This paper presents a framework for shape matching and classification through scale-space decomposition of 3D models. The algorithm is based on recent developments in efficient hierarchical decomposition of a point distribution in metric space using its spectral properties. Through spectral decomposition, we reduce the problem of matching to that of computing a mapping and distance measure between vertex-labeled rooted trees. We use a dynamic programming scheme to compute distances between trees corresponding to solid models. Empirical evaluation of the algorithm on an extensive set of 3D matching trials demonstrates both robustness and efficiency of the overall approach. Lastly, a technique for comparing shape matchers and classifiers is introduced and the scale-space method is compared with six other known shape matching algorithms.
Issue Section:
Research Papers
1.
Han
, J.-H.
, Regli
, W. C.
, and Pratt
, M. J.
, 2000
, “Algorithms for Feature Recognition from Solid Models: A Status Report
,” IEEE J. Rob. Autom.
, 16
(6
), pp. 782
–796
.2.
Shah
, J.
, Anderson
, D.
, Kim
, Y. S.
, and Joshi
, S.
, 2001
, “A Discourse on Geometric Feature Recognition from cad Models
,” ASME J. Comput. Inf. Sci. Eng.
, 1
(1
), pp. 41
–51
.3.
Elinson, A., Nau, D. S., and Regli, W. C., 1997. “Feature-based Similarity Assessment of Solid Models,” In Fourth Symposium on Solid Modeling and Applications, C. Hoffman and W. Bronsvoort, Eds., ACM, ACM Press, pp. 297–310. Atlanta, GA.
4.
Regli
, W. C.
, and Cicirello
, V.
, 2000
, “Managing Digital Libraries for Computer-aided Design
,” Comput.-Aided Des.
, 32
(2
), pp. 119
–132
. Special Issue on CAD After 2000. Mohsen Rezayat, Guest Editor.5.
Cicirello, V., and Regli, W. C., 1999. “Resolving Non-uniqueness in Design Feature Histories,” In Fifth Symposium on Solid Modeling and Applications, D. Anderson and W. Bronsvoort, Eds., ACM, ACM Press. Ann Arbor, MI.
6.
Cicirello, V. A., 1999, “Intelligent Retrieval of Solid Models,” Master’s thesis, Drexel University, Geometric and Intelligent Computing Laboratory, Department of Mathematics and Computer Science, Philadelphia, PA 19104, June 1999.
7.
Cicirello, V., and Regli, W., 2001. “Machining Feature-based Comparisons of Mechanical Parts,” In International Conference on Shape Modeling and Applications, ACM SIGGRAPH, the Computer Graphics Society and EURO-GRAPHICS, IEEE Computer Society Press, pp. 176–187.
8.
Cicirello
, V.
, and Regli
, W. C.
, 2002
, “An Approach to a Feature-based Comparison of Solid Models of Machined Parts
,” Artificial Intelligence for Engineering Design, Analysis, and Manufacturing (AIEDAM)
, 16
(5
) [November], pp. 385
–399
.9.
Ramesh, M. M., Yip-Hoi, D., and Dutta, D., 2000, “A Decomposition Methodology for Machining Feature Extraction,” In ASME Design Engineering Technical Conferences, Computers in Engineering Conference, American Association of Mechanical Engineers, ASME Press. DETC2000/CIE-14645.
10.
Sun, T.-L., Su, C.-J., Mayer, R. J., and Wysk, R. A., 1995, “Shape Similarity Assessment of Mechanical Parts Based on Solid Models,” In ASME Design for Manufacturing Conference, Symposium on Computer Integrated Concurrent Design, R. Gadh, Ed., ASME, pp. 953–962.
11.
McWherter, D., Peabody, M., Shokoufandeh, A., and Regli, W., 2001. “Transformation Invariant Similarity Assessment of Solid Models,” In ASME Design Engineering Technical Conferences, ASME, ASME Press. DETC2001/DFM-21191.
12.
McWherter
, D.
, Peabody
, M.
, Shokoufandeh
, A.
, and Regli
, W.
, 2001
, “Solid Model Databases: Techniques and Empirical Results
,” ASME J. Comput. Inf. Sci. Eng.
1
(4
), pp. 300
–310
.13.
