CN103366393A

CN103366393A - Method for generating hollow embossment in combination with multiple input ways

Info

Publication number: CN103366393A
Application number: CN2013102758137A
Authority: CN
Inventors: 王美丽; 常建; 张建军
Original assignee: Northwest A&F University
Current assignee: Northwest A&F University
Priority date: 2013-06-28
Filing date: 2013-06-28
Publication date: 2013-10-23
Anticipated expiration: 2033-06-28
Also published as: CN103366393B

Abstract

The invention discloses a multi-input method for generating hollow reliefs. Starting from a three-dimensional model, the line drawing, rendering picture and depth map of the three-dimensional model are sequentially obtained, and then the final hollow relief is synthesized and generated through an optimization method. The hollow relief generation method combined with multiple input methods saves time and labor compared with traditional manual production, is easy to save and edit, and can be processed into relief objects.

Description

A Method for Generating Hollow Relief Combining Multiple Input Methods

技术领域technical field

本发明涉及计算机图形学技术领域，尤其是涉及一种结合多输入方式镂空浮雕生成方法。The invention relates to the technical field of computer graphics, in particular to a method for generating hollow reliefs combined with multiple input methods.

背景技术Background technique

数字浮雕产生技术目前可以分为基于图像的浮雕生成技术、基于直接3D建模的浮雕生成技术以及基于模型操作的浮雕生成技术。基于图像的浮雕生成技术生成的浮雕不能正确的产生浮雕高度，且不具备实际意义；基于直接3D建模的浮雕生成技术比较繁琐，一切都需要从头做起，制作大量的数字浮雕不切实际。目前还没有针对镂空浮雕的生成技术。Digital relief generation technology can be divided into image-based relief generation technology, relief generation technology based on direct 3D modeling, and relief generation technology based on model manipulation. The relief generated by the image-based relief generation technology cannot generate the relief height correctly, and has no practical significance; the relief generation technology based on direct 3D modeling is cumbersome, everything needs to be done from scratch, and it is impractical to produce a large number of digital reliefs. There are currently no generative techniques for hollow reliefs.

发明内容Contents of the invention

本发明所要解决的技术问题是：提供一种结合多输入方式镂空浮雕生成方法，较传统手工制作省时省力，而且易于保存、编辑，并且可以加工成浮雕物品。The technical problem to be solved by the present invention is to provide a method for generating hollow reliefs combined with multiple input methods, which saves time and labor compared with traditional manual production, and is easy to save and edit, and can be processed into relief objects.

为解决上述技术问题，本发明的技术方案是：一种结合多输入方式镂空浮雕生成方法，由三维模型出发，依次获取三维模型的线条图、渲染图和深度图，然后通过优化方法合成并生成最后的镂空浮雕。In order to solve the above-mentioned technical problems, the technical solution of the present invention is: a method for generating hollow reliefs combined with multiple input methods, starting from the 3D model, sequentially obtaining the line drawing, rendering picture and depth map of the 3D model, and then synthesizing and generating the three-dimensional model through an optimization method The final openwork relief.

进一步的，在获取三维模型的线条图的步骤中，包括获取轮廓线和其他线条；Further, in the step of obtaining the line drawing of the three-dimensional model, including obtaining contour lines and other lines;

轮廓线获取方法：n(p)·v＝0 (1)Contour acquisition method: n(p) v=0 (1)

p是曲面上的点，n是法线，v是观察向量，通过投影曲面可见部分到图像平面上，就可以提取轮廓线以及骨架线；p is a point on the surface, n is the normal line, and v is the observation vector. By projecting the visible part of the surface onto the image plane, the contour line and skeleton line can be extracted;

其他线条是指脊线和谷线：Other lines refer to ridges and valleys:

$w w = = \frac{v v - - ((n no ((p p)) \cdot \cdot v v)) \cdot \cdot n no ((p p))}{| | | | v v - - ((n no ((p p)) \cdot \cdot v v)) \cdot \cdot n no ((p p)) | | | |} - - - - - - ((22))$

${&dtri;}_{w} (n (p) \cdot v) = 0,$ and ${&dtri;}_{w} {&dtri;}_{w} (n (p) \cdot v) > 0 - - - (3)$ ${&dtri;}_{w} (no (p) \cdot v) = 0,$ and ${&dtri;}_{w} {&dtri;}_{w} (no (p) &Center Dot; v) > 0 - - - (3)$

K_r＝0，and ${&dtri;}_{w} K_{r} > 0 - - - (4)$ _Kr = 0, and ${&dtri;}_{w} K_{r} > 0 - - - (4)$

借助于公式(2)、(3)、(4)可以提取脊线和谷线，然而提取的线条过多，不适合最终的镂空浮雕生成，可以通过拉普拉斯算子对其进行光滑，With the help of formulas (2), (3), and (4), the ridges and valleys can be extracted. However, the extracted lines are too many and are not suitable for the final hollow relief generation. They can be smoothed by the Laplacian operator.

