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.
[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