McWherter, D., Peabody, M., Shokoufandeh, A., and Regli, W., 2001. “Database Techniques for Indexing and Clustering of Solid Models,” In Sixth ACM/SIGGRAPH Symposium on Solid Modeling and Applications, D. Dutta and H.-P. Seidel, Eds., ACM, ACM Press, pp. 78–87.
14.
Snead, C. S., 1989. Group Technology: Foundations for Competitive Manufacturing. Van Nostrand Reinhold, New York.
15.
Ames, A. L., 1991, “Production Ready Feature Recognition Based Automatic Group Technology Part Coding,” In Symposium on Solid Modeling Foundations and CAD/CAM Applications, J. Rossignac and J. Turner, Eds., ACM SIGGRAPH, ACM Press, pp. 161–169.
16.
Shah
, J. J.
, and Bhatnagar
, A.
, 1989
, “Group Technology Classification from Feature-based Geometric Models
,” Manufacturing Rev.
2
(3
), pp. 204
–213
.17.
Bond, A., and Jain, R., 1988, “The Formal Definition and Automatic Extraction of Group Technology Codes,” In ASME Design Technical Conferences, Computers in Engineering Conference, pp. 537–542.
18.
Henderson
, M.
, and Musti
, S.
, 1988
, “Automated Group Technology Part Coding from a Three-dimensional Cad Database
,” J. Eng. Ind.
, 110
(3
), pp. 278
–287
.19.
Ham
, I.
, Marion
, D.
, and Rubinovich
, J.
, 1986
, “Developing a Group Technology Coding and Classification Scheme
,” Ind. Eng. (N. Y., 1922-1931)
, 18
(7
), pp. 90
–97
.20.
The Digital Michelangelo Project, http://graphics.stanford.edu/projects/mich/.
21.
Thompson, W. B., Riesenfeld, R. F., and Owen, J. C., 1996, “Determining the Similarity of Geometric Models,” In Proceedings of the ARPA Image Understanding Workshop.
22.
Thompson
, W. B.
, Owen
, J.
, de St. Germain
, H.
, Stark
, S.
Jr.,, and Henderson
, T.
, 1999
, “Feature-based Reverse Engineering of Mechanical Parts
,” IEEE J. Rob. Autom.
, 12
(1
), pp. 57
–66
.23.
Hilaga, M., Shinagawa, Y., Kohmura, T., and Kunii, T. L., 2001, “Topology Matching for Fully Automatic Similarity Estimation of 3D Shapes,” In SIGGRAPH, ACM Press, pp. 203–212.
24.
Osada, R., Funkhouser, T., Chazelle, B., and Dobkin, D., 2001, “Matching 3D Models with Shape Distributions,” In International Conference on Shape Modeling and Applications, 154–166, Ed., ACM SIGGRAPH, the Computer Graphics Society and Eurographics, IEEE Computer Society Press.
25.
Osada
, R.
, Funkhouser
, T.
, Chazelle
, B.
, and Dobkin
, D.
, 2002
, “Shape Distributions
,” ACM Trans. Graphics, 21(4).26.
Funkhouser
, T.
, Min
, P.
, Kazhdan
, M.
, Chen
, J.
, Halderman
, A.
, Dobkin
, D.
, and Jacobs
, D.
, 2003
, “A Search Engine for 3D Models
,” ACM Trans. Graphics, 22(1).27.
Kazhdan, M., Chazelle, B., Dobkin, D., Funkhouser, T., and Rusinkiewicz, S., 2003, “A Reflective Symmetry Descriptor for 3D Models,” Algorithmica, To appear.
28.
Kazhdan, M., Funkhouser, T., and Rusinkiewicz, S., 2003, “Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors,” In Symposium on Geometry Processing.
29.
Kazhdan, M., Funkhouser, T., and Rusinkiewicz, S., 2002, “Harmonic 3D Shape Matching,” In SIGGRAPH.
30.
Elad, M., Tal, A., and Ar, S., 2001, “Content Based Retrieval of VRML Objects—An Iterative and Interactive Approach,” In The Sixth Eurographics Workshop in Multimedia, pp. 97–108.
31.
