Shape similarity assessment is a fundamental geometric reasoning problem that finds application in several different product design and manufacturing applications. A computationally efficient way to assess shape similarity is to first abstract 3D object shapes into shape signatures and use shape signatures to perform similarity assessment. Several different types of shape signatures have been developed in the past. This paper provides a survey of existing algorithms for computing and comparing shape signatures. Our survey consists of a description of the desired properties of shape signatures, a scheme for classifying different types of shape signatures, and descriptions of representative algorithms for computing and comparing shape signatures. This survey concludes by identifying directions for future research.
Issue Section:
Technical Papers
1.
Alva
, U.
, and Gupta
, S. K.
, 2001
, “Automated Design of Sheet Metal Punches for Bending Multiple Parts in a Single Setup.
” Rob. Comput.-Integr. Manufact.
, 17
(1/2
), pp. 33
–47
.2.
Gupta
, S. K.
, and Bourne
, D. A.
, 1999
, “Sheet Metal Bending: Generating Shared Setups.
” ASME J. Manuf. Sci. Eng.
, 121
, pp. 689
–694
, November.3.
Burbidge J. L., 1975, The Introduction of Group Technology. Heinemann, London.
4.
Santini, S., and Jain, R., 1995, “Similarity Matching,” In 2nd Asian Conference on Computer Vision, Singapore, December.
5.
Arbter
, K.
, Snyder
, W. E.
, Burkhardt
, H.
, and Hirzinger
, G.
, 1990
, “Application of Affine-invariant Fourier Descriptors to Recognition of 3-D Objects.
” IEEE Trans. Pattern Anal. Mach. Intell.
, 12
(7
), pp. 640
–647
, July.6.
Arkin
, E. M.
, Chew
, L. P.
, Huttenlocher
, D. P.
, Kedem
, K.
, and Mitchell
, J. S.
, 1991
, “An Efficiently Computable Metric for Comparing Polygonal Shapes.
” IEEE Trans. Pattern Anal. Mach. Intell.
, 13
(3
), pp. 209
–216
, March.7.
Young
, I.
, Walker
, J.
, and Bowie
, J.
, 1974, “An Analysis Technique for Biological Shape.” Information and Control, 25(4), pp. 357–370, August.8.
Lin
, Y.
, Dou
, J.
, and Wang
, H.
, 1992
, “Contour Shape Description Based on Arch Height Function.
” Pattern Recogn.
, 25
(1
), pp. 17
–23
.9.
Alt, H., and Guibas, L. J., 1996, Discrete Geometric Shapes: Matching, Interpolation, and Approximation: A Survey. Technical Report B96-11, EVL-1996-142, Institute of Computer Science, Freie Universita¨t Berlin, December.
10.
Loncaric
, S.
, 1998
, “A Survey of Shape Analysis Techniques.
” Pattern Recogn.
, 31
(8
), pp. 983
–1001
, August.11.
Veltkmap, R. C., 2001, “Shape Matching: Similarity Measures and Algorithms.” In International Conference on Shape Modeling and Applications, Genova, Italy, May.
12.
Keim, D. A., 1999, “Efficient Geometry-based Similarity Search of 3D Spatial Databases.” In ACM SIGMOD International Conference on Management of Data, Philadelphia, PA, June.
13.
Arman
, F.
, and Aggrawal
, J.
, 1993
, “Model-based Object Recognition in Dense-range Images-A Review.
” ACM Comput. Surv.
, 25
(1
), pp. 5
–43
, March.14.
Chew
, L. P.
, Goodrich
, M. T.
, Huttenlocher
, D. P.
, Kedem
, K.
, Kleinberg
, J. M.
, and Kravets
, D.
, 1997, “Geometric Pattern Matching under Euclidean Motion.” Computational Geometry: Theory and Application, 7(1-2), pp. 113–124, January.15.
Rubner, Y., Tomasi, C., and Guibas, L., 1998, “A Metric for Distributions with Applications to Image Databases.” In 6th International Conference on Computer Vision, Bombay, India, January.
16.
Siddiqi
, K.
, Shokoufandeh
, A.
, Dickenson
, S. J.
, and Zucker
, S. W.
, 1998
, “Shock Graphs and Shape Matching.
” Int. J. Comput. Vis.
