纹理映射、合成与替换算法研究
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摘要
纹理指包含一定重复模式又呈现一定随机性的事件，它可以描述自然界中非常广阔的自然现象，例如：声音、图像、视频、运动及几何曲面等等。图形学中的纹理主要指位图图像。采用纹理可以有效表现景物表面的细节特征，增强绘制的真实感。由于纹理技术在影视娱乐、工业设计和虚拟仿真等方面的广泛应用，关于纹理的研究一直是计算机图形学、计算机视觉以及图像处理领域的研究热点。
本文围绕当前纹理研究中的若干热点问题：约束纹理映射、三维纹理合成、图像和视频的纹理替换及纹理技术在非真实感绘制中的应用等方面展开研究：
(1)约束纹理映射。纹理映射一般指将二维纹理映射到三维景物表面的过程。可以有效地表现景物表面的纹理细节，提高景物绘制的真实感。本文提出一种基于调和映射的约束纹理映射方法，利用调和映射建立纹理平面和参数化后网格模型的对应关系，给出约束纹理映射问题的一个解析解。由于调和映射具有保持映射能量最小的性质，该方法可以最小化约束纹理映射可能导致的扭曲形变。同时我们还提出一种对映射效果实时优化的算法，有效减少了约束纹理映射的后期交互。
纹理映射的有效性是约束纹理映射的一个关键问题。本文提出一种基于分块映射的方法，把纹理图像和网格模型按照特征点进行有效剖分并建立对应关系，实现对应的映射，保持了纹理映射这个特殊参数化问题的有效性。由于该方法不需要对网格模型预先参数化，从而提高了纹理映射的效率。同样的思想应用于网格模型的形状过渡也取得了良好的效果。
(2)三维纹理合成。纹理合成指由一张给定小样本纹理生成大区域纹理的过程。本文提出一种在复杂网格模型表面生成纹理的算法。该算首先建立网格模型的基网格表示，在基网格上合成纹理，然后把合成效果映射回原始网格；在网格模型上建立的基网格可以应用于不同纹理的合成。本文还提出一种对三角形网格的附加纹理图像压缩存储的方法，节约了纹理内存。通过对纹理图像上任意点的邻域预处理编码的方法，进一步提高了合成效率。
(3)图像和视频的纹理替换。纹理替换指在图像／视频的目标区域采用新的纹理替换原有纹理，在未知原始几何和光源信息的情况下，使替换后目标区域保持原纹理依附在表面上产生的自然变形和光照效果。纹理替换在虚拟展示、影视娱乐等方面有巨大的应用前景。本文通过求解Possion方程保持替换后纹理的依附变形，通过把RGB颜色空间转换到YCbCr颜色空间以及传递Y颜色分量，保持了原纹理的光照效果。
Texture means the thing with repetitive patterns and stochastic attribute. It can describe a wide variety of natural phenomena, such as sound, image, video, motion, surface geometry and so on. Texture in computer graphics generally refers to bitmap image. By means of texture technique, it can simulate efficiently the geometry details of the rendered scene, and meanwhile enhance the visual richness. For the wide applications in TV and file producing, digital entertainment, industrial design and virtual simulation, etc., the research on texture has been one of the hottest topics in computer graphic, vision and image processing.
In this thesis, some key problems in texture technique: texture mapping, texture synthesis, texture replacement and its application in Non-photo realistic (NPR) rendering are explored, and some new approaches are proposed:
(1) Constrained texture mapping. Texture mapping is the process of mapping an image onto the 3D model, it can enrich effectively the reality of the rendered scene. This thesis develops a novel constrained texture mapping method based harmonic maps. It constructs the one-to-one correspondence between each point on the embedded meshes and the one on the texture plane, and gives an analytical solution to this problem. The energy minimization characteristic of the harmonic map preserves the low distortion that may yield in the process of texture mapping. Additionally, a real-time optimization algorithm is introduced for reducing the interaction of constrained texture mapping.
The validity of constrained texture mapping is an important issue, this paper introduces a "divide-and-conquer" method that can ensure its validity. The method divides the texture plane as well as the mesh model into corresponding patches based on the specified feature points, and realizes the mapping for each pair of patches. As the pre-process of parametrization is abandoned, the method is executed with high efficiency. The similar idea can be extended to mesh metamorphosis.