Ip, C. Y., Lapadat, D., Sieger, L., and Regli, W., 2002. “Using Shape Distributions to Compare Solid Models,” In Seventh ACM/SIGGRAPH Symposium on Solid Modeling and Applications, H.-P. Seidel, Ed., ACM, ACM Press, pp. 273–280.
32.
Ip, C. Y., Sieger, L., Regli, W., and Shokoufandeh, A., 2003, “Automated Learning of Model Classifications,” In Eighth ACM/SIGGRAPH Symposium on Solid Modeling and Applications, G. Elber and V. Shapiro, Eds., ACM, ACM Press, pp. 322–327.
33.
Cyr, C. M., and Kimia, B. B., 2001, “3D Object Recognition Using Shape Similarity-based Aspect Graph,” In Proceedings of the Eighth International Conference On Computer Vision (ICCV-01), pp. 254–261.
34.
Shapiro
, L. G.
, and Haralick
, R. M.
, 1981
, “Structural Descriptions and Inexact Matching
,” IEEE Trans. Pattern Anal. Mach. Intell.
, 3
, pp. 504
–519
.35.
Kim
, W.
, and Kak
, A. C.
, 1991
, “3D Object Recognition Using Bipartite Matching Embedded in Discrete Relaxation
,” IEEE Trans. Pattern Anal. Mach. Intell.
, 13
(3
), pp. 224
–251
.36.
Pelillo
, M.
, Siddiqi
, K.
, and Zucker
, S.
, 1999
, “Matching Hierarchical Structures Using Association Graphs
,” IEEE Trans. Pattern Anal. Mach. Intell.
, 21
(11
) [November], pp. 1105
–1120
.37.
Gold
, S.
, and Rangarajan
, A.
, 1996
, “A Graduated Assignment Algorithm for Graph Matching
,” IEEE Trans. Pattern Anal. Mach. Intell.
, 18
(4
), pp. 377
–388
.38.
Siddiqi
, K.
, Shokoufandeh
, A.
, Dickinson
, S.
, and Zucker
, S.
, 1999
, “Shock Graphs and Shape Matching
,” Int. J. Comput. Vis.
, 30
, pp. 1
–24
.39.
Shokoufandeh, A., Dickinson, S., Jo¨nsson, C., Bretzner, L., and Lindeberg, T., 2002, “On the Representation and Matching of Qualitative Shape at Multiple Scales,” In Proceedings, 7th European Conference on Computer Vision, vol. 3, pp. 759–775.
40.
Luo
, B.
, and Hancock
, E. R.
, 2001
, “Structural Matching Using the EM Algorithm and Singular Value Decomposition
,” IEEE Trans. Pattern Anal. Mach. Intell.
, 23
, pp. 1120
–1136
.41.
Veltkamp, R. C., 2001, “Shape Matching: Similarity Measures and Algorithms,” In International Conference on Shape Modeling and Applications, 188–197, Ed., ACM SIGGRAPH, the Computer Graphics Society and EUROGRAPH-ICS, IEEE Computer Society Press pp.
42.
Tangelder, J. W., and Veltkamp, R. C., “Polyhedral Model Comparison and Retrieval Using Weighted Point Sets,” In The eight annual conference of the Advanced School for Computing and Imaging, pp. 223–230.
43.
Cormen, T. H., Leiserson, C. L., and Rivest, R. L., 2001, Introduction to Algorithms, MIT Press.
44.
Thomasian, A., Castelli, V., and Li, C.-S., 1998, “Clustering and Singular Value Decomposition for Approximate Indexing in High Dimensional Spaces,” In The Seventh International Conference on Information and Knowledge Management Table of Contents, pp. 201–207.
45.
Golub, G. H., and van Loan, C. F., 1989, Matrix Computations. John Hopkins Press.
46.
Wang
, J. T. L.
, Shapiro
, B. A.
, Shasha
, D.
, Zhang
, K.
, and Currey
, K. M.
, 1998
, “An Algorithm for Finding the Largest Approximately Common Substructures of Two Trees
,” IEEE Trans. Pattern Anal. Mach. Intell.
, 20
, pp. 889
–895
.47.
Novotni, M., and Klein, R., 2003. “3D Zernike Descriptors for Content Based Shape Retrieval,” In Proceedings of the eighth ACM symposium on Solid modeling and applications, ACM Press, pp. 216–225.
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