, 35
(1
), pp. 13
–32
, November.17.
Thacker
, N.
, Riocreux
, P.
, and Yates
, R.
, 1995, “Assessing the Completeness Properties of Pairwise Geometric Histograms.” Image and Vision Computing, 13(5), pp. 423–429, June.18.
Zhang, D., and Hebert, M., 1999, “Harmonic Maps and Their Applications in Surface Matching.” In IEEE Conference on Computer Vision and Pattern Recognition, Fort Collins, CO, June.
19.
Mori G., Belongie S., and Malik J., 2001, “Shape Contexts Enable Efficient Retrieval of Similar Shapes.” In IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Kauai Marriott, Hawaii, December.
20.
Ramesh
, M.
, Yip-Hoi
, D.
, and Dutta
, D.
, 2001
, “Feature-based Shape Similarity Measurement for Retrieval of Mechanical Parts.
” J. Comput. Inf. Sci. Eng.
, 1
(3
), pp. 245
–256
, September.21.
Cicirello, V. A., and Regli, W. C., 2001, “Machining Feature-based Comparisons of Mechanical Parts.” In International Conference on Shape Modeling and Applications, Genova, Italy, May.
22.
Elinson, A., Nau, D. S., and Regli, W. C., 1997, “Feature-based Similarity Assessment of Solid Models.” In 4th Symposium on Solid Modeling and Applications, Atlanta, GA, May.
23.
Elinson, A., Nau D., and Regli, W. C., 1996, “Solid Similarity Measurements.” Technical report ISR-TR96-63, Institute for Systems Research, University of Maryland.
24.
Srinivas, G., Fasse, D. E., and Marefat, M. M., 1998, “Retrieval of Similarly Shaped Parts from a CAD Database.” In IEEE International Conference on Systems, Man, and Cybernetics, San Diego, CA, October.
25.
Hebert
, M.
, Ikeuchi
, K.
, and Delingette
, H.
, 1995
, “A Spherical Representation for Recognition of Free-form Surfaces.
” IEEE Trans. Pattern Anal. Mach. Intell.
, 17
(7
), pp. 681
–690
, July.26.
Huttenlocher, D., and Kedem, K., 1990, “On Computing the Minimum Hausdorff Distance for Point Sets Under Translation.” In 6th ACM Symposium Computational Geometry, Berkeley, CA, June.
27.
Shum, H., Hebert, M., and Ikeuchi, K., 1996, “On 3d Shape Similarity.” In IEEE Conference on Computer Vision and Pattern Recognition, San Francisco, CA, June.
28.
Schwarz
, J.
, and Scharir
, M.
, 1987
, “Identification of Partially Obscured Objects in Two and Three Dimensions by Matching Noisy Characteristic Curves.
” Int. J. Robot. Res.
, 6
(2
), pp. 29
–44
, Summer.29.
Tuzikov
, A. V.
, Roerdink
, J. B. T. M.
, and Heijmans
, H. J. A. M.
, 2000
, “Similarity Measures for Convex Polyhedra Based on Minkowski Addition.
” Pattern Recogn.
, 33
(6
), pp. 979
–995
, June.30.
Ghosh
, P. K.
, and Haralick
, R. M.
, 1996
, “Mathematical Morphological Operations of Boundary-represented Geometric Objects.
” J. Math. Imaging Vision
, 6
(2–3
), pp. 199
–222
, June.31.
Grunbaum, B., 1967, Convex Polytopes. Interscience publishers.
32.
Ghosh
, P. K.
, 1993
, “A Unified Computational Framework for Minkowski Operations.
” Comput. Graphics
, 17
(4
), pp. 357
–378
.33.
Osada, R., Funkhouser T., Chazelle, B., and Dobkin, D., 2001, “Matching 3D Models with Shape Distributions.” In International Conference on Shape Modeling and Applications, Genova, Italy, May.
34.
Shen
, H. C.
, and Wong
, A. K. C.
, 1983
, “Generalized Texture Representation and Metric.
” Comput. Vis. Graph. Image Process.
, 23
(2
), pp. 187
–206
, August.35.
Werman
, M.
, Peleg
, S.
, and Rosenfeld
, A.
, 1985
, “A Distance Metric for Multidimensional Histograms.
” Comput. Vis. Graph. Image Process.
