 may be used not only to store application software installed in the radial basis function-based continuous image enlarging apparatus 1 and various types of data, such as codes of the radial basis function-based continuous image enlarging program 01, but also to temporarily store data that has been output or is to be output.
The processor 12 may be a Central Processing Unit (CPU), controller, microcontroller, microprocessor or other data Processing chip in some embodiments, and is used for executing program codes stored in the memory 11 or Processing data, such as executing the radial basis function-based continuous image magnification program 01.
The communication bus 13 is used to realize connection communication between these components.
The network interface 14 may optionally include a standard wired interface, a wireless interface (e.g., WI-FI interface), typically used to establish a communication link between the apparatus 1 and other electronic devices.
Optionally, the apparatus 1 may further comprise a user interface, which may comprise a Display (Display), an input unit such as a Keyboard (Keyboard), and optionally a standard wired interface, a wireless interface. Alternatively, in some embodiments, the display may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch device, or the like. Therein, the display, which may also be referred to as a display screen or display unit, is suitable for displaying information processed in the radial basis function based continuous type image magnification device 1 and for displaying a visualized user interface.
Fig. 2 shows only the radial basis function based continuous type image magnifying apparatus 1 having the components 11 to 14 and the radial basis function based continuous type image magnifying program 01, and it will be understood by those skilled in the art that the structure shown in fig. 1 does not constitute a limitation of the radial basis function based continuous type image magnifying apparatus 1, and may include fewer or more components than those shown, or may combine some components, or may arrange different components.
In the embodiment of the apparatus 1 shown in fig. 2, a continuous image magnification program 01 based on a radial basis function is stored in the memory 11; the processor 12 executes the radial basis function based continuous image enlarging program 01 stored in the memory 11 to implement the following steps:
step one, selecting an image needing to be amplified as an original image.
In the preferred embodiment of the present invention, assume that the original image has coordinates (x, y) of M rows and N columns. If the original image is denoted as f (x, y), and the coordinates of the enlarged image are (u, v), the enlargement of the original image is realized by:
namely, it is
Wherein a is the magnification in the x direction, b is the magnification in the y direction, a > 1, b > 1. When a > 1 magnifies in the x direction, b > 1 magnifies in the y direction, and when a is b, the images before and after the magnification have the same aspect ratio.
In actual calculations, images need to be represented and stored in discrete values. In view of ease of programming and presentation, and uniformity of format, the original image is represented as follows: assuming that the width of each pixel is 1, f (x, y) represents the value of the pixel (x, y) on the upper right two-dimensional coordinate system with the lower left in the original image as the origin, where x, y are positive integers or 0. In this way, the original image is represented in digital text.
Subsequent interpolation of f (x, y) yields f*(x, y) are continued over their domain of definition, a correspondence is established such that for each point on the magnified image g (u, v), there is f*A point on (x, y) corresponds to this, forming a continuous enlargement of the image.
And secondly, performing interpolation processing on the original image based on the radial basis function Multi-Quadric to obtain an interpolation image of the original image.
A radial basis function is a real-valued function whose value depends only on the distance from the origin, i.e., Φ (x) ═ Φ (| x |), or may also be the distance to any point c, which is called the center point, i.e., Φ (x, c) ═ Φ (| x-c |). Any function Φ that satisfies the property Φ (x) ═ Φ (| | x |), can be called a radial basis function. Common radial basis functions are: the gauss distribution function of the Kriging method, the Multi-Quadric function of Hardy, and the thin plate spline of Duchon. The invention selects a Multi-Quadric function as a radial basis function.
The Multi-Quadric function is abbreviated as MQ, and the formula is as follows:wherein c is the above value.
