移动最小二乘图像变形方法研究
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摘要
图像变形是一种基于变形控制特征,根据一定的变形函数生成平滑、具有真实感的变形效果的图像处理技术。该技术可以被广泛应用在虚拟现实、计算机动画、医学图像处理以及影视娱乐等各个领域。本文对基于特征曲线及移动最小二乘优化方法的图像变形技术进行了研究。
研究了基于控制点的移动最小二乘图像变形方法。首先分析了基于控制点的移动最小二乘图像变形方法的数学模型,根据变形需要设置特征控制点。研究了基于点集的仿射、相似以及刚性变换的变形函数,基于变形函数通过移动控制点生成变形后的新图像。并对仿射、相似以及刚性变形效果进行了比较。
在基于点集的图像变形方法的基础上,研究了一种基于控制曲线集的移动最小二乘图像变形方法。根据源图像中的形状信息或变形需要来设置关键点,生成三次样条特征曲线,然后移动该特征曲线到新的位置根据变型函数实现图像的变形。推导了基于曲线集的仿射、相似和刚性变形函数,实现图像的真实感变形。
为了保持图像变形的实时性,在曲线集的图像变形方法基础上研究了一种基于OpenGL纹理映射的加速算法。对源图像进行网格划分,利用变形函数计算出网格点变形后的坐标,在OpenGL中生成变形后的网格点框架:将变形前的二维图像转化为纹理映射到网格点框架上,从而提高了图像变形速度,达到实时性的变形效果。
基于上述图像变形方法的分析研究,开发了一个图像变形处理系统,实现了基于点、基于曲线和基于网格点的移动最小二乘图像变形,每种变形方法中包括仿射、相似和刚性变换三种变形效果。该变形系统利用Visual C++的MFC框架实现了可视化操作界面,用户使用方便。
Image deformation is an image processing technique, which creates smooth and realistic deformation results based on deformation control features and definite deformation functions. This technique is widely used in virtual reality, computer animation, medical image processing and movie & TV field.
A point-based image deformation method using moving least squares(MLS) is studied. First, point-based MLS mathematic model is analyzed and the feature control points are set according to deformation requirement. The point-based transformation functions are studied to compute afflne, similarity and rigid deformations of image and obtain image deformation results by moving control points. Then comparison of affine, similarity and rigid image deformation results is made.
Based on the research above, a MLS image deformation method using control curves is studied. According to shape information or deformation requirement, key points are set to create cubic-spline curves. The curves are moved to new positions to control the deformation of image. Then the transformation functions based on control curves are deduced to compute affine, similarity and rigid deformations of image and realize realistic image deformation results.
To keep the real time of image deformation, an accelerated algorithm of curve-based image deformation is implemented by OpenGL texture mapping. The original image is partitioned by grid and the deformed coordinates of every grid vertex are computed. Then deformed image framework is created in OpenGL; 2D image before deformation is translated into texture and mapped to the deformed image framework, which accelerates time cost and realizes the real time of image deformation.
A system of image deformation has been exploited based on the above-mentioned methods. It can realize MLS image deformation based on points, curves and grid vertices. Every deformation method concludes affine, similarity and rigid deformations of image. The experimental results show that the system has visual operation interface and makes the operation convenient for users.
研究了基于控制点的移动最小二乘图像变形方法。首先分析了基于控制点的移动最小二乘图像变形方法的数学模型,根据变形需要设置特征控制点。研究了基于点集的仿射、相似以及刚性变换的变形函数,基于变形函数通过移动控制点生成变形后的新图像。并对仿射、相似以及刚性变形效果进行了比较。
在基于点集的图像变形方法的基础上,研究了一种基于控制曲线集的移动最小二乘图像变形方法。根据源图像中的形状信息或变形需要来设置关键点,生成三次样条特征曲线,然后移动该特征曲线到新的位置根据变型函数实现图像的变形。推导了基于曲线集的仿射、相似和刚性变形函数,实现图像的真实感变形。
为了保持图像变形的实时性,在曲线集的图像变形方法基础上研究了一种基于OpenGL纹理映射的加速算法。对源图像进行网格划分,利用变形函数计算出网格点变形后的坐标,在OpenGL中生成变形后的网格点框架:将变形前的二维图像转化为纹理映射到网格点框架上,从而提高了图像变形速度,达到实时性的变形效果。
基于上述图像变形方法的分析研究,开发了一个图像变形处理系统,实现了基于点、基于曲线和基于网格点的移动最小二乘图像变形,每种变形方法中包括仿射、相似和刚性变换三种变形效果。该变形系统利用Visual C++的MFC框架实现了可视化操作界面,用户使用方便。
Image deformation is an image processing technique, which creates smooth and realistic deformation results based on deformation control features and definite deformation functions. This technique is widely used in virtual reality, computer animation, medical image processing and movie & TV field.