, 32
(3
), pp. 328
–336
, December.36.
Ip, Cheuk Yiu, Lapadat, D., Sieger, L., and Regli, W. C., 2002, “Using Shape Distributions to Compare Solid Models.” In 7th Syposium on Solid Modeling and Applications, Saarbru¨cken, Germany, June.
37.
Kaparthi
, S.
, and Suresh
, N. C.
, 1991
, “A Neural Network System for Shape Based Classification and Coding of Rotational Part.
” Int. J. Prod. Res.
, 29
(9
), pp. 1771
–1784
.38.
Khanna, T., 1990, Foundations of Neural Networks. Addison Wesley.
39.
Lippmann
, R. P.
, 1989
, “Pattern Classification Using Neural Networks.
” IEEE Commun. Mag.
, 27
(11
), pp. 47
–64
, November.40.
Anderson, J. A., and Rosenfeld, E., 1988, Neurocomputing—Foundations of Research. MIT Press, Cambridge, MA.
41.
Chung
, Y.
, and Kusiak
, A.
, 1994
, “Grouping Parts with a Neural Network.
” J. Manuf. Syst.
, 13
(4
), pp. 262
–275
.42.
Hecht-Nielsen, R., 1989, “Theory of Backpropagation Neural Networks.” In IEEE International Joint Conference on Neural Networks, Washington D.C., June.
43.
McWherter, D., Peabody, M., Shokoufandeh, A., and Regli, W. C., 2001, “Database Techniques for Archival of Solid Models,” In 6th ACM/SIGGRAPH Symposium on Solid Modeling and Applications, Ann Arbor, MI, June.
44.
Joshi
, S.
, and Chang
, T. C.
, 1988
, “Graph-based Heuristics for Recognition of Machined Features from a 3D Solid Model
,” Comput.-Aided Des.
, 20
, pp. 58
–66
.45.
Chung, F. R. K., 1997, “Spectral Graph Theory.” In American Mathematical Society’s Regional Conference Series in Mathematics No. 92, Providence, RI.
46.
McWherter, D., Peabody, M., Regli, W. C., and Shokoufandeh, A., 2001, “Transformation Invariant Shape Similarity Comparison of Solid Models.” In ASME 6th Design for Manufacturing Conference, Pittsburgh, PA, Sept.
47.
Reeb
, G.
, 1946
, “On the Singular Points of a Completely Integrable Pfaff Form or of a Numerical Function.
” Acad. Sci., Paris, C. R.
, 222
, pp. 847
–849
.48.
Lazarus, F., and Verroust, A., 1999, “Level Set Diagrams of Polyhedral Objects.” In ACM Solid Modeling, Ann Arbor, MI, June.,
49.
Takahashi, S., Shinagawa Y., and Kunii, T. L., 1997, “A Feature-based Approach for Smooth Surfaces,” In 4th ACM Symposium on Solid Modeling and Applications, Atlanta, GA, May.
50.
Hilaga, M., Shinagawa Y., Kohmura, Taku, and Kunii, T. L., 2001, “Topology Matching for Fully Automatic Similarity Estimation of 3D Shapes.” In ACM SIGGRAPH, Los Angeles, CA, August.
51.
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 Design for Manufacturing Symposium, ASME Design Technical Conference, Boston, MA, September.
52.
Tsai
, W. H.
, and Yu
, S. S.
, 1985
, “Attributed String Matching with Merging for Shape Recognition.
” IEEE Trans. Pattern Anal. Mach. Intell.
, 7
(4
), pp. 453
–462
, July.53.
Rea, H. J., Corney, J. R., Clark, D. E. R., Pritchard, J., Breaks, M. L., and MacLeod, R. A., 2001, “Part-Sourcing in a Global Market,” In 2001 Interna-tional Conference on eCommerce Engineering, IceCE 2001, Xi’an, P. R. China, September.
54.
Sung, R., Rea, H. J. Corney, J. R., Clark, D. E. R., Pritchard, J., Breaks, M. L., and MacLeod R. A., 2002, “Assessing the Effectiveness of Filters for Shape Matching.” In 2002 ASME International Mechanical Engineering Congress & Exposition, IMECE ’02. New Orleans, LA, November.
Copyright © 2003
by ASME
You do not currently have access to this content.