$L L (({x x}_{i i})) = = \frac{11}{{Σw Σw}_{ij ij}} \underset{j j &Element; &Element; N N ((i i))}{Σ Σ} {w w}_{ij ij} (({x x}_{j j} - - {x x}_{i i})) - - - - - - ((55)) . .$

进一步的，在获取三维模型的渲染图步骤中，采用兰伯特渲染图输入，兰伯特渲染图提供重要的视觉信息以生成产生镂空浮雕的高度，Further, in the step of obtaining the rendering image of the 3D model, the Lambert rendering image is used as input, and the Lambert rendering image provides important visual information to generate the height of the hollow relief,

I＝α(n(p)·m(p)) (6)。I=α(n(p) m(p)) (6).

进一步的，在获取三维模型的深度图步骤中，三维模型可以提供高度信息。Further, in the step of acquiring the depth map of the 3D model, the 3D model can provide height information.

进一步的，权利要求2-4中所述的三种获取均由同一视点和同一投影平面获得，定义浮雕网格的像素值为其四个邻居像素的平均值，Further, the three acquisitions described in claims 2-4 are all obtained from the same viewpoint and the same projection plane, and the pixel value of the defined relief grid is the average value of its four neighbor pixels,

$I I ((x x,, y the y)) = = \frac{11}{44} ((I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})) + + I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})) + + I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) + + I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})))) - - - - - - ((77))$

其梯度由公式(8)求得Its gradient is obtained by formula (8)

$&dtri; &dtri; I I = = (\begin{matrix} \frac{&PartialD; &PartialD; I I ((x x,, y the y))}{&PartialD; &PartialD; \underset{\cdot &Center Dot;}{x x}} \\ \frac{&PartialD; &PartialD; I I ((x x,, y the y))}{&PartialD; &PartialD; y the y} \end{matrix}) - - - - - - ((88));;$

$= = (\begin{matrix} \frac{11}{22} ((I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) + + I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})))) \\ \frac{11}{22} ((I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})) + + I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})) - - I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})))) \end{matrix})$

公式(7)、(8)结合后面的公式重建镂空浮雕的表面；Formulas (7), (8) reconstruct the surface of the hollow relief in conjunction with the following formulas;

首先通过线条输入方程获取线条图，First get the line plot by entering the equation with the line,

${E E.}_{w w} = = {Σ Σ}_{x x = = 11}^{m m - - 11} {Σ Σ}_{y the y = = 11}^{n no - - 11} S S ((x x,, y the y)) {((\frac{11}{22} ((I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) + + I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})))) - - G G ((\frac{{&PartialD; &PartialD; I I}_{w w}}{&PartialD; &PartialD; x x}))))}^{22}$

$+ + {Σ Σ}_{x x = = 11}^{m m - - 11} {Σ Σ}_{y the y = = 11}^{n no - - 11} S S ((x x,, y the y)) {((\frac{11}{22} ((I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})) + + I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})) - - I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})))) - - G G ((\frac{{&PartialD; &PartialD; I I}_{w w}}{&PartialD; &PartialD; y the y}))))}^{22} - - - - - - ((99))$

再通过兰伯特渲染图方程获取渲染图，Then obtain the rendering image through the Lambert rendering image equation,

${E E.}_{L L} = = {Σ Σ}_{x x = = 11}^{m m - - 11} {Σ Σ}_{y the y = = 11}^{n no - - 11} {((\frac{11}{22} ((I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) + + I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})))) - - G G ((\frac{{&PartialD; &PartialD; I I}_{L L}}{&PartialD; &PartialD; x x}))))}^{22}$

$+ + {Σ Σ}_{x x = = 11}^{m m - - 11} {Σ Σ}_{y the y = = 11}^{n no - - 11} {((\frac{11}{22} ((I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})) + + I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})) - - I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})))) - - G G ((\frac{{&PartialD; &PartialD; I I}_{L L}}{&PartialD; &PartialD; x x}))))}^{22} - - - - - - ((1010))$