A point-based image deformation method using moving least squares(MLS) is studied. First, point-based MLS mathematic model is analyzed and the feature control points are set according to deformation requirement. The point-based transformation functions are studied to compute afflne, similarity and rigid deformations of image and obtain image deformation results by moving control points. Then comparison of affine, similarity and rigid image deformation results is made.
Based on the research above, a MLS image deformation method using control curves is studied. According to shape information or deformation requirement, key points are set to create cubic-spline curves. The curves are moved to new positions to control the deformation of image. Then the transformation functions based on control curves are deduced to compute affine, similarity and rigid deformations of image and realize realistic image deformation results.
To keep the real time of image deformation, an accelerated algorithm of curve-based image deformation is implemented by OpenGL texture mapping. The original image is partitioned by grid and the deformed coordinates of every grid vertex are computed. Then deformed image framework is created in OpenGL; 2D image before deformation is translated into texture and mapped to the deformed image framework, which accelerates time cost and realizes the real time of image deformation.
A system of image deformation has been exploited based on the above-mentioned methods. It can realize MLS image deformation based on points, curves and grid vertices. Every deformation method concludes affine, similarity and rigid deformations of image. The experimental results show that the system has visual operation interface and makes the operation convenient for users.
引文
[1]何斌,马天予,王运坚等.Visual C++数字图像处理.北京:人民邮电出版社,2001.
[2]潘云鹤,董金祥,陈德人.计算机图形学:原理、方法及应用.北京高等教育出版社,2003.
[3]吴立德.计算机视觉.上海:复旦大学出版社,1993.
[4]马颂德,张正友.计算机视觉—计算理论与实践.北京:科学出版社,1998.
[5]Sonka M,Hlavac V,Boyle R.图像处理、分析与机器视觉(第二版).北京:人民邮电出版社,2003.
[6]Warren J,Ju T,Eichele Get al.A geometric database for gene expression data.In SGP 03:Proceedings of the 2003 Eurographics,ACM SIGGRAPH,2003:166-176.
[7]Keysers P,Deselaers P,Gollan C et al.Deformation Models for Image Recognition.IEEE Transactions on Pattern Analysis and Machine Intelligence.2007,29(8):1422-1435.
[8]王城峰,陈建平.基于特征点的图像变形技术及应用.广西师范大学学报,2003,21(1):450-454.
[9]Smythe D B.A two-pass mesh warping algorithm for object transformation and image interpolation.ILM Computer Graphics Department,San Rafael,Calif,1990,Technical Report 1030.
[10]Hui Fang,Hart J.C.Detail Preserving Shape Deformation in Image Editing.ACM Trans,Graph,2007,26(3):12-16.
[11]Summer R W,Schmid J,Pauly M,Embedded Deformation for Shape Manipulation.ACM Trans,Graph,2007,26(3):80-86.
[12]Wolberg G.Digital image warping.IEEE Computer Society Press,Los Alamitos,Calif,1990.
[13]MacCracken R,Joy K I.Free-form deformations with lattices of arbitrary topology.In proceedings of ACM SIGGRAPH 1996,ACM Press,1996:181-188.
[14]Sederberg T W,Parry S R.Free-form deformation of solid geometric models.In Proceedings of ACM SIGGRAPH 1986,ACM Press,1986:151-160.
[15]Milliron T,Jensen R,Barzel R et al.A Frumework for Geometric Warps and Deformations.ACM Trans,Graphics,2002,21(1):20-51.
[16]Kho Y,Garland M.Sketching Mesh Deformations.International Conference on Computer Graphics and Interactive Techniques.Los Angeles,California.2005:934-941.
[17]Blanco F R,Oliveira M M.Instant Mesh Deformation.Proceedings of the 2008 symposium on Interactive 3D graphics and games,Redwood City,California.2008:71-78.
[18]Beier T,Neely S.Feature-based image metamorphosis.SIGGRAPH' 92 Conference Proceedings,Chicago,Illinois,U.S.1992,26:34-42.
[19]王建宁,董峰,石教英.基于三角形对应关系的Morphing技术.中国图像图形学报,1998,3(8): 641-646.
[20]于学春,李宗民,于广斌.一种基于扫描线的图像变形算法.工程图学学报,2006,(03):92-96.
