3D CAD model search: A regularized manifold learning approach

3D model matching has been widely studied in computer vision, graphics and robotics. While there is much success made in the matching of natural objects, most of these approaches consider smooth surfaces and are not suitable for computer aided design (CAD) models because of their complex topology and singular structures. This paper presents a novel spectral approach for the 3D CAD model matching in the framework of manifold learning. The 3D models are treated as undirected graphs. A regularized Laplacian spectrum approach is applied to solve this problem where the regularization term is used to characterize the shape geometries. Spectral distributions of different models are obtained and then compared by their divergence for model retrieval. The proposed approach is tested with models from known 3D CAD database for verification.

[1]  Christopher D. Manning,et al.  Introduction to Information Retrieval , 2010, J. Assoc. Inf. Sci. Technol..

[2]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[3]  Niklas Peinecke,et al.  Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids , 2006, Comput. Aided Des..

[4]  Edwin R. Hancock,et al.  Graph matching and clustering using spectral partitions , 2006, Pattern Recognit..

[5]  Hao Zhang,et al.  A spectral approach to shape-based retrieval of articulated 3D models , 2007, Comput. Aided Des..

[6]  Chitra Dorai,et al.  Shape Spectrum Based View Grouping and Matching of 3D Free-Form Objects , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Ali Shokoufandeh,et al.  Solid Model Databases: Techniques and Empirical Results , 2001, J. Comput. Inf. Sci. Eng..

[8]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[9]  Nikolaos G. Bourbakis,et al.  3-D Object Recognition Using 2-D Views , 2008, IEEE Transactions on Image Processing.

[10]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[11]  William C. Regli,et al.  An approach to a feature-based comparison of solid models of machined parts , 2002, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[12]  Bernard Chazelle,et al.  Shape distributions , 2002, TOGS.

[13]  David S. Watkins,et al.  Fundamentals of Matrix Computations: Watkins/Fundamentals of Matrix Computations , 2005 .

[14]  Ali Shokoufandeh,et al.  Scale-Space Representation and Classification of 3D Models , 2003, J. Comput. Inf. Sci. Eng..

[15]  June-Ho Yi,et al.  Model-Based 3D Object Recognition Using Bayesian Indexing , 1998, Comput. Vis. Image Underst..

[16]  Christopher M. Bishop,et al.  Neural networks and machine learning , 1998 .

[17]  J. Wade Davis,et al.  Statistical Pattern Recognition , 2003, Technometrics.

[18]  JungHyun Han,et al.  Manufacturing feature recognition from solid models: a status report , 2000, IEEE Trans. Robotics Autom..

[19]  John Hart,et al.  ACM Transactions on Graphics , 2004, SIGGRAPH 2004.

[20]  Edwin R. Hancock,et al.  Pattern Vectors from Algebraic Graph Theory , 2005, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Kilian Q. Weinberger,et al.  Distance Metric Learning for Large Margin Nearest Neighbor Classification , 2005, NIPS.

[22]  David S. Watkins,et al.  Fundamentals of matrix computations , 1991 .

[23]  Hui Huang,et al.  Surface Mesh Smoothing, Regularization, and Feature Detection , 2008, SIAM J. Sci. Comput..

[24]  Szymon Rusinkiewicz,et al.  Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors , 2003, Symposium on Geometry Processing.

[25]  Hugues Hoppe,et al.  Progressive meshes , 1996, SIGGRAPH.

[26]  Qiang Ji,et al.  Machine interpretation of CAD data for manufacturing applications , 1997, CSUR.

[27]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[28]  Jami J. Shah,et al.  A Discourse on Geometric Feature Recognition From CAD Models , 2001, J. Comput. Inf. Sci. Eng..