然后通过深度方程获取深度图，Then the depth map is obtained by the depth equation,

${E E.}_{d d} = = {Σ Σ}_{x x = = 22}^{m m - - 11} {Σ Σ}_{y the y = = 22}^{n no - - 11} {(\begin{matrix} h h ((x x + + 11,, y the y)) + + h h ((x x - - 11,, y the y)) + + h h ((x x,, y the y + + 11)) \\ + + h h ((x x,, y the y - - 11)) - - 44 h h ((x x,, y the y)) - - g g ((x x,, y the y)) \end{matrix})}^{22} - - - - - - ((1111))$

最后通过能量减小优化法合成镂空浮雕，Finally, the hollow relief is synthesized by the energy reduction optimization method,

W＝w_dE_d+w_LE_L+w_wE_w (12)W＝w _d E _d +w _L E _L +w _w E _w (12)

约束条件： $\underset{h}{\min n} E (h)$ Restrictions: $\underset{h}{\min no} E. (h)$

s.t.h＜0，-h＜h_max (13)sth<0, -h<h _max (13)

求解：Solve:

${E E.}_{h h} = = {Σ Σ}_{x x = = 11}^{m m} {Σ Σ}_{y the y = = 11}^{n no} {((h h ((x x,, y the y)) - - {h h}^{* *}))}^{22} - - - - - - ((1414))$

其中h^*＝-θlog(1-θh(x，y))，θ控制压缩程度where h ^* = -θlog(1-θh(x,y)), θ controls the degree of compression

采用了上述技术方案，本发明的有益效果为：Adopt above-mentioned technical scheme, the beneficial effect of the present invention is:

本发明的创新性在于首次提出提取三维模型的线条图作为生成镂空浮雕的首要任务，提取的线条图可以生成镂空浮雕的轮廓，然而为了实现浮雕之间的平滑过渡，同时提取三维模型的渲染图和高度图。结合基于能量最小的优化算法生成最终的三维镂空浮雕。基于三维模型的镂空浮雕生成方法较传统手工制作省时省力，而且易于保存、编辑，并且可以加工成浮雕物品。The innovation of the present invention lies in that it is the first time to propose to extract the line drawing of the three-dimensional model as the primary task of generating the hollow relief. The extracted line drawing can generate the outline of the hollow relief. However, in order to realize the smooth transition between the reliefs, the rendering of the three-dimensional model is extracted at the same time. and a heightmap. Combined with an optimization algorithm based on energy minimization to generate the final 3D hollow relief. The method of hollow relief generation based on 3D model saves time and effort compared with traditional manual production, and is easy to save and edit, and can be processed into relief objects.

附图说明Description of drawings

图1是本发明实施例的镂空浮雕生成原理图；Fig. 1 is the schematic diagram of the generation of the hollow relief of the embodiment of the present invention;

图2是本发明实施例的镂空浮雕曲面的像素示意图；Fig. 2 is a pixel schematic diagram of a hollow relief curved surface according to an embodiment of the present invention;

图3(a)、(b)、(c)、(d)分别是本发明实施例的镂空浮雕效果图，其中左侧为输入三维模型，右侧为生成的镂空浮雕模型；Fig. 3 (a), (b), (c), (d) are respectively the hollow relief renderings of the embodiment of the present invention, wherein the left side is the input three-dimensional model, and the right side is the generated hollow relief model;

具体实施方式Detailed ways

下面结合附图和实施例对本发明进一步说明。The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

如图1、图2和图3共同所示，一种结合多输入方式镂空浮雕生成方法，由三维模型出发，依次获取三维模型的线条图、渲染图和深度图，然后通过优化方法合成并生成最后的镂空浮雕。本发明的创新性在于首次提出提取三维模型的线条图作为生成镂空浮雕的首要任务，提取的线条图可以生成镂空浮雕的轮廓，然而为了实现浮雕之间的平滑过渡，同时提取三维模型的渲染图和高度图。结合基于能量最小的优化算法生成最终的三维镂空浮雕。As shown in Fig. 1, Fig. 2 and Fig. 3 together, a method for generating hollowed-out reliefs combined with multiple input methods starts from the 3D model and sequentially obtains the line drawing, rendering picture and depth map of the 3D model, and then synthesizes and generates them through an optimization method The final openwork relief. The innovation of the present invention lies in that it is the first time to propose to extract the line drawing of the three-dimensional model as the primary task of generating the hollow relief. The extracted line drawing can generate the outline of the hollow relief. However, in order to realize the smooth transition between the reliefs, the rendering of the three-dimensional model is extracted at the same time. and a heightmap. Combined with an optimization algorithm based on energy minimization to generate the final 3D hollow relief.