The interpolation processing of the original image by using the radial basis function Multi-Quadric comprises the following steps:
1. known to be defined as [0, M-1 ]]×[0，N-1]Set of data points ofFinding a function:
wherein, M and N represent that the original image is M rows and N columns, R is the definition domain interval of the data point set, and R is3Representing a defined domain data dimensionDegree, lambdajIn order to interpolate the conditional weights of the image,in order to be a radial basis function,
the interpolation condition is satisfied:
wherein,
it is clear that the interpolation problem described above is for an arbitrary set of data pointsWhen in useSolutions which are mutually different exist pairwise and the only necessary condition is that: symmetric matrices are all non-singular, so that it can be guaranteed that the interpolation problem has a solution and a unique solution:
when the shape parameters in the Multi-Quadric interpolation function are small, the solution of the Multi-Quadric function is almost a piecewise linear function, and the smoothness is good.
2. And selecting a radial basis function Multi-Quadric point to be interpolated and an interpolation reference point.
For image f*It is feasible to construct an interpolation format solution for each non-integer point of (x, y) with only a small number of its surrounding integer points. The interpolation of the radial basis function has certain shielding property, and the influence of data points with longer distance is very greatIs small. The interpolation reference point is selected by adopting a method similar to bicubic interpolation, except that the bicubic interpolation takes 4 × 4 to 16 integer points around the point to be interpolated as the interpolation reference point, and S integer points around the point to be interpolated are taken as the interpolation reference point in the preferred embodiment of the invention, and S can be specified by a user. If the point to be interpolated is too close to one or both edges of the image to directly obtain its surrounding S points, the S points are adjusted to have the smallest sum of the distances from all points to the point to be interpolated and just not to cross the boundary. Based on this, f can be obtained from solving equation 1*(x, y) defines a function value for each point on the domain, thereby obtaining an interpolated image of the original image.
And thirdly, performing space extension processing on the interpolation image based on the radial basis function Multi-Quadric to obtain a magnification ratio, and performing discretization processing on the interpolation image to form an amplified image.
Let the magnification in the x direction be a, the magnification in the y direction be b, where a > 1, b > 1, and f for a curved surface z*(x, y) is extended in x direction by a times in equal proportion and in y direction by b times in equal proportion, and a curved surface w is obtained as g*(u, v) wherein g*(u, v) domain of definitionR2The representation defines a domain data dimension.
The specific solving process is as follows:
let curved surface z be f*(x, y) at any point (x)0，y0，z0) Which is g on the curved surface*The corresponding point on (u, v) is (u)0，v0，W0) The corresponding relationship is expressed as follows:
also, is provided withIf any one pixel (u1, v1) in the enlarged image g (u, v), the curved surface w is g*(u1, v1, w1) at a point (u, v) where the curved surface z is f*The corresponding point on (x, y) is (x)1，y1，z1) The correspondence is as follows:
using the last step f*(x, y), g is obtained*(u, v), take g*(u, v) all integer points in the defined domain constitute the magnified image g (u, v). Since this image is [ aM]Line, [ bN]If u, v can be obtained as follows: u is more than or equal to 0 and less than or equal to [ aM%]-1，0≤v≤[bN]-1。
And fourthly, calculating Euclidean distances of the gray matrixes of the original image and the amplified image, and judging the similarity of the original image and the amplified image.
The distance between the images reflects the similarity of the images, and the smaller the distance, the higher the similarity. An M x N image is considered as a point in M x N dimensional european image space with e1, e 2...... eMN as a set of basis for the space, where ekN +1 corresponds to an ideal point source located at (k, l). So that an image x is (x)1，x2，...，xMN) (wherein xkN +1Is the gray value of pixel (k, l) corresponds to a point in image space.
And (4) judging the image amplification effect by calculating the Euclidean distance between the two images. Metric coefficient matrix G ═ Gij)MN×MNThe distance of the two images in image space is determined:
if all ofLong equality of the basis vectors of (2), then gijTotally dependent on eiAnd ejAngle of (theta)ijAt this time, the distance measure of the two images is as follows:
the Euclidean distance between two images is calculated, a threshold value is set, if the Euclidean distance obtained through calculation is larger than the set threshold value, the images are shown to be amplified continuously, the larger the value is, the better the image amplification effect is, and the clearer the visual effect is.