[21]Igarashi T,Moscovich T,Hughes J F.As-rigid-as-possible shape manipulation,ACM Trans,Graph,2005,24(3):1134-1141.
[22]Ran L,Amicis R B,Conti G.Interactive Spline-Driven Deformation for Free-Form Surface Styling.Proceedings of the 2006 ACM symposium on Solid and physical modeling,Cardiff,Wales.2006:139-147.
[23]Lee S,Chwa K Y,Hahn Jet al.Image morphing using deformation techniques.The Journal of Visualization and Computer Animation,1996,7(1):3-23.
[24]Terzopoulos D,Platt J,Barr A etal.Elastically deformable models.1997,21(4):205-214.
[25]李旭东,张振跃.非对称径向基函数与稳定边界图像变形算法.计算机辅助设计与图形学学报,2004,16(6):747-752.
[26]Levin D.The approximation power of moving least squares.Mathematics of Computation,1998,67(224):1517-1531.
[27]Weng Y L,Xu W W,Wu Y C et al.2D Shape Deformation Using Nonlinear Least Squares Optimization.The Visual Computer,2006,22(9):653-660.
[28]Schaefer S,McPhail T,Warren J.Image Deformation Using Moving Least Squares.ACM SIGGRAPH,2006:533-540.
[29]Heeger D J,Bergen J R.Pyramid-based texture analysis synthesis.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.Los Angeles,1995:229-238.
[30]De Boner J S.Multiresolution sampling procedure for analysisand synthesis of texture images.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.Los Angeles,1997:361-368.
[31]Simoncelli E P,Portilla J.Texture characterization via joint statistics of wavelet coefficient magnitudes.Proceedings of the 5th International Conference on Image Processing.Los Angeles,1998:62-66.
[32]Efros A A,Lung T K.Texture synthesis by nonparametric sampling.Proceedings of IEEE International Conference on Computer Vision.Corfu,1999:1033-1038.
[33]Wei L Y,Levoy M.Fast texture synthesis using tree-structured vector quantization.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.Los Angeles,2000:479-488.
[34]Ashikhmin M.Synthesizing natural textures.Proceedings of the 2001 ACM Symposium on Interactive 3D Graphics.Los Angeles,2001:217-226.
[35]Tong X,Zhang J,Liu Let al.Synthesis of bidirectional texture functions on arbitrary surfaces.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.San Antonio,2002:665-672.
[36]Lefebvre S,Hoppe H.Parallel controllable texture synthesis.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.Los Angeles,2005:777-786.
[37]Lefebvre S,Hoppe H.Appearance-space texture synthesis.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.Boston,2006:541-548.
[38]Xu Y Q,Guo B,Shum H Y.Chaos mosaic:fast and memory efficient texture synthesis.Redmond:Microsoft Research,MSR TR 2000 32,2000.
[39]Efros A A,Freeman W T.Image quilting for texture synthesis and transfer.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.Los Angeles,2001:341-347.
[40]Liang L,Liu C,Xu Y Q et al.Real time texture synthesis using patch based sampling.ACM Transactions on Graphics,2001,20(3):127-150.
[41]Kwatra V,Schodl A,Essa Iet al.Graphcut textures:image and video synthesis using graph cuts.ACM Transactions on Graphics,2003,22(3):277-286.
[42]Cohen M F,Shade J,Hiller S et al.Wang tiles for image and texture generation[J].ACM Transactions on Graphics,2003,22(3):287-294.
[43]Ng T Y,Wen C H,Tan T Set al.Generating anω-tile set for texture synthesis[C]Proceedingsof Computer Graphics International.New York,2005:177-184.
[44]韩媛媛,黎蔚,陈家新.一种快速块拼贴纹理合成算法.微电子学与计算机机,2008,25(5):770-772.
[45]聂俊岚,王艳芬.块纹理合成中纹理块尺寸自适应算法.计算机辅助设计与图形学学报,2008,20(10):4530-4534.
[46]Wu Q,Yu Y Z.Feature matching and deformation for texture synthesis.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.New York,2004:364-367.
[47]Zhang Peng,Peng Silong.Structure2based texture synthesis.Journal of Computer2Aided Design & Computer Graphics,2004,16(3):290-296.
[48]Yang Gang,Wang Wencheng,Wu Enhua.Texture synthesis by the border image[J].Journal of Computer Research and Development.2005,42(12):2118-2125.
[49]王海鹏.图形图像变形技术研究.西安:西北工业大学,2000.
