基于扩散距离与几何约束的模型内蕴自对称检测
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摘要
针对三维网格模型几何处理中提高算法效率和拓扑噪声不敏感性的要求,提出了基于扩散几何约束的非刚性三维模型内蕴自对称检测方法。通过计算模型的Laplace-Beltrami算子来提取顶点的热核特征描述符,比较描述符之间的扩散距离,与基于谱图理论约束的几何相似性矩阵有效融合,实现形状度量的优化;最后通过线性检测的方式快速获取模型对称点集合,实现模型的自对称形状分析。实验结果进一步验证了该方法不仅能够高效地实现等距非刚性变换模型的内蕴自对称性检测,而且对于残缺模型的对称分析更具有鲁棒性。
Aiming at the requirement related to the insensitivity under efficiency and topological noise during the geometry processing of 3 D shapes,this paper proposed an optimized algorithm,which detected the intrinsic self-symmetry among the non-rigid shapes based on heat diffusion geometric constraints. Firstly,it extracted the heat kernel signature descriptor of the vertex by computing the Laplace-Beltrami operator of the model. Compared the diffusion distance between heat kernel signature descriptors,it fused of the geometric similarity matrix based on spectral graph theory,optimized the shape metric. Finally,it obtained a set of symmetric point pairs by searching loop. A series of experimental results show that the proposed algorithm can effectively detect intrinsic self-symmetry for isometric non-rigid transformation model.
Aiming at the requirement related to the insensitivity under efficiency and topological noise during the geometry processing of 3 D shapes,this paper proposed an optimized algorithm,which detected the intrinsic self-symmetry among the non-rigid shapes based on heat diffusion geometric constraints. Firstly,it extracted the heat kernel signature descriptor of the vertex by computing the Laplace-Beltrami operator of the model. Compared the diffusion distance between heat kernel signature descriptors,it fused of the geometric similarity matrix based on spectral graph theory,optimized the shape metric. Finally,it obtained a set of symmetric point pairs by searching loop. A series of experimental results show that the proposed algorithm can effectively detect intrinsic self-symmetry for isometric non-rigid transformation model.
引文
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[21]Belkin M,Sun Jian,Wang Yusu.Discrete Laplace operator on meshed surfaces[C]//Proc of the 24th Annual Symposium on Computational Geometry.New York:ACM Press,2008:278-287.
[22]姜巍,徐凯,程志全,等.一种通用的局部内蕴对称检测算法[J].计算机辅助设计与图形学报,2013,25(7):974-979.
[23]Gliklikh Y E.Stochastic analysis on manifolds[M]//Global and Stochastic Analysis with Application to Mathematical Physics,Theoretical and Mathematical Physics.London:Springer,2011:139-168.
[24]Bronstein A M,Bronstein M M,Guibas L,et al.Shape Google:geometric words and expressions for invariant shape retrieval[J].ACM Trans on Graphics,2011,30(1):Article No 1.
[2]Mitra N J,Pauly M,Wand M,et al.Symmetry in 3D geometry:extraction and applications[J].Computer Graphics Forum,2013,32(6):1-23.
[3]Zabrodsky H,Peleg S,Avni,D.Symmetry as a continuous feature[J].IEEE Trans on Pattern Analysis and Machine Intelligence,1995,17(12):1154-1166.
[4]Kazhdan M,Chazelle B,Dobkin D,et al.A reflective symmetry descriptor for 3D models[J].Algorithmica,2004,38(1):201-225.
[5]Podolak J,Shilane P,Golovinskiy A,et al.A planar-reflective symmetry transform for 3D shapes[J].ACM Trans on Graphics,2006,25(3):549-559.
[6]Mitra N J,Guibas L J,Pauly M.Partial and approximate symmetry detection for 3D geometry[J].ACM Trans on Graphics,2006,25(3):560-568.
[7]Sipiran I,Gregor R,Schreck T.Approximate symmetry detection in partial 3D Meshes[J].Computer Graphics Forum,2014,33(7):131-140.
[8]Bokeloh M,Berner A,Wand H P,et al.Symmetry detection using feature lines[J].Computer Graphics Forum,2009,28(2):697-706.
[9]Ovsjanikov M,Sun Jian,Guibas L.Global intrinsic symmetries of shapes[J].Computer Graphics Forum,2008,27(5):1341-1348.
[10]Xu Kai,Zhang Hao,Jiang Wei,et al.Multi-Scale partial intrinsic symmetry detection[J].ACM Trans on Graphics,2009,31(6):1-10.
[11]苏梦,万丽莉,苗振江.一种基于扩散几何的非刚体三维形状分割方法[J].计算机辅助设计与图形学报,2015,27(4):605-613.
[12]Raviv D,Bronstein M M,Bronstein A M,et al.Affine-invariant diffusion geometry for the analysis of deformable 3D shapes[C]//Proc of IEEE Conference on Computer Vision and Pattern Recognition.Washington DC:IEEE Computer Society,2011:2361-2367.
[13]Bronstein A M,Bronstein M M,Kimmel R.et al.A Gromov-Hausdorff framework with diffusion geometry for topologically-robust nonrigid shape matching[J].International Journal of Computer Vision,2010,89(2-3):266-286.
[14]Bronstein M,Bronstein A.Analysis of diffusion geometry methods for shape recognition[J].IEEE Trans on Pattern Analysis and Machine Intelligence,2009,33(5):1065-1071.
[15]Sun Jian,Ovsjanikov M,Guibas L.A concise and provably informative multi-scale signature based on heat diffusion[J].Computer Graph Forum,2009,28(5):1383-1392.
[16]Raviv D,Bronstein A M,Bronstein M M,et al.Symmetries of nonrigid shapes[C]//Proc of the 11th IEEE International Conference on Computer Vision.Washington DC:IEEE Computer Society,2007:1-7.
[17]Raviv D,Bronstein A M,Bronstein M M,et al.Full and partial symmetries of non-rigid shapes[J].International Journal of Computer Vision,2010,89(1):18-39.
[18]Coifman R R,Lafon S.Diffusion maps[J].Applied and Computational Harmonic Analysis,2006,21(1):5-30.
[19]De La Porte J,Herbst B M,Hereman W,et al.An introduction to diffusion maps[C]//Proc of the 19th Symposium on Pattern Recognition Association of South Africa.2008:741-750.
[20]Liu Rong,Zhang Hao.Segmentation of 3D meshes through spectral clustering[C]//Proc of the 12th Pacific Conference on Computer Graphics and Applications.Washington DC:IEEE Computer Society,2004:298-305.
[21]Belkin M,Sun Jian,Wang Yusu.Discrete Laplace operator on meshed surfaces[C]//Proc of the 24th Annual Symposium on Computational Geometry.New York:ACM Press,2008:278-287.
[22]姜巍,徐凯,程志全,等.一种通用的局部内蕴对称检测算法[J].计算机辅助设计与图形学报,2013,25(7):974-979.
[23]Gliklikh Y E.Stochastic analysis on manifolds[M]//Global and Stochastic Analysis with Application to Mathematical Physics,Theoretical and Mathematical Physics.London:Springer,2011:139-168.
[24]Bronstein A M,Bronstein M M,Guibas L,et al.Shape Google:geometric words and expressions for invariant shape retrieval[J].ACM Trans on Graphics,2011,30(1):Article No 1.