3D object comparison based on shape descriptors

Due to the recent improvements of 3D digitalisation, the number of 3D models available on the web is growing more and more, and there is an increasing demand for tools supporting the automatic search for 3D objects in digital archives. Existing methods for 3D shape retrieval roughly filter shape information and are mainly based on reasoning at the geometric level. In this paper, we discuss the advantages of approaching the shape matching problem through 3D graph descriptors, which describe the shape as a configuration of relevant subparts. In our approach, shapes are compared using a graph matching technique able to identify the most similar object portions. In particular, we investigate the properties of these descriptors and of our matching method in the CAD context.

[1]  Gabriella Sanniti di Baja,et al.  Curve skeletonization of surface-like objects in 3D images guided by voxel classification , 2002, Pattern Recognit. Lett..

[2]  Martti Mäntylä,et al.  Introduction to Solid Modeling , 1988 .

[3]  Sven J. Dickinson,et al.  Skeleton based shape matching and retrieval , 2003, 2003 Shape Modeling International..

[4]  Christoph M. Hoffmann,et al.  Geometric and Solid Modeling , 1989 .

[5]  Silvia Biasotti,et al.  An overview on properties and efficacy of topological skeletons in shape modeling , 2003, 2003 Shape Modeling International..

[6]  Tosiyasu L. Kunii,et al.  Surface coding based on Morse theory , 1991, IEEE Computer Graphics and Applications.

[7]  G. Renner,et al.  Medial surface generation and refinement , 1997 .

[8]  B KimiaBenjamin,et al.  Shapes, shocks, and deformations I , 1995 .

[9]  Alan Liu,et al.  3D/2D Registration via Skeletal Near Projective Invariance in Tubular Objects , 1998, MICCAI.

[10]  R. Pollack,et al.  Advances in Discrete and Computational Geometry , 1999 .

[11]  Richard E. Parent,et al.  Automated generation of control skeletons for use in animation , 2002, The Visual Computer.

[12]  Remco C. Veltkamp,et al.  Polyhedral Model Retrieval Using Weighted Point Sets , 2003, Int. J. Image Graph..

[13]  Tony DeRose,et al.  Multiresolution analysis for surfaces of arbitrary topological type , 1997, TOGS.

[14]  Ali Shokoufandeh,et al.  Indexing using a spectral encoding of topological structure , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[15]  Richard M. Leahy,et al.  Automated graph-based analysis and correction of cortical volume topology , 2001, IEEE Transactions on Medical Imaging.

[16]  Silvia Biasotti,et al.  3D Shape Matching through Topological Structures , 2003, DGCI.

[17]  Benjamin B. Kimia,et al.  On the Local Form and Transitions of Symmetry Sets, Medial Axes, and Shocks , 2004, International Journal of Computer Vision.

[18]  Jarek Rossignac,et al.  Blowing Bubbles for Multi-Scale Analysis and Decomposition of Triangle Meshes , 2003, Algorithmica.

[19]  M. Spagnuolo,et al.  Shape understanding by contour-driven retiling , 2003, The Visual Computer.

[20]  David P. Dobkin,et al.  A search engine for 3D models , 2003, TOGS.

[21]  Lee R. Nackman,et al.  Three-Dimensional Shape Description Using the Symmetric Axis Transform I: Theory , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  Dominique Attali,et al.  Computing and Simplifying 2D and 3D Continuous Skeletons , 1997, Comput. Vis. Image Underst..

[23]  Ching Y. Suen,et al.  Thinning Methodologies - A Comprehensive Survey , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  William S. Massey,et al.  Algebraic Topology: An Introduction , 1977 .

[25]  Alexander Russell,et al.  Computational topology: ambient isotopic approximation of 2-manifolds , 2003, Theor. Comput. Sci..

[26]  Ali Shokoufandeh,et al.  Scale-space representation of 3D models and topological matching , 2003, SM '03.

[27]  Anne Verroust-Blondet,et al.  Extracting skeletal curves from 3D scattered data , 1999, Proceedings Shape Modeling International '99. International Conference on Shape Modeling and Applications.

[28]  Taku Komura,et al.  Topology matching for fully automatic similarity estimation of 3D shapes , 2001, SIGGRAPH.

[29]  Deborah Silver,et al.  Parameter-Controlled Volume Thinning , 1999, Graph. Model. Image Process..

[30]  Jack Snoeyink,et al.  Computing contour trees in all dimensions , 2000, SODA '00.

[31]  Azriel Rosenfeld,et al.  Digital Geometry: Introduction and Bibliography , 1997 .

[32]  Ayellet Tal,et al.  Polyhedral surface decomposition with applications , 2002, Comput. Graph..

[33]  Arthur W. Toga,et al.  Eecient Skeletonization of Volumetric Objects , 1999 .

[34]  A. Ben Hamza,et al.  Geodesic Object Representation and Recognition , 2003, DGCI.

[35]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[36]  Ali Shokoufandeh,et al.  REEB GRAPH BASED SHAPE RETRIEVAL FOR CAD , 2003 .

[37]  Horst Bunke,et al.  A New Algorithm for Error-Tolerant Subgraph Isomorphism Detection , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[38]  Roddy MacLeod,et al.  Coarse Filters for Shape Matching , 2002, IEEE Computer Graphics and Applications.

[39]  A. Requicha.  GEOMETRIC MODELING : A First Course , 2022 .

[40]  D. Silver,et al.  Real-time volume manipulation , 2003 .

[41]  Dietmar Saupe,et al.  3D Model Retrieval with Spherical Harmonics and Moments , 2001, DAGM-Symposium.

[42]  Anne Verroust-Blondet,et al.  Level set diagrams of polyhedral objects , 1999, SMA '99.

[43]  Horst Bunke,et al.  A graph distance metric based on the maximal common subgraph , 1998, Pattern Recognit. Lett..

[44]  B. Falcidieno,et al.  Invited Lecture: A Shape Abstraction Paradigm for Modeling Geometry and Semantics , 1998 .

[45]  Gunilla Borgefors,et al.  On Digital Distance Transforms in Three Dimensions , 1996, Comput. Vis. Image Underst..

[46]  Herbert Edelsbrunner,et al.  Hierarchical morse complexes for piecewise linear 2-manifolds , 2001, SCG '01.

[47]  Bernard Chazelle,et al.  Matching 3D models with shape distributions , 2001, Proceedings International Conference on Shape Modeling and Applications.

[48]  Stina Svensson,et al.  Curve skeletonization of surface-like objects in 3D images guided by voxel classification , 2002 .

[49]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.