基于三角网格的图像表示方法研究
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摘要
图像表示方法在计算机图形学、图像处理、模式识别等研究等领域内具有重要的研究意义。图像的三角网格表示模型借助于计算几何中的三角化思想，能有效地对图像进行表示，而且其结果可用于视频通信、三维重建等领域。
将计算几何中的三角形化方法用于图像的三角网格表示，研究了三种图像三角化的算法。
基于边界特征点的初始三角网格生成算法(CPBT算法)利用Soble算子提取边界特征点，然后采用改进的Lawson算法生成初始的DT网格。CPBT算法提取的特征点数约比四元树算法减少了13．6％，比FAACA算法减少了14．5％；重建图像的质量略低于FAACA算法，高于四元树算法。
基于多边形划分的三角网格生成算法(PPBT算法)首先利用区域搜索算法找到若干多边形区域，将图像划分为若干个多边形；然后将多边形进行三角剖分即可得到图像的三角网格。PPBT算法在CPBT的基础上将顶点数P减少了5％-13％，PSNR则提高了2％-8％。
基于灰度分布的三角网格生成算法(GDBT算法)利用小波多阶变换将图像进行矩形分块，每一块根据图像的灰度分布用四种初始三角形划分进行表示；然后根据相邻块的不同情况将初始三角划分网格化，得到一个初始的三角网格；最后进行细分。从实验结果看，在重建图像质量达到30左右时，GDBT算法得到的三角网格规模略高于WBT算法；但GDBT算法的计算复杂程度明显低于WBT算法。另外，其没有打破矩形子块的分割方式使其便于进行存储优化，也比较利于进行并行计算。
综合考虑灰度误差极小化准则和灰度误差均匀化准则设计了一种三角网格的细化算法。算法对初始网格进行反复细化，随着迭代的进行和三角形的个数不断增加，每个三角形面积不断减小，三角形会不断逼近图像，直到满足准则，迭代停止。但细化得到的三角网格可能会出现一些比较狭长或面积很小的三角形，针对这些问题研究了一种三角网格的优化算法。
对三角形网格的存储进行了研究，给出了两种基本的存储方法，并针对基于图像灰度分布的表示方法研究了一种记录稀疏网格和生成规则的三角网格数据结构，取得了很好的压缩效果。重建时只要利用生成规则即可得到细分三角网格的数据，然后再利用本文提出的平面插值方法进行重建即可。实验数据表明在采用优化方法进行存储后，与原存储方式相比压缩比可以达到4．5左右，与原始图像相比可以取得2至4的压缩比，而且压缩以后并不会破坏其重建图像的质量，重建图像的PSNR仍能达到35左右。这种方法对有效减少三角网格的数据量十分有效。
以优化存储结构为基础，对视频中连续多帧图像进行了前向跟踪分析，研究了一种多帧压缩和重建算法。实验结果表明，采用这种方法存储后，连续8帧的压缩比能达到3左右。如果采用根据初始网格差异提取细分网格差异的多帧压缩算法，8帧的压缩比提高到14，这一结果证明这种多帧压缩算法具有较好的应用前景。
研究了一种采用平面插值进行图像重建的方法，该方法可以利用三角形三个顶点的灰度值自动计算三角形内部任意点的灰度值，这种方法重建的图像效果明显好于内部所有的点采用同一灰度值的方法，可以有效提高重建图像的主客观质量。
对基于本文图像三角网格表示的立体造型算法进行研究，以人脸作为研究对象，实现了利用单幅图像进行人脸面部的三维重建。
理论分析和试验结果表明，图像的三角网格表示方法能有效支持图像表示、三维重建和视频压缩。
Image representation is an important issue is computer graphics, image processing, pattern recognition. Based on computational geometry of the triangle, triangular mesh represention model of image is efficient to represent image, which has great use in video communication, three dimentional reconstruction and so on.
With respect to the triangular method in computational geometry, three triangulation approaches of image are proposed.
Referring to the idea of contour extraction, characteristic points of image border can be extracted by use of Soble operator, Denauley triangular mesh can be initialized with improved Lawson algorithm .Compared with quadtree and FAACA approaches, the number of characteristic points of CPBT approach decreases by 13.6% and 14.5% respectively. The noise ratio of reconstructed image is lese than FAACA and more then quadtree.