And when the Euclidean distance is smaller than the set threshold, repeatedly executing the second step to the fourth step, continuously changing the parameter range, and continuously amplifying the image until the calculation result is equal to or larger than the set threshold, so that the continuous amplification of the image is realized.
Alternatively, in other embodiments, the radial basis function based continuous image magnifying procedure may be further divided into one or more modules, and the one or more modules are stored in the memory 11 and executed by one or more processors (in this embodiment, the processor 12) to implement the present invention.
For example, referring to fig. 3, a schematic diagram of program modules of a radial basis function based continuous image enlargement program in an embodiment of the radial basis function based continuous image enlargement apparatus according to the present invention is shown, in which the radial basis function based continuous image enlargement program can be divided into an image conversion module 10, an image interpolation module 20, an image enlargement module 30, a similarity determination module 40, and a radial basis function based continuous image enlargement module 50, exemplarily:
the image conversion module 10 is configured to: an image needing enlargement processing is selected as an original image, and the original image is displayed and stored in a mode of converting the original image into discrete values.
The image interpolation module 20 is configured to: and carrying out interpolation processing on the original image based on the radial basis function to obtain an interpolation image of the original image.
Optionally, the radial basis function is a Multi-Quadric function.
Optionally, the interpolating the original image by using the radial basis function Multi-Quadric includes:
known to be defined as [0, M-1 ]]×[0，N-1]Set of data points ofFinding an image function:
wherein, M and N represent that the original image is M rows and N columns, R is the definition domain interval of the data point set, and R is3Representing a domain data dimension, λjIn order to interpolate the conditional weights of the image,in order to be a radial basis function,
the interpolation condition is satisfied:
wherein,
for the image function f*Each of (x, y) is not integerCounting points, namely selecting S integer points around a point to be interpolated as interpolation reference points, wherein S is specified by a user;
solving formula 1 to obtain f*(x, y) defines a function value for each point on the domain, thereby obtaining an interpolated image of the original image.
The image magnification module 30 is configured to: and carrying out space extension processing on the interpolation image based on the radial basis function Multi-Quadric to obtain the magnification, and carrying out discretization processing on the interpolation image to form an amplified image.
Optionally, the performing spatial extension processing on the interpolated image to obtain a magnification factor, and performing discretization processing on the interpolated image to form an enlarged image includes:
the magnification of the interpolation image in the x direction is set as a, the magnification in the y direction is set as b, and the curve z is set as f*(x, y) is extended in x direction by a times in equal proportion and in y direction by b times in equal proportion, and a curved surface w is obtained as g*(u, v) wherein a > 1, b > 1, g*(u, v) has the domain definition of R2To define the domain dimension, the specific solving process is as follows:
curved surface z ═ f*(x, y) at any point (x)0，y0，z0) On a curved surface w ═ g*The corresponding point on (u, v) is (u)0，v0，w0) The corresponding relationship is expressed as follows:
when any one pixel (u1, v1) in the enlarged image g (u, v) is set, the curved surface w is g*(u1, v1, w1) at point (u, v) on curved surface z ═ f*Corresponding point (x) on (x, y)1，y1，z1) The correspondence of (a) is as follows:
using said f*(x, y), finding g*(u, v), take g*(u, v) all integer points in the defined domain constitute the magnified image g (u, v), where image g (u, v) is [ aM []Line, [ bN]Column, then the value range of u, v is: u is more than or equal to 0 and less than or equal to [ aM%]-1，0≤v≤[bN]-1。
The similarity judging module 40 is configured to: and calculating Euclidean distances of gray matrixes of the original image and the amplified image, and judging the similarity of the original image and the amplified image.
