Abstract
Combining the properties of conformal geometry and graph-based topological information, a non-rigid 3D object retrieval methodology is proposed, which is both robust and efficient in terms of retrieval accuracy and computation speed. While graph-based methods are robust to non-rigid object deformations, they require intensive computation which can be reduced by the use of appropriate representations, addressed through geometry-based methods. In this respect, we present a 3D object retrieval methodology, which combines the above advantages in a unified manner. Furthermore, we propose a string matching strategy for the comparison of graphs which describe 3D objects.
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Agathos, A., Pratikakis, I., Papadakis, P., Perantonis, S.J., Azariadis, P.N., Sapidis, N.S.: 3D articulated object retrieval using a graph-based representation. Vis. Comput. 1301–1319 (2010)
Beckman, F.S. Jr.: On isometries of Euclidean spaces. Proc. Am. Math. Soc. 4(5), 810–815 (1953). doi:10.2307/2032415
Ben-Chen, M., Gotsman, C.: Characterizing shape using conformal factors. In: 3DOR, pp. 1–8 (2008)
Biasotti, S., Giorgi, D., Spagnuolo, M., Falcidieno, B.: Reeb graphs for shape analysis and applications. Theor. Comput. Sci. 392(1–3), 5–22 (2008)
Biasotti, S., Patané, G., Spagnuolo, M., Falcidieno, B., Barequet, G.: Shape approximation by differential properties of scalar functions. Comput. Graph. 34, 252–262 (2010). doi:10.1016/j.cag.2010.03.013
Bimbo, A.D., Pala, P.: Content-based retrieval of 3D models. ACM Trans. Multimed. Comput. Commun. Appl. 2, 20–43 (2006)
Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Efficient computation of isometry-invariant distances between surfaces. SIAM J. Sci. Comput. 28, 1812–1836 (2006). doi:10.1137/050639296
Bronstein, A., Bronstein, M., Kimmel, R.: Numerical Geometry of Non-Rigid Shapes, 1 edn. Springer, Berlin (2008)
Bronstein, A.M., Bronstein, M.M., Kimmel, R., Mahmoudi, M., Sapiro, G.: A Gromov-hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching. Int. J. Comput. Vis. 89, 266–286 (2010)
Carlsson, G., Zomorodian, A., Collins, A., Guibas, L.: Persistence barcodes for shapes. In: Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, SGP’04, pp. 124–135. ACM Press, New York (2004)
Chen, D.Y., Shen, Y.T., Tian, X.P., Ouhyoung, M.: On visual similarity based 3D model retrieval. In: Eurographics Computer Graphics Forum, pp. 223–232 (2003)
Cole-McLaughlin, K., Edelsbrunner, H., Harer, J., Natarajan, V., Pascucci, V.: Loops in reeb graphs of 2-manifolds. Discrete Comput. Geom. 32, 231–244 (2004). doi:10.1007/s00454-004-1122-6. http://portal.acm.org/citation.cfm?id=1013907.1013914
de Berg, M., van Kreveld, M.: Trekking in the alps without freezing or getting tired. In: Lengauer, T. (ed.) Algorithms—ESA’93. Lecture Notes in Computer Science, vol. 726, pp. 121–132. Springer, Berlin/Heidelberg (1993)
Dey, T., Giesen, J., Goswami, S.: Shape segmentation and matching with flow discretization. In: Algorithms and Data Structures. Lecture Notes in Computer Science, vol. 2748, pp. 25–36. Springer, Berlin/Heidelberg (2003)
Elad, A., Kimmel, R.: On bending invariant signatures for surfaces. IEEE Trans. Pattern Anal. Mach. Intell. 25(10), 1285–1295 (2003). doi:10.1109/TPAMI.2003.1233902
Floyd, R.W.: Algorithm 97: shortest path. Commun. ACM 5, 345 (1962). doi:10.1145/367766.368168
Gal, R., Shamir, A., Cohen-Or, D.: Pose-oblivious shape signature. IEEE Trans. Vis. Comput. Graph. 13(2), 261–271 (2007)
Giorgi, D., Biasotti, S., Paraboschi, L.: Shape retrieval contest 2007: watertight models track. In: Veltkamp, R.C., ter Haar, F.B (eds.) SHREC 2007: 3D Shape Retrieval Contest. Technical Report UU-CS-2007-015, pp. 5–10. Utrecht University, Utrecht (2007)