(2) 3D texture synthesis. Given a texture sample, texture synthesis generates a big size texture that has the similar appearance with the sample. This thesis presents a fast 3D texture synthesis method based on base domain mapping. It first synthesizes texture on the based domain of the input model, which is built adaptively, then maps the result
本文围绕当前纹理研究中的若干热点问题：约束纹理映射、三维纹理合成、图像和视频的纹理替换及纹理技术在非真实感绘制中的应用等方面展开研究：
(1)约束纹理映射。纹理映射一般指将二维纹理映射到三维景物表面的过程。可以有效地表现景物表面的纹理细节，提高景物绘制的真实感。本文提出一种基于调和映射的约束纹理映射方法，利用调和映射建立纹理平面和参数化后网格模型的对应关系，给出约束纹理映射问题的一个解析解。由于调和映射具有保持映射能量最小的性质，该方法可以最小化约束纹理映射可能导致的扭曲形变。同时我们还提出一种对映射效果实时优化的算法，有效减少了约束纹理映射的后期交互。
纹理映射的有效性是约束纹理映射的一个关键问题。本文提出一种基于分块映射的方法，把纹理图像和网格模型按照特征点进行有效剖分并建立对应关系，实现对应的映射，保持了纹理映射这个特殊参数化问题的有效性。由于该方法不需要对网格模型预先参数化，从而提高了纹理映射的效率。同样的思想应用于网格模型的形状过渡也取得了良好的效果。
(2)三维纹理合成。纹理合成指由一张给定小样本纹理生成大区域纹理的过程。本文提出一种在复杂网格模型表面生成纹理的算法。该算首先建立网格模型的基网格表示，在基网格上合成纹理，然后把合成效果映射回原始网格；在网格模型上建立的基网格可以应用于不同纹理的合成。本文还提出一种对三角形网格的附加纹理图像压缩存储的方法，节约了纹理内存。通过对纹理图像上任意点的邻域预处理编码的方法，进一步提高了合成效率。
(3)图像和视频的纹理替换。纹理替换指在图像／视频的目标区域采用新的纹理替换原有纹理，在未知原始几何和光源信息的情况下，使替换后目标区域保持原纹理依附在表面上产生的自然变形和光照效果。纹理替换在虚拟展示、影视娱乐等方面有巨大的应用前景。本文通过求解Possion方程保持替换后纹理的依附变形，通过把RGB颜色空间转换到YCbCr颜色空间以及传递Y颜色分量，保持了原纹理的光照效果。
Texture means the thing with repetitive patterns and stochastic attribute. It can describe a wide variety of natural phenomena, such as sound, image, video, motion, surface geometry and so on. Texture in computer graphics generally refers to bitmap image. By means of texture technique, it can simulate efficiently the geometry details of the rendered scene, and meanwhile enhance the visual richness. For the wide applications in TV and file producing, digital entertainment, industrial design and virtual simulation, etc., the research on texture has been one of the hottest topics in computer graphic, vision and image processing.
In this thesis, some key problems in texture technique: texture mapping, texture synthesis, texture replacement and its application in Non-photo realistic (NPR) rendering are explored, and some new approaches are proposed:
(1) Constrained texture mapping. Texture mapping is the process of mapping an image onto the 3D model, it can enrich effectively the reality of the rendered scene. This thesis develops a novel constrained texture mapping method based harmonic maps. It constructs the one-to-one correspondence between each point on the embedded meshes and the one on the texture plane, and gives an analytical solution to this problem. The energy minimization characteristic of the harmonic map preserves the low distortion that may yield in the process of texture mapping. Additionally, a real-time optimization algorithm is introduced for reducing the interaction of constrained texture mapping.
The validity of constrained texture mapping is an important issue, this paper introduces a "divide-and-conquer" method that can ensure its validity. The method divides the texture plane as well as the mesh model into corresponding patches based on the specified feature points, and realizes the mapping for each pair of patches. As the pre-process of parametrization is abandoned, the method is executed with high efficiency. The similar idea can be extended to mesh metamorphosis.
(2) 3D texture synthesis. Given a texture sample, texture synthesis generates a big size texture that has the similar appearance with the sample. This thesis presents a fast 3D texture synthesis method based on base domain mapping. It first synthesizes texture on the based domain of the input model, which is built adaptively, then maps the result
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