Considerd with the partition of area, an image can be divided into a number of polygonal regions, and then each polygon carry can be triangulated, thus an image is represented by a triangular mesh. Compared with CPBT approach, the numbers of vertex of PPBT goes down 5%-13% and the noise ration(PSNR) increases 2%~8%.
With respect to the distributing of gray scale, first of all, the image is divided to rectangles with multi-stage wavelet transform. Each rectangle can be to respresented by four initiail regular triangle templates. Then the trianguation partition can be transformed into initial triangulate mesh. The initial triangulate mesh can be divided ulteriorly. The experiment indicates that the size of triangulate mesh is a little larger than WBT, but its complexity is less than WBT distinctly. In addition, regular rectangle block can be in favor of space refinement and parallel computation.
A technique on refinement of original triangular mesh which apply to the above three methods is devised. This algorithm considers both small errors and homogenization errors of gray scale on the initial of grid. That is, if the maximum absolute error is less than or equal to pre-given gate threshold, the iteration will stop; Otherwise, the maximum absolute error location is priority to the new iteration.
Two basic methods of triangular mesh storage and advanced a data structure are introduced, which records sparse grids and generated rules, and made a good compression results. This method records the spare grid and sub-point sequence formed by initial triangular mesh. In the reconstruction we can get refinement triangular mesh data from generating rules and by plane interpolated methods.The experiments shows that the compress ratio of refinement approach is 4.5 times and 2-4 times to original approach and original image respectively. The noise ratio(PSNR) of reconstructed image is 35. It is obvious that the approach can reduce storage space effiently.
Based on the optimized storage approach, the continious frames are analyzed, then a compress method of multi-frame is proposed. The experiment result indicates that the compress ratio of contimuious 8 frames can be 3. Considered with the initial triangular mesh, the compress ratio can increase to 14. The result can prove that the multi-frame compress algorithm has good applicated foreground.
A method of image reconstruction by plane interpolation is put forward. This method used the gray value of the triangle vertices to automatically calculate the gray value at any point within it and significantly shows better results than that all the points inside have the same gray value.
Based on the image of triangular mesh, with the human face for the study object,the research of three-dimensional reconstruction is touched upon.
From the theoretical analysis and the experimental results, the image represention model based on triangular mesh is capable of supporting image represention,three dimentional reconstruction and video compression.
将计算几何中的三角形化方法用于图像的三角网格表示，研究了三种图像三角化的算法。
基于边界特征点的初始三角网格生成算法(CPBT算法)利用Soble算子提取边界特征点，然后采用改进的Lawson算法生成初始的DT网格。CPBT算法提取的特征点数约比四元树算法减少了13．6％，比FAACA算法减少了14．5％；重建图像的质量略低于FAACA算法，高于四元树算法。
基于多边形划分的三角网格生成算法(PPBT算法)首先利用区域搜索算法找到若干多边形区域，将图像划分为若干个多边形；然后将多边形进行三角剖分即可得到图像的三角网格。PPBT算法在CPBT的基础上将顶点数P减少了5％-13％，PSNR则提高了2％-8％。
基于灰度分布的三角网格生成算法(GDBT算法)利用小波多阶变换将图像进行矩形分块，每一块根据图像的灰度分布用四种初始三角形划分进行表示；然后根据相邻块的不同情况将初始三角划分网格化，得到一个初始的三角网格；最后进行细分。从实验结果看，在重建图像质量达到30左右时，GDBT算法得到的三角网格规模略高于WBT算法；但GDBT算法的计算复杂程度明显低于WBT算法。另外，其没有打破矩形子块的分割方式使其便于进行存储优化，也比较利于进行并行计算。
综合考虑灰度误差极小化准则和灰度误差均匀化准则设计了一种三角网格的细化算法。算法对初始网格进行反复细化，随着迭代的进行和三角形的个数不断增加，每个三角形面积不断减小，三角形会不断逼近图像，直到满足准则，迭代停止。但细化得到的三角网格可能会出现一些比较狭长或面积很小的三角形，针对这些问题研究了一种三角网格的优化算法。
对三角形网格的存储进行了研究，给出了两种基本的存储方法，并针对基于图像灰度分布的表示方法研究了一种记录稀疏网格和生成规则的三角网格数据结构，取得了很好的压缩效果。重建时只要利用生成规则即可得到细分三角网格的数据，然后再利用本文提出的平面插值方法进行重建即可。实验数据表明在采用优化方法进行存储后，与原存储方式相比压缩比可以达到4．5左右，与原始图像相比可以取得2至4的压缩比，而且压缩以后并不会破坏其重建图像的质量，重建图像的PSNR仍能达到35左右。这种方法对有效减少三角网格的数据量十分有效。
以优化存储结构为基础，对视频中连续多帧图像进行了前向跟踪分析，研究了一种多帧压缩和重建算法。实验结果表明，采用这种方法存储后，连续8帧的压缩比能达到3左右。如果采用根据初始网格差异提取细分网格差异的多帧压缩算法，8帧的压缩比提高到14，这一结果证明这种多帧压缩算法具有较好的应用前景。