[50]Alexa M,Cohen-Or D,Levin D.As-rigid-as-possible shape interpolation.In proceedings of ACM SIGGRAPH,ACM Press/Addison-Wesley Publishing Co.New York,NY,USA,2000:157-164.
[51]Horn B.Closed-form solution of absolute orientation using unit quaternions.Journal of the Optical Society of America,April 1987,A4:29-642.
[52]Paul B,Dan X.Multiresolution image morphing in wavelet domain.Proceedings in International Conference on Visualization(2000),London,England,2000:309-314.
[53]孙家广.计算机图形学[M].北京:清华大学出版社,2005.
[54]全惠云.数值分析与应用程序.武汉:武汉大学出版社,2007.
[55]Shreiner D,Woo M,Neider J,Davis T.OpenGL编程指南.北京:机械工业出版社,2005.
[2]潘云鹤,董金祥,陈德人.计算机图形学:原理、方法及应用.北京高等教育出版社,2003.
[3]吴立德.计算机视觉.上海:复旦大学出版社,1993.
[4]马颂德,张正友.计算机视觉—计算理论与实践.北京:科学出版社,1998.
[5]Sonka M,Hlavac V,Boyle R.图像处理、分析与机器视觉(第二版).北京:人民邮电出版社,2003.
[6]Warren J,Ju T,Eichele Get al.A geometric database for gene expression data.In SGP 03:Proceedings of the 2003 Eurographics,ACM SIGGRAPH,2003:166-176.
[7]Keysers P,Deselaers P,Gollan C et al.Deformation Models for Image Recognition.IEEE Transactions on Pattern Analysis and Machine Intelligence.2007,29(8):1422-1435.
[8]王城峰,陈建平.基于特征点的图像变形技术及应用.广西师范大学学报,2003,21(1):450-454.
[9]Smythe D B.A two-pass mesh warping algorithm for object transformation and image interpolation.ILM Computer Graphics Department,San Rafael,Calif,1990,Technical Report 1030.
[10]Hui Fang,Hart J.C.Detail Preserving Shape Deformation in Image Editing.ACM Trans,Graph,2007,26(3):12-16.
[11]Summer R W,Schmid J,Pauly M,Embedded Deformation for Shape Manipulation.ACM Trans,Graph,2007,26(3):80-86.
[12]Wolberg G.Digital image warping.IEEE Computer Society Press,Los Alamitos,Calif,1990.
[13]MacCracken R,Joy K I.Free-form deformations with lattices of arbitrary topology.In proceedings of ACM SIGGRAPH 1996,ACM Press,1996:181-188.
[14]Sederberg T W,Parry S R.Free-form deformation of solid geometric models.In Proceedings of ACM SIGGRAPH 1986,ACM Press,1986:151-160.
[15]Milliron T,Jensen R,Barzel R et al.A Frumework for Geometric Warps and Deformations.ACM Trans,Graphics,2002,21(1):20-51.
[16]Kho Y,Garland M.Sketching Mesh Deformations.International Conference on Computer Graphics and Interactive Techniques.Los Angeles,California.2005:934-941.
[17]Blanco F R,Oliveira M M.Instant Mesh Deformation.Proceedings of the 2008 symposium on Interactive 3D graphics and games,Redwood City,California.2008:71-78.
[18]Beier T,Neely S.Feature-based image metamorphosis.SIGGRAPH' 92 Conference Proceedings,Chicago,Illinois,U.S.1992,26:34-42.
[19]王建宁,董峰,石教英.基于三角形对应关系的Morphing技术.中国图像图形学报,1998,3(8): 641-646.
[20]于学春,李宗民,于广斌.一种基于扫描线的图像变形算法.工程图学学报,2006,(03):92-96.
[21]Igarashi T,Moscovich T,Hughes J F.As-rigid-as-possible shape manipulation,ACM Trans,Graph,2005,24(3):1134-1141.
[22]Ran L,Amicis R B,Conti G.Interactive Spline-Driven Deformation for Free-Form Surface Styling.Proceedings of the 2006 ACM symposium on Solid and physical modeling,Cardiff,Wales.2006:139-147.
[23]Lee S,Chwa K Y,Hahn Jet al.Image morphing using deformation techniques.The Journal of Visualization and Computer Animation,1996,7(1):3-23.
[24]Terzopoulos D,Platt J,Barr A etal.Elastically deformable models.1997,21(4):205-214.
[25]李旭东,张振跃.非对称径向基函数与稳定边界图像变形算法.计算机辅助设计与图形学学报,2004,16(6):747-752.