The functions or operation steps of the image conversion module 10, the image interpolation module 20, the image amplification module 30, the similarity determination module 40 and other program modules implemented when executed are substantially the same as those of the above embodiments, and are not repeated herein.
Furthermore, an embodiment of the present invention further provides a computer-readable storage medium, where a radial basis function-based continuous image magnification program is stored on the computer-readable storage medium, where the radial basis function-based continuous image magnification program is executable by one or more processors to implement the following operations:
selecting an image needing to be amplified as an original image, and converting the original image into a discrete value mode for representing and storing;
performing interpolation processing on the original image based on the radial basis function to obtain an interpolation image of the original image;
and carrying out space extension processing on the interpolation image based on the radial basis function Multi-Quadric to obtain the magnification, and carrying out discretization processing on the interpolation image to form an amplified image.
The embodiment of the computer-readable storage medium of the present invention is substantially the same as the embodiments of the continuous image magnifying device and method based on radial basis function, and will not be described herein in detail.
It should be noted that the above-mentioned numbers of the embodiments of the present invention are merely for description, and do not represent the merits of the embodiments. And the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, apparatus, article, or method that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, apparatus, article, or method. The term "comprising" is used to specify the presence of stated features, integers, steps, operations, elements, components, groups, integers, operations, elements, components, groups, elements, groups, integers, operations, elements.
Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better implementation manner. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium (e.g., ROM/RAM, magnetic disk, optical disk) as described above and includes instructions for enabling a terminal device (e.g., a mobile phone, a computer, a server, or a network device) to execute the method according to the embodiments of the present invention.
The above description is only a preferred embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, which are made by using the contents of the present specification and the accompanying drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (10)
1. A continuous image amplification method based on radial basis functions is characterized by comprising the following steps:
selecting an image needing to be amplified as an original image, and converting the original image into a discrete value mode for representing and storing;
performing interpolation processing on the original image based on the radial basis function to obtain an interpolation image of the original image;
and performing space extension processing on the interpolation image based on the radial basis function to obtain a magnification ratio, and performing discretization processing on the interpolation image to form an amplified image.
2. The continuous image magnification method based on radial basis functions as claimed in claim 1, wherein the radial basis functions are Multi-Quadric functions.
3. The method as claimed in claim 2, wherein the interpolating the original image using the radial basis functions comprises:
known to be defined as [0, M-1 ]]×[0,N-1]Set of data points ofFinding an image function:
wherein, M and N represent that the original image is M rows and N columns, R is the definition domain interval of the data point set, and R is3Representing a domain data dimension, λjIn order to interpolate the conditional weights of the image,in order to be a radial basis function,
the interpolation condition is satisfied:
wherein,
for the image function f*(x, y) selecting S x S integer points around the point to be interpolated as interpolation reference points for each non-integer point in the (x, y), wherein S is specified by a user;
solving formula 1 to obtain f*(x, y) defines a function value for each point on the domain, thereby obtaining an interpolated image of the original image.
4. The method according to any one of claims 1 to 3, wherein the spatially expanding the interpolated image to obtain a magnification and discretizing the interpolated image to form an enlarged image comprises:
the magnification of the interpolation image in the x direction is set as a, the magnification in the y direction is set as b, and the curved surface z is set as f*(x, y) is extended in x direction by a times in equal proportion and in y direction by b times in equal proportion, and a curved surface w is obtained as g (u, v), wherein a is>1，b>1, g (u, v) has the domain definition of R2To define the domain dimension, the specific solving process is as follows:
curved surface z ═ f*(x, y) at any point (x)0，y0，z0) The corresponding point on the curved surface w ═ g (u, v) is (u, v)0，v0，w0) The corresponding relationship is expressed as follows:
when any one of the pixels (u1, v1) in the enlarged image g (u, v) is set, the points (u1, v1, w1) on the curved surface w (g × u, v) are f on the curved surface z*Corresponding point (x) on (x, y)1，y1，z1) The correspondence of (a) is as follows:
using said f*(x, y), finding g (u, v), and constructing an enlarged image g (u, v) by taking all integer points of g (u, v) in the definition domain, wherein the image g (u, v) is [ aM []Line, [ bN]Column, then the value range of u, v is: u is more than or equal to 0 and less than or equal to [ aM%]-1，0≤v≤[bN]-1。
5. The radial basis function based continuous image magnification method as claimed in claim 4, further comprising:
and calculating Euclidean distances of gray matrixes of the original image and the amplified image, and judging the similarity of the original image and the amplified image.