研究了一种采用平面插值进行图像重建的方法，该方法可以利用三角形三个顶点的灰度值自动计算三角形内部任意点的灰度值，这种方法重建的图像效果明显好于内部所有的点采用同一灰度值的方法，可以有效提高重建图像的主客观质量。
对基于本文图像三角网格表示的立体造型算法进行研究，以人脸作为研究对象，实现了利用单幅图像进行人脸面部的三维重建。
理论分析和试验结果表明，图像的三角网格表示方法能有效支持图像表示、三维重建和视频压缩。
Image representation is an important issue is computer graphics, image processing, pattern recognition. Based on computational geometry of the triangle, triangular mesh represention model of image is efficient to represent image, which has great use in video communication, three dimentional reconstruction and so on.
With respect to the triangular method in computational geometry, three triangulation approaches of image are proposed.
Referring to the idea of contour extraction, characteristic points of image border can be extracted by use of Soble operator, Denauley triangular mesh can be initialized with improved Lawson algorithm .Compared with quadtree and FAACA approaches, the number of characteristic points of CPBT approach decreases by 13.6% and 14.5% respectively. The noise ratio of reconstructed image is lese than FAACA and more then quadtree.
Considerd with the partition of area, an image can be divided into a number of polygonal regions, and then each polygon carry can be triangulated, thus an image is represented by a triangular mesh. Compared with CPBT approach, the numbers of vertex of PPBT goes down 5%-13% and the noise ration(PSNR) increases 2%~8%.
With respect to the distributing of gray scale, first of all, the image is divided to rectangles with multi-stage wavelet transform. Each rectangle can be to respresented by four initiail regular triangle templates. Then the trianguation partition can be transformed into initial triangulate mesh. The initial triangulate mesh can be divided ulteriorly. The experiment indicates that the size of triangulate mesh is a little larger than WBT, but its complexity is less than WBT distinctly. In addition, regular rectangle block can be in favor of space refinement and parallel computation.
A technique on refinement of original triangular mesh which apply to the above three methods is devised. This algorithm considers both small errors and homogenization errors of gray scale on the initial of grid. That is, if the maximum absolute error is less than or equal to pre-given gate threshold, the iteration will stop; Otherwise, the maximum absolute error location is priority to the new iteration.
Two basic methods of triangular mesh storage and advanced a data structure are introduced, which records sparse grids and generated rules, and made a good compression results. This method records the spare grid and sub-point sequence formed by initial triangular mesh. In the reconstruction we can get refinement triangular mesh data from generating rules and by plane interpolated methods.The experiments shows that the compress ratio of refinement approach is 4.5 times and 2-4 times to original approach and original image respectively. The noise ratio(PSNR) of reconstructed image is 35. It is obvious that the approach can reduce storage space effiently.
Based on the optimized storage approach, the continious frames are analyzed, then a compress method of multi-frame is proposed. The experiment result indicates that the compress ratio of contimuious 8 frames can be 3. Considered with the initial triangular mesh, the compress ratio can increase to 14. The result can prove that the multi-frame compress algorithm has good applicated foreground.
A method of image reconstruction by plane interpolation is put forward. This method used the gray value of the triangle vertices to automatically calculate the gray value at any point within it and significantly shows better results than that all the points inside have the same gray value.
Based on the image of triangular mesh, with the human face for the study object,the research of three-dimensional reconstruction is touched upon.
From the theoretical analysis and the experimental results, the image represention model based on triangular mesh is capable of supporting image represention,three dimentional reconstruction and video compression.
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