[26]Levin D.The approximation power of moving least squares.Mathematics of Computation,1998,67(224):1517-1531.
[27]Weng Y L,Xu W W,Wu Y C et al.2D Shape Deformation Using Nonlinear Least Squares Optimization.The Visual Computer,2006,22(9):653-660.
[28]Schaefer S,McPhail T,Warren J.Image Deformation Using Moving Least Squares.ACM SIGGRAPH,2006:533-540.
[29]Heeger D J,Bergen J R.Pyramid-based texture analysis synthesis.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.Los Angeles,1995:229-238.
[30]De Boner J S.Multiresolution sampling procedure for analysisand synthesis of texture images.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.Los Angeles,1997:361-368.
[31]Simoncelli E P,Portilla J.Texture characterization via joint statistics of wavelet coefficient magnitudes.Proceedings of the 5th International Conference on Image Processing.Los Angeles,1998:62-66.
[32]Efros A A,Lung T K.Texture synthesis by nonparametric sampling.Proceedings of IEEE International Conference on Computer Vision.Corfu,1999:1033-1038.
[33]Wei L Y,Levoy M.Fast texture synthesis using tree-structured vector quantization.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.Los Angeles,2000:479-488.
[34]Ashikhmin M.Synthesizing natural textures.Proceedings of the 2001 ACM Symposium on Interactive 3D Graphics.Los Angeles,2001:217-226.
[35]Tong X,Zhang J,Liu Let al.Synthesis of bidirectional texture functions on arbitrary surfaces.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.San Antonio,2002:665-672.
[36]Lefebvre S,Hoppe H.Parallel controllable texture synthesis.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.Los Angeles,2005:777-786.
[37]Lefebvre S,Hoppe H.Appearance-space texture synthesis.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.Boston,2006:541-548.
[38]Xu Y Q,Guo B,Shum H Y.Chaos mosaic:fast and memory efficient texture synthesis.Redmond:Microsoft Research,MSR TR 2000 32,2000.
[39]Efros A A,Freeman W T.Image quilting for texture synthesis and transfer.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.Los Angeles,2001:341-347.
[40]Liang L,Liu C,Xu Y Q et al.Real time texture synthesis using patch based sampling.ACM Transactions on Graphics,2001,20(3):127-150.
[41]Kwatra V,Schodl A,Essa Iet al.Graphcut textures:image and video synthesis using graph cuts.ACM Transactions on Graphics,2003,22(3):277-286.
[42]Cohen M F,Shade J,Hiller S et al.Wang tiles for image and texture generation[J].ACM Transactions on Graphics,2003,22(3):287-294.
[43]Ng T Y,Wen C H,Tan T Set al.Generating anω-tile set for texture synthesis[C]Proceedingsof Computer Graphics International.New York,2005:177-184.
[44]韩媛媛,黎蔚,陈家新.一种快速块拼贴纹理合成算法.微电子学与计算机机,2008,25(5):770-772.
[45]聂俊岚,王艳芬.块纹理合成中纹理块尺寸自适应算法.计算机辅助设计与图形学学报,2008,20(10):4530-4534.
[46]Wu Q,Yu Y Z.Feature matching and deformation for texture synthesis.Computer Graphics Proceedings,Annual Conference Series,ACM SIGGRAPH.New York,2004:364-367.
[47]Zhang Peng,Peng Silong.Structure2based texture synthesis.Journal of Computer2Aided Design & Computer Graphics,2004,16(3):290-296.
[48]Yang Gang,Wang Wencheng,Wu Enhua.Texture synthesis by the border image[J].Journal of Computer Research and Development.2005,42(12):2118-2125.
[49]王海鹏.图形图像变形技术研究.西安:西北工业大学,2000.
[50]Alexa M,Cohen-Or D,Levin D.As-rigid-as-possible shape interpolation.In proceedings of ACM SIGGRAPH,ACM Press/Addison-Wesley Publishing Co.New York,NY,USA,2000:157-164.
[51]Horn B.Closed-form solution of absolute orientation using unit quaternions.Journal of the Optical Society of America,April 1987,A4:29-642.
[52]Paul B,Dan X.Multiresolution image morphing in wavelet domain.Proceedings in International Conference on Visualization(2000),London,England,2000:309-314.
[53]孙家广.计算机图形学[M].北京:清华大学出版社,2005.
[54]全惠云.数值分析与应用程序.武汉:武汉大学出版社,2007.
[55]Shreiner D,Woo M,Neider J,Davis T.OpenGL编程指南.北京:机械工业出版社,2005.