基于改进的函数映射理论的三维模型间对应关系
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摘要
针对不同姿态下三维等距模型间的对应关系,提出一种基于函数映射理论的改进算法.首先对由Laplace-Beltrami算子分解出的特征描述符添加对角描述符约束,并将该约束添加到函数映射框架中对其进行改进,利用改进后的函数映射建立模型间的初始对应关系;其次,采用迭代最近点算法与K近邻算法优化初始对应关系;最后,结合优化后的函数映射关系和迪杰斯特拉-最远点采样算法构建点到点的对应关系.仿真实验结果表明,与已有算法相比,改进的函数映射理论可以计算出更加准确的映射关系矩阵,进而减小了由该矩阵构建的点到点对应关系的等距误差.
In order to explore the corresponding relationship between 3 D isometric models with different attitude,an improved algorithm based on function mapping theory is proposed.Firstly,the diagonal descriptor constraint is added to the feature descriptor calculated by decomposition of Laplace-Beltrami operator,then this constraint is improved by adding it into the functional mapping framework,and the initial correspondence between shapes is established by using the functional map theory.Secondly,the initial shape correspondences are optimized by fusion of the iterative nearest point algorithm and the K-nearest neighbor algorithm.Finally,the point-to-point correspondences are constructed by combining optimized functional map and Dijkstra-farthest point sampling algorithm.The experimental results show that the improved functional map can calculate a more accurate correspondence matrix compared with the existing algorithms,and the isometric error of the point-to-point correspondence constructed by this method can be reduced.
In order to explore the corresponding relationship between 3 D isometric models with different attitude,an improved algorithm based on function mapping theory is proposed.Firstly,the diagonal descriptor constraint is added to the feature descriptor calculated by decomposition of Laplace-Beltrami operator,then this constraint is improved by adding it into the functional mapping framework,and the initial correspondence between shapes is established by using the functional map theory.Secondly,the initial shape correspondences are optimized by fusion of the iterative nearest point algorithm and the K-nearest neighbor algorithm.Finally,the point-to-point correspondences are constructed by combining optimized functional map and Dijkstra-farthest point sampling algorithm.The experimental results show that the improved functional map can calculate a more accurate correspondence matrix compared with the existing algorithms,and the isometric error of the point-to-point correspondence constructed by this method can be reduced.
引文
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[21] CORMAN E,OVSJANIKOV M,CHAMBOLLE A.Continuous matching via vector field flow[J].Computer Graphics Forum,2015,34(5):129-139.
[22] VESTNER M,LITMAN R,RODOLA E,et al.Product manifold filter:non-rigid shape correspondence via kernel density estimation in the product space[C]//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition.Honolulu HI:IEEE Press,2017:3327-3336.
[23] MEYER M,DESBRUN M,SCHRODER P,et al.Discrete differential-geometry operators for triangulated 2-manifolds[J].Visualization and mathematics III,2003:35-57.
[24] NOGNENG D,OVSJANIKOV M.Informative descriptor preservation via commutativity for shape matching[J].Computer Graphics Forum,2017,36(2):259-267.
[2] KAICK O V,ZHANG H,HAMARNEH G,et al.A survey on shape correspondence[J].Computer Graphics Forum,2011,30(6):1681-1707.
[3] 刘志,尹世超,潘翔,等.基于特征线条的三维模型检索方法[J].计算机辅助设计与图形学学报,2016,28(9):1514-1520.
[4] 杨军,张鹏.结合拓扑持续性和热扩散理论的3维模型分割[J].中国图象图形学报,2018,266(6):113-121.
[5] BERKITEN S,HALBER M,SOLOMON J,et al.Learning detail transfer based on geometric features[J].Computer Graphics Forum,2017,36(2):361-373.
[6] 杨军,史纪东.由粗到精的三维等距模型对应关系计算[J].重庆邮电大学学报(自然科学版),2018,30(6):803-811.
[7] CHEN Q,KOLUTUN V.Robust nonrigid registration by convex optimization[C]//IEEE International Conference on Computer Vision.Washington,DC:IEEE Press,2015:2039-2047.
[8] REN K Y,SUN H X,JIA Q X,et al.Urban scene recognition by graphical model and 3d geometry[J].The Journal of China Universities of Posts and Telecommunications,2011,18(3):110-119.
[9] RAVIV D,BRONSTEIN A M,BRONSTEIN M M,et al.Equi-Affine invariant geometry for shape analys[J].Journal of Mathematical Imaging & Vision,2014,50(1/2):144-163.
[10] BRONSTEIN A M.Generalized multidimensional scaling:a framework for isometry-invariant partial surface matching[J].Proceedings of the National Academy of Sciences of the United States of America,2006,103(5):1168-1172.
[11] AIGERMAN N,LIPMAN Y.Orbifold tutte embeddings[J].ACM Transactions on Graphics,2015,34(6):1-12.
[12] OVSJANIKOV M,BEN-CHEN M,SOLOMON J,et al.Functional maps:a flexible representation of maps between shapes[J].ACM Transactions on Graphics,2012,31(4):1-11.
[13] KOVNATSKY A,BRONSTEIN M M,BRONSTEIN A M,et al.Coupled quasi-harmonic bases[J].Computer Graphics Forum,2013,32(2):439-448.
[14] EMANUELE R,MOELLER M,CREMERS D.Point-wise map recovery and refinement from functional correspondence[J].Computer Science,2015:25-32.
[15] BOSCAINI D,MASCI J,EMANUELE R,et al.Learning shape correspondence with anisotropic convolutional neural networks[J].Learning Correspondence with Anisotropic CNN,2016:3189-3197.
[16] SUN J,OVSJANIKOV M,GUIBAS L.A concise and provably informative multi-scale signature based on heat diffusion[J].Computer Graphics Forum,2009,28(5):383-1392.
[17] AUBRY M,SCHLICKEWEI U,CREMERS D.The wave kernel signature:a quantum mechanical approach to shape analysis[C]//Proceedings of the 2011 IEEE Conference on Computer Vision Workshops.Barcelona:IEEE Press,2011:1626-1633.
[18] 杨军,闫寒,王茂正.融合特征描述符约束的三维等距模型对应关系计算[J].中国图象图形学报,2016,21(5):628-635.
[19] KIM V G,LIPMAN Y,FUNKHOUSER T.Blended intrinsic maps[J].ACM Transactions on Graphics,2011,30(4):76-79.
[20] 杨军,闫寒.校准三维模型基矩阵的函数映射的对应关系计算[J].武汉大学学报(信息科学版),2018,43(10):1518-1525.
[21] CORMAN E,OVSJANIKOV M,CHAMBOLLE A.Continuous matching via vector field flow[J].Computer Graphics Forum,2015,34(5):129-139.
[22] VESTNER M,LITMAN R,RODOLA E,et al.Product manifold filter:non-rigid shape correspondence via kernel density estimation in the product space[C]//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition.Honolulu HI:IEEE Press,2017:3327-3336.
[23] MEYER M,DESBRUN M,SCHRODER P,et al.Discrete differential-geometry operators for triangulated 2-manifolds[J].Visualization and mathematics III,2003:35-57.
[24] NOGNENG D,OVSJANIKOV M.Informative descriptor preservation via commutativity for shape matching[J].Computer Graphics Forum,2017,36(2):259-267.