Differential Geometry Approach to 3D Partially Similar Object Matching
GUO Ke-Hua1,2, LIU Chuan-Cai1, YANG Jing-Yu1
1.School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 2100942. School of Information Science and Engineering, Central South University, Changsha 410083
Abstract:Based on Gaussian curvature and mean curvature, a 3D partially similar object matching approach is proposed. Firstly, the point-pair set is constructed by filtrating points with similar inherent characteristic. Next, the triangle-pair set is formed after searching similar triangles in the point-pair set. Finally, scoring function is employed to determine the optimal transformation in triangle-pair set. Experimental results show good matching efficiency and running time complexity in the partial surface matching of irregular surfaces.
郭克华,刘传才,杨静宇. 三维局部相似目标匹配的微分几何方法*[J]. 模式识别与人工智能, 2008, 21(5): 586-591.
GUO Ke-Hua, LIU Chuan-Cai, YANG Jing-Yu. Differential Geometry Approach to 3D Partially Similar Object Matching. , 2008, 21(5): 586-591.
[1] Claes P, Vandermeulen D, van Gool L, et al. Robust and Accurate Partial Surface Registration Based on Variational Implicit Surfaces for Automatic 3D Model Building // Proc of the 5th International Conference on 3D Digital Imaging and Modeling. Ottawa, Canada, 2005: 385-392 [2] Osada R, Funkhouser T, Chazelle B. Shape Distributions. ACM Trans on Graphics, 2002, 21(4): 807-832 [3] Tarte S M, Talib H, Ballester M, et al. Evaluating Partial Surface Matching for Fracture Reduction Assessment // Proc of the 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro. Arlington, USA, 2006: 514-517 [4] Shatsky M, Nussinov R, Wolfson H J. Flexible Protein Alignment and Hinge Detection. Proteins, 2002, 48(2): 242-256 [5] Alt H, Brass P, Godau M, et al. Computing the Hausdorff Distance of Geometric at Terns and Shapes. Technical Report, B01-07, Berlin, Germany: Freie Universitt. Fachbereich Mathematik und Informatik, 2001 [6] Besl P J, McKay N D. A Method for Registration of 3D Shapes. IEEE Trans on Pattern Analysis and Machine Intelligence, 1992, 14(2): 239-256 [7] Barequet G, Sharir M. Partial Surface Matching by Using Directed Footprints. Computational Geometry: Theory and Applications, 1999, 12(1): 45-62 [8] Barequet G, Sharir M. Partial Surface and Volume Matching in Three Dimensions. IEEE Trans on Pattern Analysis and Machine Intelligence, 1997, 19(9): 929- 948 [9] Kreyszig E. Differential Geometry. Mineola, USA: Dover, 1991 [10] Cheng Yimin, Ding Hongxia, Wang Yixiao, et al. Curved Object Recognition Based on Geometrical Features. Journal of Image and Graphics, 2000, 5(7): 573-579 (in Chinese) (程义民,丁红侠,王以孝,等.基于几何特征的曲面物体识别.中国图象图形学报, 2000, 5(7): 573-579) [11] Besl P J, Jain R C. Segmentation through Variable-Order Surface Fitting. IEEE Trans on Pattern Analysis and Machine Intelligence, 1988, 10(2): 167-192