在获取三维模型的线条图的步骤中，包括获取轮廓线和其他线条；In the step of obtaining the line drawing of the three-dimensional model, including obtaining contour lines and other lines;

轮廓线获取方法：n(p)·v＝0 (1)Contour acquisition method: n(p) v=0 (1)

其他线条是指脊线和谷线：Other lines refer to ridges and valleys:

$w w = = \frac{v v - - ((n no ((p p)) \cdot &Center Dot; v v)) \cdot &Center Dot; n no ((p p))}{| | | | v v - - ((n no ((p p)) \cdot &Center Dot; v v)) \cdot &Center Dot; n no ((p p)) | | | |} - - - - - - ((22))$

${&dtri;}_{w} (n (p) \cdot v) = 0,$ and ${&dtri;}_{w} {&dtri;}_{w} (n (p) \cdot v) > 0 - - - (3)$ ${&dtri;}_{w} (no (p) &Center Dot; v) = 0,$ and ${&dtri;}_{w} {&dtri;}_{w} (no (p) \cdot v) > 0 - - - (3)$

在获取三维模型的渲染图步骤中，采用兰伯特渲染图输入，兰伯特渲染图提供重要的视觉信息以生成产生镂空浮雕的高度，In the step of obtaining the rendering of the 3D model, the Lambert rendering is used as input, and the Lambert rendering provides important visual information to generate the height of the hollow relief,

I＝α(n(p)·m(p)) (6)。I=α(n(p) m(p)) (6).

在获取三维模型的深度图步骤中，三维模型可以提供高度信息。In the step of obtaining the depth map of the 3D model, the 3D model can provide height information.

上述的三种获取均由同一视点和同一投影平面获得，定义浮雕网格的像素值为其四个邻居像素的平均值，The above three acquisitions are obtained from the same viewpoint and the same projection plane, and the pixel value of the defined relief grid is the average value of its four neighbor pixels,

其梯度由公式(8)求得Its gradient is obtained by formula (8)

最后通过能量减小优化法合成镂空浮雕，Finally, the hollow relief is synthesized through the energy reduction optimization method,

W＝w_dE_d+w_LE_L+w_wE_w (12)W＝w _d E _d +w _L E _L +w _w E _w (12)

约束条件： $\min_{h} E (h)$ Restrictions: $\min_{h} E. (h)$

s.f.h＜0，-h＜h_max (13)sfh<0, -h<h _max (13)

求解：Solve:

综上所述，基于三维模型的镂空浮雕生成方法较传统手工制作省时省力，而且易于保存、编辑，并且可以加工成浮雕物品。To sum up, the method of hollow relief generation based on 3D model saves time and effort compared with traditional manual production, and is easy to save and edit, and can be processed into relief objects.

本发明不局限于上述具体的实施方式，本领域的普通技术人员从上述构思出发，不经过创造性的劳动，所作出的种种变换，均落在本发明的保护范围之内。The present invention is not limited to the above-mentioned specific implementation manners, and various transformations made by those skilled in the art starting from the above-mentioned concept without creative work all fall within the protection scope of the present invention.

Claims

1. A hollow relief generation method in combination with multiple input modes, characterized in that, starting from a three-dimensional model, sequentially obtain line drawings, rendering images and depth maps of the three-dimensional model, then synthesize and generate the final hollow relief by an optimization method.

2. A kind of hollow out relief generation method in conjunction with multi-input mode as claimed in claim 1, is characterized in that, in the step of obtaining the line drawing of three-dimensional model, comprises obtaining contour line and other lines;

Contour acquisition method: n(p) v=0 (1)

p is a point on the surface, n is the normal line, and v is the observation vector. By projecting the visible part of the surface onto the image plane, the contour line and skeleton line can be extracted;

Other lines refer to ridges and valleys:

w w = = \frac{v v - - ((n no ((p p)) \cdot \cdot v v)) \cdot \cdot n no ((p p))}{| | | | v v - - ((n no ((p p)) \cdot \cdot v v)) \cdot \cdot n no ((p p)) | | | |} - - - - - - ((22))

{&dtri;}_{w} (no (p) \cdot v) = 0,

and

{&dtri;}_{w} {&dtri;}_{w} (no (p) &Center Dot; v) > 0 - - - (3)

_Kr = 0, and

{&dtri;}_{w} K_{r} > 0 - - - (4)

With the help of formulas (2), (3), and (4), the ridges and valleys can be extracted. However, the extracted lines are too many and are not suitable for the final hollow relief generation. They can be smoothed by the Laplacian operator.

L L (({x x}_{i i})) = = \frac{11}{{Σw Σw}_{ij ij}} \underset{j j &Element; &Element; N N ((i i))}{Σ Σ} {w w}_{ij ij} (({x x}_{j j} - - {x x}_{i i})) - - - - - - ((55)) . .