Hamza, A.B., Krim, H.: Geodesic object representation and recognition. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds.) Discrete Geometry for Computer Imagery. Lecture Notes in Computer Science, vol. 2886, pp. 378–387. Springer, Berlin/Heidelberg (2003)
Hilaga, M., Shinagawa, Y., Kohmura, T., Kunii, T.L.: Topology matching for fully automatic similarity estimation of 3D shapes. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH’01, pp. 203–212. ACM Press, New York (2001)
Jain, V., Zhang, H.: A spectral approach to shape-based retrieval of articulated 3D models. Comput. Aided Des. 39, 398–407 (2007)
Järvelin, K., Kekäläinen, J.: Cumulated gain-based evaluation of ir techniques. ACM Trans. Inf. Syst. 20, 2002 (2002)
Kazhdan, M., Funkhouser, T., Rusinkiewicz, S.: Rotation invariant spherical harmonic representation of 3D shape descriptors. In: SGP’03: Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 156–164. Eurographics Association, Aire-la-Ville (2003)
Kim, D., Park, I., Yun, I., Lee, S.: A new mpeg-7 standard: perceptual 3-d shape descriptor. In: Aizawa, K., Nakamura, Y., Satoh, S. (eds.) Advances in Multimedia Information Processing—PCM 2004. Lecture Notes in Computer Science, vol. 3332, pp. 238–245. Springer, Berlin/Heidelberg (2005)
Kuhn, H.W.: The Hungarian method for the assignment problem. In: J’únger, M., Liebling, T.M., Naddef, D., Nemhauser, G.L., Pulleyblank, W.R., Reinelt, G., Rinaldi, G., Wolsey, L.A. (eds.) 50 Years of Integer Programming 1958–2008, pp. 29–47. Springer, Berlin/Heidelberg (2010)
Lian, Z., Godil, A., Fabry, T., Furuya, T., Hermans, J., Ohbuchi, R., Shu, C., Smeets, D., Suetens, P., Vandermeulen, D., Wuhrer, S.: SHREC’10 track: non-rigid 3D shape retrieval. In: Daoudi, M., Schreck, T., Spagnuolo, M., Pratikakis, I., Veltkamp, R.C., Theoharis, T. (eds.) 3DOR, pp. 101–108. Eurographics Association, Aire-la-Ville (2010)
Lian, Z., Godil, A., Bustos, B., Daoudi, M., Hermans, J., Kawamura, S., Kurita, Y., Lavoué, G., Nguyen, H.V., Ohbuchi, R., Ohkita, Y., Ohishi, Y., Reuter, F.P.M., Sipiran, I., Smeets, D., Suetens, P., Tabia, H., Vandermeulen, D.: SHREC’11 track: shape retrieval on non-rigid 3D watertight meshes. In: 3DOR’11, pp. 79–88 (2011)
Mademlis, A., Daras, P., Tzovaras, D., Strintzis, M.G.: 3D object retrieval using the 3D shape impact descriptor. Pattern Recognit. 42, 2447–2459 (2009)
Meyer, M., Desbrun, M., Schroder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. Math. Vis. 3, 1–26 (2002)
Papadakis, P., Pratikakis, I., Perantonis, S., Theoharis, T.: 3D object retrieval using an efficient and compact hybrid shape descriptor. In: Eurographics Workshop on 3D Object Retrieval, pp. 9–16 (2008)
Papadakis, P., Pratikakis, I., Theoharis, T., Perantonis, S.: PANORAMA: a 3D shape descriptor based on panoramic views for unsupervised 3D object retrieval. Int. J. Comput. Vis. 89, 177–192 (2009). doi:10.1007/s11263-009-0281-6
Peyré, G., Cohen, L.D.: Geodesic remeshing using front propagation. Int. J. Comput. Vis. 69, 145–156 (2006). doi:10.1007/s11263-006-6859-3
Reuter, M., Wolter, F.E., Peinecke, N.: Laplace-beltrami spectra as ‘shape-dna’ of surfaces and solids. Comput.-Aided Des. 38, 342–366 (2006). doi:10.1016/j.cad.2005.10.011. Symposium on Solid and Physical Modeling 2005
Rustamov, R.M.: Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Proceedings of the fifth Eurographics Symposium on Geometry Processing, pp. 225–233. Eurographics Association, Aire-la-Ville (2007). http://portal.acm.org/citation.cfm?id=1281991.1282022
Sebastian, T.B., Klein, P.N., Kimia, B.B.: Recognition of shapes by editing shock graphs. In: IEEE International Conference on Computer Vision, pp. 755–762 (2001)
Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics. Computer Vision, and Materials Science, vol. 11. Cambridge University Press, Cambridge (1999). http://www.amazon.com/Level-Methods-Fast-Marching-Computational/dp/0521645573
Sfikas, K., Theoharis, T., Pratikakis, I.: ROSy+: 3D object pose normalization based on pca and reflective object symmetry with application in 3D object retrieval. Int. J. Comput. Vis. 91, 262–279 (2010). doi:10.1007/s11263-010-0395-x
Sfikas, K., Pratikakis, I., Theoharis, T.: ConTopo: non-rigid 3D object retrieval using topological information guided by conformal factors. In: 3DOR’11, pp. 25–32 (2011)
Shilane, P., Min, P., Kazhdan, M., Funkhouser, T.: The Princeton shape benchmark. In: Shape Modeling and Applications, pp. 167–178 (2004)
Shinagawa, Y., Kunii, T.L., Kergosien, Y.L.: Surface coding based on Morse theory. IEEE Comput. Graph. Appl. 11, 66–78 (1991)
Siddiqi, K., Shokoufandeh, A., Dickinson, S.J., Zucker, S.W.: Shock graphs and shape matching. Int. J. Comput. Vis. 35, 13–32 (1999). doi:10.1023/A:1008102926703. http://dl.acm.org/citation.cfm?id=335600.335602
Sundar, H., Silver, D., Gagvani, N., Dickinson, S.: Skeleton based shape matching and retrieval. In: Shape Modeling International, pp. 130–139 (2003). doi:10.1109/SMI.2003.1199609
Takahashi, S., Shinagawa, Y., Kunii, T.L.: A feature-based approach for smooth surfaces. In: Proceedings of the Fourth ACM Symposium on Solid Modeling and Applications, SMA’97, pp. 97–110. ACM Press, New York (1997)
Tangelder, J., Veltkamp, R.: A survey of content based 3D shape retrieval methods. Multimed. Tools Appl. 39, 441–471 (2008)
Tarasov, S.P., Vyalyi, M.N.: Construction of contour trees in 3D in o(nlogn) steps. In: Proceedings of the Fourteenth Annual Symposium on Computational Geometry, SCG’98, pp. 68–75. ACM Press, New York (1998)
Tierny, J., Vandeborre, J.P., Daoudi, M.: Partial 3D shape retrieval by reeb pattern unfolding. Comput. Graph. Forum 28(1), 41–55 (2009)
Tung, T., Schmitt, F.: The augmented multiresolution reeb graph approach for content-based retrieval of 3D shapes. Int. J. Shape Model. 11(1), 91–120 (2005)
Wang, S., Wang, Y., Jin, M., Gu, X., Samaras, D.: 3D surface matching and recognition using conformal geometry. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2006)
Xiang, P., Hua, C., Gang, F., Chuan, Z.: Pose insensitive 3D retrieval by Poisson shape histogram. In: Shi, Y., van Albada, G., Dongarra, J., Sloot, P. (eds.) Computational Science—ICCS 2007. Lecture Notes in Computer Science, vol. 4488, pp. 25–32. Springer, Berlin/Heidelberg (2007)
Zaharia, T., Preteux, F.J.: 3d-shape-based retrieval within the Mpeg-7 framework, pp. 133–145. SPIE (2001). doi:10.1117/12.424969. http://link.aip.org/link/?PSI/4304/133/1
Zhang, J., Siddiqi, K., Macrini, D., Shokoufandeh, A., Dickinson, S.: Retrieving articulated 3-d models using medial surfaces and their graph spectra. In: Rangarajan, A., Vemuri, B., Yuille, A. (eds.) Energy Minimization Methods in Computer Vision and Pattern Recognition, Lecture Notes in Computer Science, vol. 3757, pp. 285–300. Springer, Berlin/Heidelberg (2005)
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This research has been co-financed by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)—Research Funding Program: THALIS.
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Sfikas, K., Theoharis, T. & Pratikakis, I. Non-rigid 3D object retrieval using topological information guided by conformal factors. Vis Comput 28, 943–955 (2012). https://doi.org/10.1007/s00371-012-0714-z
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DOI: https://doi.org/10.1007/s00371-012-0714-z