基于谱对称的形状配准方法
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摘要
针对现有三维形状配准方法中存在左右翻转的错误匹配问题,提出了基于内蕴对称特征检测的高效形状配准算法。首先,通过热核与几何约束构建模型的内蕴自对称点对;其次,基于谱嵌入特征空间分析提取模型的内蕴对称平面,并依据模型表面法向量有效识别模型的左右结构属性;然后,根据内蕴对称点对获得模型的一致性谱对称结构描述;最后,引入一致性点漂移算法(CPD),实现基于谱对称的非刚性模型的形状配准,有效避免了模型配准中的左右结构翻转问题。实验进一步论证了这种方法不仅有效提高了模型匹配的效率,而且能有效识别同类模型的结构特征,对于非刚性模型的配准具有较强的鲁棒性。
Aiming at the issue of symmetric flips in the process of 3 D shape registration,this paper developed an efficient shape registration algorithm based on intrinsic symmetric feature detection. Firstly,it constructed intrinsic symmetric point pairs of the model by heat kernel signature( HKS) and geometric constraints. Secondly,based on the spectral embedding space analysis,it extracted the intrinsic symmetric plane of the model and effectively identified the symmetrical properties of the model according to the model surface normal vector,to get intrinsic symmetry point pair. Therefore it presented the consistent spectral symmetry structure of the model. Finally,combining the coherent point drift( CPD) method,this paper implemented the shape registration of non-rigid model based on spectral symmetry. The experimental results show that the matching method is efficient and robust to the non-rigid deformable shape matching. Moreover,the structural features in same category models are also effectively identified.
Aiming at the issue of symmetric flips in the process of 3 D shape registration,this paper developed an efficient shape registration algorithm based on intrinsic symmetric feature detection. Firstly,it constructed intrinsic symmetric point pairs of the model by heat kernel signature( HKS) and geometric constraints. Secondly,based on the spectral embedding space analysis,it extracted the intrinsic symmetric plane of the model and effectively identified the symmetrical properties of the model according to the model surface normal vector,to get intrinsic symmetry point pair. Therefore it presented the consistent spectral symmetry structure of the model. Finally,combining the coherent point drift( CPD) method,this paper implemented the shape registration of non-rigid model based on spectral symmetry. The experimental results show that the matching method is efficient and robust to the non-rigid deformable shape matching. Moreover,the structural features in same category models are also effectively identified.
引文
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[21]Jain V,Zhang Hao,Van Kaick O. Non-rigid spectral correspondence of triangle meshes[J]. International Journal of Shape Modeling,2007,13(1):101-124.
[22] Van Kaick O,Zhang Hao,Hamarneh G. Bilateral maps for partial matching[J]. Computer Graphics Forum,2013,32(6):189-200.
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[26]Sun Jian,Ovsjanikov M,Guibas L. A concise and provably informative multi-scale signature based on heat diffusion[J]. Computer Graphics Forum,2009,28(5):1383-1392.
[27]Litman R,Bronstein A M,Bronstein M M. Diffusion-geometric maximally stable component detection in deformable shapes[J]. Computers&Graphics,2011,35(3):549-560.
[28]Jain V,Zhang Hao,Van Kaick O. Non-rigid spectral correspondence of triangle meshes[J]. International Journal of Shape Modeling,13(1):101-124.
[29] Van Kaick O,Zhang Hao,Hamarneh G. Bilateral maps for partial matching[J]. Computer Graphics Forum,2013,32(6):189-200.
[30]Gelfand N,Ikemoto L,Rusinkiewicz S,et al. Geometrically stable sampling for the ICP algorithm[C]//Proc of the 4th IEEE International Conference on 3D Digital Imaging and Modeling. Washington DC:IEEE Computer Society,2003:260-267.
[31]Jain V,Zhang Hao. Robust 3D shape correspondence in the spectral domain[C]//Proc of IEEE International Conference on Shape Modeling and Applications. Washington DC:IEEE Computer Society,2006:19.
[32]Gelfand N,Ikemoto L,Rusinkiewicz S,et al. Geometrically stable sampling for the ICP algorithm[C]//Proc of IEEE International Conference on 3D Digital Imaging and Modeling. Piscataway,NJ:IEEE Press,2003:260-267.
[33]Myronenko A,Song Xubo. Point set registration:coherent point drift[J]. IEEE Trans on Pattern Analysis&Machine Intelligence,2010,32(12):2262-2275.
[2] Kazhdan M,Funkhouser T,Rusinkiewicz S. Symmetry descriptors and 3D shape matching[C]//Proc of Eurographics/ACM SIGGRAPH Symposium on Geometry Processing. New York:ACM Press,2004:115-123.
[3] Podolak J,Shilane P,Golovinskiy A,et al. A planar-reflective symmetry transform for 3D shapes[J]. ACM Trans on Graph,2006,25(3):549-559.
[4] Rustamov R M. Augmented planar reflective symmetry transforms[J]. The Visual Computer,2008,24(6):423-433.
[5] Martinet A,Soler C,Holzschuch N,et al. Accurate detection of symmetries in 3D shapes[J]. ACM Trans on Graph,2006,25(2):439-464.
[6] Thrun S,Wegbreit B. Shape from symmetry[C]//Proc of the 10th IEEE International Conference on Computer Vision. Washington DC:IEEE Computer Society,2005:1824-1831.