3. a kind of hollow relief generation method in conjunction with multi-input mode as claimed in claim 1, is characterized in that, in the rendering step of obtaining three-dimensional model, adopts Lambert's rendering input, and Lambert's rendering provides important visual information to generate the height of the openwork relief,

I=α(n(p) m(p)) (6).

4. A method for generating hollow reliefs combined with multiple input methods according to claim 1, characterized in that, in the step of obtaining the depth map of the 3D model, the 3D model can provide height information.

5. a kind of hollow out relief generation method in conjunction with multi-input mode as claimed in claim 1, is characterized in that, three kinds of acquisitions described in claim 2-4 are all obtained by same viewpoint and same projection plane, define relief network The pixel value of the grid is the average value of its four neighbor pixels,

I I ((x x,, y the y)) = = \frac{11}{44} ((I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})) + + I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})) + + I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) + + I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})))) - - - - - - ((77))

Its gradient is obtained by formula (8)

&dtri; &dtri; I I = = (\begin{matrix} \frac{&PartialD; &PartialD; I I ((x x,, y the y))}{&PartialD; &PartialD; \underset{\cdot &Center Dot;}{x x}} \\ \frac{&PartialD; &PartialD; I I ((x x,, y the y))}{&PartialD; &PartialD; y the y} \end{matrix}) - - - - - - ((88));;

= = (\begin{matrix} \frac{11}{22} ((I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) + + I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})))) \\ \frac{11}{22} ((I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})) + + I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})) - - I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})))) \end{matrix})

Formulas (7), (8) reconstruct the surface of the hollow relief in conjunction with the following formulas;

First get the line plot by entering the equation with the line,

{E E.}_{w w} = = {Σ Σ}_{x x = = 11}^{m m - - 11} {Σ Σ}_{y the y = = 11}^{n no - - 11} S S ((x x,, y the y)) {((\frac{11}{22} ((I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) + + I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})))) - - G G ((\frac{{&PartialD; &PartialD; I I}_{w w}}{&PartialD; &PartialD; x x}))))}^{22}

+ + {Σ Σ}_{x x = = 11}^{m m - - 11} {Σ Σ}_{y the y = = 11}^{n no - - 11} S S ((x x,, y the y)) {((\frac{11}{22} ((I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})) + + I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})) - - I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})))) - - G G ((\frac{{&PartialD; &PartialD; I I}_{w w}}{&PartialD; &PartialD; y the y}))))}^{22} - - - - - - ((99))

Then obtain the rendering image through the Lambert rendering image equation,

{E E.}_{L L} = = {Σ Σ}_{x x = = 11}^{m m - - 11} {Σ Σ}_{y the y = = 11}^{n no - - 11} {((\frac{11}{22} ((I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) + + I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})))) - - G G ((\frac{{&PartialD; &PartialD; I I}_{L L}}{&PartialD; &PartialD; x x}))))}^{22}

+ + {Σ Σ}_{x x = = 11}^{m m - - 11} {Σ Σ}_{y the y = = 11}^{n no - - 11} {((\frac{11}{22} ((I I ((x x + + \frac{11}{22},, y the y + + \frac{11}{22})) + + I I ((x x - - \frac{11}{22},, y the y + + \frac{11}{22})) - - I I ((x x + + \frac{11}{22},, y the y - - \frac{11}{22})) - - I I ((x x - - \frac{11}{22},, y the y - - \frac{11}{22})))) - - G G ((\frac{{&PartialD; &PartialD; I I}_{L L}}{&PartialD; &PartialD; x x}))))}^{22} - - - - - - ((1010))

Then the depth map is obtained by the depth equation,

{E.}_{d} = Σ_{x = 2}^{m - 1} Σ_{the y = 2}^{no - 1} {(\begin{matrix} h (x + 1, the y) + h (x - 1, the y) + h (x, the y + 1) \\ + h (x, the y - 1) - 4 h (x, the y) - g (x, the y) \end{matrix})}^{2} . - - - (11)

Finally, the hollow relief is synthesized by the energy reduction optimization method,

E＝w _d E _d +w _L EL+w _w E _w (12)

Restrictions:

\min_{h} E. (h)

sth<0, -h<h _max (13)

Solve:

{E E.}_{h h} = = {Σ Σ}_{x x = = 11}^{m m} {Σ Σ}_{y the y = = 11}^{n no} {((h h ((x x,, y the y)) - - {h h}^{* *}))}^{22} - - - - - - ((1414))

where h ^* =-θlog(1-θh(x,y)), θ controls the degree of compression.