Abstract
New technologies for shape acquisition and rendering of digital shapes have simplified the process of creating virtual scenes; nonetheless, shape annotation, recognition and manipulation of both the complete virtual scenes and even of subparts of them are still open problems.
Once the main components of a virtual scene are represented by structural descriptions, this paper deals with the problem of comparing two (or more) sets of 3D objects, where each model is represented by an attributed graph. We will define a new distance to estimate the possible similarities among the sets of graphs and we will validate our work using a shape graph [1].
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References
Biasotti, S., Giorgi, D., Spagnuolo, M., Falcidieno, B.: Size functions for 3D shape retrieval. In: Eurographics Symposium on Geometry Processing, pp. 239–242 (2006)
Falcidieno, B., Spagnuolo, M.: A shape abstraction paradigm for modeling geometry and semantics. In: Computer Graphics International, pp. 646–657 (1998)
Torsello, A., Hidovic-Rowe, D., Pelillo, M.: Polynomial-time metrics for attributed trees. IEEE Trans. on Pattern Anlysis and Machine Intelligence 27(7), 1087–1099 (2005)
Bunke, H., Shearer, K.: A graph distance metric based on the maximal common subgraph. Pattern Recognition Letters 19, 255–259 (1998)
Fernández, M.L., Valiente, G.: A graph distance metric combining maximum common subgraph and minimum common supergraph. Pattern Recognition Letters 22, 753–758 (2001)
Marini, S., Spagnuolo, M., Falcidieno, B.: From exact to approximate maximum common subgraph. In: Brun, L., Vento, M. (eds.) GbRPR 2005. LNCS, vol. 3434, pp. 263–272. Springer, Heidelberg (2005)
Shokoufandeh, A., Macrini, D., Dickinson, S., Siddiqi, K., Zucker, S.W.: Indexing hierarchical structures using graph spectra. IEEE Trans. on Pattern Anlysis and Machine Intelligence 27(7), 1125–1140 (2005)
Robles-Kelly, A., Hancock, E.R.: Graph matching using adjacency matrix Markov chains. In: The British Machine Vision Conference, University of Manchester, Manchester, UK, pp. 383–390 ( 2001)
Wilson, R.C., Hancock, E.R., Luo, B.: Pattern vectors from algebraic graph theory. IEEE Trans. on Pattern Anlysis and Machine Intelligence 27, 1112–1124 (2005)
Bapat, R.B.: Distance matrix and Laplacian of a tree with attached graphs. Linear Algebra and its Applications 411, 295–308 (2005)
Demirci, M.F., Shokoufandeh, A., Keselman, Y., Bretzner, L., Dickinson, S.: Object recognition as many-to-many feature matching. International Journal of Computer Vision 69(2), 203–222 (2006)
Rubner, Y., Tomasi, C., Guibas, L.J.: The earth mover’s distance as a metric for image retrieval. International Journal of Computer Vision 40(2), 99–121 (2000)
Paraboschi, L., Biasotti, S., Falcidieno, B.: 3d scene comparison using topological graphs. In: Eurographics Italian Chapter, Trento (Italy), pp. 87–93 (2007)
Horaud, R., Sossa, H.: Polyhedral object recognition by indexing. Pattern Recognition 28(12), 1855–1870 (1995)
Mohar, B.: The Laplacian spectrum of graphs. Graph Theory, Combinatorics, and Applications 2, 871–898 (1991)
Franklin, J.N.: Matrix theory. Dover Publications, Mineola (1993)
Chen, D., Ouhyoung, M., Tian, X., Shen, Y.: On visual similarity based 3D model retrieval. Computer Graphics Forum 22, 223–232 (2003)
Kazhdan, M., Funkhouser, T., Rusinkiewicz, S.: Rotation invariant spherical harmonic representation of 3D shape descriptors. In: Eurographics Symposium on Geometry Processing, pp. 167–175 ( 2003)
Dong, S., Bremer, P.T., Garland, M., Pascucci, V., Hart, J.C.: Spectral surface quadrangulation. ACM Trans. on Graphics 25(3), 1057–1066 (2006)
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Paraboschi, L., Biasotti, S., Falcidieno, B. (2007). Comparing Sets of 3D Digital Shapes Through Topological Structures. In: Escolano, F., Vento, M. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2007. Lecture Notes in Computer Science, vol 4538. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72903-7_11
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DOI: https://doi.org/10.1007/978-3-540-72903-7_11
Publisher Name: Springer, Berlin, Heidelberg
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