[7] Simari P,Kalogerakis E,Singh K. Folding meshes:hierarchical mesh segmentation based on planar symmetry[C]//Proc of the 4th Eurographics Symposium on Geometry Processing. Aire-la-Ville,Switzerland:Eurographics Association,2006:111-119.
[8] Mitra N J,Guibas L J,Pauly M. Partial and approximate symmetry detection for 3D geometry[J]. ACM Trans on Graph,2006,25(3):560-568.
[9] Mitra N,Guibas L,Pauly M. Symmetrization[J]. ACM Trans on Graphics,2007,26(3):article No 63.
[10]Lipman Y,Funkhouser T. Mobius voting for surface correspondence[J]. ACM Trans on Graph,2009,28(3):article No 72.
[11] Lipman Y,Chen Xiaobai,Daubechies I,et al. Symmetry factored embedding[J]. ACM Trans on Graph,2010,29(4):article No103.
[12]Riklin-Raviv T,Sochen N,Kiryati N. On symmetry,perceptivity and level-set based segmentation[J]. IEEE Trans on Pattern Analysis and Machine Intelligence,2009,31(8):1458-1471.
[13]Ovsjanikov M,Sun Jian,Guibas L. Global intrinsic symmetries of shapes[J]. Computer Graphics Forum,2008,27(5):1341-1348.
[14]Ovsjanikov M,Li W,Guibas L,et al. Exploration of continuous variability in collections of 3D shapes[J]. ACM Trans on Graph,2011,30(4):article No 33.
[15]Chertok M,Keller Y. A graph matching approach to symmetry detection and analysis[M]//Computational Intelligence Paradigms in Advanced Pattern Classification. Berlin:Springer,2012:113-144.
[16]Kim V G,Lipman Y,Chen Xiaobai,et al. Mbius transformations for global intrinsic symmetry analysis[J]. Computer Graphics Forum,2010,29(5):1689-1700.
[17]Zhang Zhiyuan,Yin Kangkang,Foong K W C. Symmetry robust descriptor for non-rigid surface matching[J]. Computer Graphics Forum,2013,32(7):355-362.
[18] Zheng Qian,Hao Zhuming,Huang Hui,et al. Skeleton-intrinsic symmetrization of shapes[J]. Computer Graphics Forum,2015,34(2):275-286.
[19]Ovsjanikov M,Ben-Chen M,Solomon J,et al. Functional maps:a flexible representation of maps between shapes[J]. ACM Trans Graph,2012,31(4):article No 30.
[20]Zhang H,Sheffer A,Cohen-Or D,et al. Deformation-driven shape correspondence[J]. Computer Graphics Forum,2008,27(5):1431-1439.
[21]Jain V,Zhang Hao,Van Kaick O. Non-rigid spectral correspondence of triangle meshes[J]. International Journal of Shape Modeling,2007,13(1):101-124.
[22] Van Kaick O,Zhang Hao,Hamarneh G. Bilateral maps for partial matching[J]. Computer Graphics Forum,2013,32(6):189-200.
[23]Tenenbaum J B,Silva V D,Langford J C. A global geometric framework for nonlinear dimensionality reduction[J]. Science,2000,290(5500):2319-2323.
[24] Belkin M,Niyogi P. Laplacian eigenmaps for dimensionality reduction and data representation[J]. Neural Computation,2002,15(6):1373-1396.
[25]Yoshiyasu Y,Yoshida E. Symmetry aware embedding for shape correspondence[J]. Computers&Graphics,2016,60(11):9-22.
[26]Sun Jian,Ovsjanikov M,Guibas L. A concise and provably informative multi-scale signature based on heat diffusion[J]. Computer Graphics Forum,2009,28(5):1383-1392.
[27]Litman R,Bronstein A M,Bronstein M M. Diffusion-geometric maximally stable component detection in deformable shapes[J]. Computers&Graphics,2011,35(3):549-560.
[28]Jain V,Zhang Hao,Van Kaick O. Non-rigid spectral correspondence of triangle meshes[J]. International Journal of Shape Modeling,13(1):101-124.
[29] Van Kaick O,Zhang Hao,Hamarneh G. Bilateral maps for partial matching[J]. Computer Graphics Forum,2013,32(6):189-200.
[30]Gelfand N,Ikemoto L,Rusinkiewicz S,et al. Geometrically stable sampling for the ICP algorithm[C]//Proc of the 4th IEEE International Conference on 3D Digital Imaging and Modeling. Washington DC:IEEE Computer Society,2003:260-267.
[31]Jain V,Zhang Hao. Robust 3D shape correspondence in the spectral domain[C]//Proc of IEEE International Conference on Shape Modeling and Applications. Washington DC:IEEE Computer Society,2006:19.
[32]Gelfand N,Ikemoto L,Rusinkiewicz S,et al. Geometrically stable sampling for the ICP algorithm[C]//Proc of IEEE International Conference on 3D Digital Imaging and Modeling. Piscataway,NJ:IEEE Press,2003:260-267.
[33]Myronenko A,Song Xubo. Point set registration:coherent point drift[J]. IEEE Trans on Pattern Analysis&Machine Intelligence,2010,32(12):2262-2275.