Abstract
This paper introduces a framework for the matching of 3D shapes represented by topological graphs. The method proposes as comparison algorithm an error tolerant graph isomorphism that includes a structured process for identifying matched areas on the input objects. Finally, we provide a series of experiments showing its capability to automatically compare complex objects starting from different skeletal representations used in Shape Modeling.
Chapter PDF
References
Attene, M., Biasotti, S., Spagnuolo, M.: Shape understanding by contour driven retiling. The Visual Computer 19(2-3), 128–137 (2003)
Biasotti, S., Marini, S., Mortara, M., Patané, G.: An overview on properties and efficacy of topological skeletons in shape modelling. In: Proc. of Shape Modelling and Applications 2003, Seoul, pp. 245–254. IEEE Press, Los Alamitos (2003)
Bunke, H., Shearer, K.: A graph distance metric based on the maximal common subgraph. Pattern Recognition Letters 19, 255–259 (1998)
Gold, S., Rangarajan, A.: A Graduated Assignment Algorithm for Graph Matching. IEEE Trans. on Patt. Anal. Mach. Intell. 18(4), 377–388 (1996)
Hétroy, F., Attali, D.: Topological Quadrangulations of Closed Triangulated Surfaces using the Reeb Graph. Graphical Models 65, 131–148 (2003)
Hilaga, M., Shinagawa, Y., Komura, T., Kunii, T.L.: Topology Matching for Fully Automatic Similarity Estimation of 3D Shapes. In: ACM Computer Graphics (Proc. of SIGGRAPH 2001), Los Angeles, pp. 203–212 (2001)
Kimia, B., Tannenbaum, A., Zucker, S.: Shapes, shocks, and deformations, I. Computer Vision 15, 189–224 (1995)
Koo, K.G., Suganthan, P.N.: Multiple Relational Graphs Mapping Using Genetic Algorithms. In: Proc. of Congr. on Evolutionary Comp, pp. 727–733 (2001)
Jones, R.: Connected Filtering and Segmentation Using Component Trees. Computer Vision and Image Understanding 75(3), 215–228 (1999)
Sundar, H., Silver, D., Gagvani, N., Dickinson, S.: Skeleton Based Shape Matching and retrieval. In: Proc. of Shape Modelling and Applications 2003, Seoul, pp. 130–139. IEEE Press, Los Alamitos (2003)
Lazarus, F., Verroust, A.: Level Set Diagrams of Polyhedral Objects. ACM Solid Modeling 1999, Ann Arbor, Michigan, pp. 130–140 (1999)
Luo, B., Hancock, E.R.: Symbolic Graph Matching using the EM Algorithm and Singular Value Decomposition. In: Proc. of Int. Conf. on Pattern Recognition, vol. 2, pp. 2141–2144 (2000)
Medasani, S., Krishnapuram, R., Choi, Y.: Graph Matching by Relaxation of Fuzzy Assignements. IEEE Trans. on Fuzzy Systems 9(1), 173–182 (2001)
Mortara, M., Patanè, G., Spagnuolo, M., Falcidieno, B., Rossignac, J.: Blowing bubbles for multi-scale analysis and decomposition of triangle meshes. In: Algorithmica, Special Issue on Shape Algorithmics. Springer, Heidelberg (to appear)
Messmer, B.T., Bunke, H.: A New Algorithm for Error Tolerant Subgraph Isomorphism Detection. IEEE Trans. Patt. Anal. Mach. Intell. 20(5), 493–504 (1998)
Milnor, J.: Morse Theory. Princeton University Press, New Jersey (1963)
Mortara, M., Patané, G.: Shape-Covering for Skeleton Extraction. Int. J. of Shape Modelling 8(2), 245–252 (2002)
Reeb, G.: Sur les points singuliers d’une forme de Pfaff complètement intégrable ou d’une fonction numérique. Comptes Rendu Acad. Sciences 222, 847–849 (1946)
Salembier, P., Oliveras, A., Garrido, L.: Anti-extensive connected operators for image and sequence processing. IEEE Trans. on Image Processing 7(4), 555–570 (1998)
Shattuck, D., Leahy, R.: Automated graph based analysis and correction of cortical vaolume topology. IEEE Trans. on Medical Imaging 20(11), 1167–1177 (2001)
Siddiqi, K., Shokoufandeh, A., Dickenson, S.J., Zucker Shock, S.W.: graphs and shape matching. In: Proc. of 6th Int. Conf on Computer Vision, pp. 222–229 (1998)
Veltkamp, R.C., Hagendoorn, M.: State-of-Art in Shape Matching. In: Lew, M. (ed.) IN Principles of Visual Information Retrieval, pp. 87–119. Springer, Heidelberg (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Biasotti, S., Marini, S., Mortara, M., Patanè, G., Spagnuolo, M., Falcidieno, B. (2003). 3D Shape Matching through Topological Structures. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds) Discrete Geometry for Computer Imagery. DGCI 2003. Lecture Notes in Computer Science, vol 2886. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39966-7_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-39966-7_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20499-2
Online ISBN: 978-3-540-39966-7
eBook Packages: Springer Book Archive