6. A radial basis function based continuous image magnifying apparatus, comprising a memory and a processor, wherein the memory stores a radial basis function based continuous image magnifying program operable on the processor, and the radial basis function based continuous image magnifying program when executed by the processor implements the following steps:
selecting an image needing to be amplified as an original image, and converting the original image into a discrete value mode for representing and storing;
performing interpolation processing on the original image based on a radial basis function Multi-Quadric to obtain an interpolation image of the original image;
and carrying out space extension processing on the interpolation image based on the radial basis function Multi-Quadric to obtain the magnification, and carrying out discretization processing on the interpolation image to form an amplified image.
7. The radial basis function-based continuous image magnification device as claimed in claim 6, wherein the interpolation processing of the original image by using the radial basis function Multi-quad comprises:
known to be defined as [0, M-1 ]]×[0,N-1]Set of data points ofFinding image functions
Wherein, M and N represent that the original image is M rows and N columns, R is the definition domain interval of the data point set, and R is3Representing a domain data dimension, λjIn order to interpolate the conditional weights of the image,in order to be a radial basis function,
the interpolation condition is satisfied:
wherein,
for the image function f*(x, y) selecting S x S integer points around the point to be interpolated as interpolation reference points for each non-integer point in the (x, y), wherein S is specified by a user;
solving formula 1 to obtain f*(x, y) defines a function value for each point on the domain, thereby obtaining an interpolated image of the original image.
8. The radial basis function-based continuous image magnifying apparatus according to claim 6 or 7, wherein the spatially expanding the interpolated image to obtain a magnification and discretizing the interpolated image to form a magnified image comprises:
the magnification of the interpolation image in the x direction is set as a, the magnification in the y direction is set as b, and the curved surface z is set as f*(x, y) is extended in x direction by a times in equal proportion and in y direction by b times in equal proportion to obtain a curved surface w ═ g (u, v),wherein, a>1，b>1, g (u, v) has the domain definition of R2To define the domain dimension, the specific solving process is as follows:
curved surface z ═ f*(x, y) at any point (x)0，y0，z0) The corresponding point on the curved surface w ═ g (u, v) is (u, v)0，v0，w0) The corresponding relationship is expressed as follows:
when any one of the pixels (u1, v1) in the enlarged image g (u, v) is set, the points (u1, v1, w1) on the curved surface w (g × u, v) are f on the curved surface z*Corresponding point (x) on (x, y)1，y1，z1) The correspondence of (a) is as follows:
using said f*(x, y), finding g (u, v), and constructing an enlarged image g (u, v) by taking all integer points of g (u, v) in the definition domain, wherein the image g (u, v) is [ aM []Line, [ bN]Column, then the value range of u, v is: u is more than or equal to 0 and less than or equal to [ aM%]-1，0≤v≤[bN]-1。
9. The radial basis function based continuous image magnifying device according to claim 7 or 8, wherein the radial basis function based continuous image magnifying program when executed by the processor further implements the steps of:
and calculating Euclidean distances of gray matrixes of the original image and the amplified image, and judging the similarity of the original image and the amplified image.
10. A computer-readable storage medium, wherein a radial basis function-based sequential image magnification program is stored on the computer-readable storage medium, and the radial basis function-based sequential image magnification program is executable by one or more processors to implement the steps of the radial basis function-based sequential image magnification method according to any one of claims 1 to 5.
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