Abstract
The computer vision and pattern recognition communities have recently witnessed a surge of feature-based methods in object recognition and image retrieval applications. These methods allow representing images as collections of “visual words” and treat them using text search approaches following the “bag of features” paradigm. In this article, we explore analogous approaches in the 3D world applied to the problem of nonrigid shape retrieval in large databases. Using multiscale diffusion heat kernels as “geometric words,” we construct compact and informative shape descriptors by means of the “bag of features” approach. We also show that considering pairs of “geometric words” (“geometric expressions”) allows creating spatially sensitive bags of features with better discriminative power. Finally, adopting metric learning approaches, we show that shapes can be efficiently represented as binary codes. Our approach achieves state-of-the-art results on the SHREC 2010 large-scale shape retrieval benchmark.
Supplemental Material
- Amores, J., Sebe, N., and Radeva, P. 2007. Context-Based object-class recognition and retrieval by generalized correlograms. Trans. Patt. Anal. Mach. Intell. 29, 10, 1818--1833. Google ScholarDigital Library
- Andreetto, M., Brusco, N., and Cortelazzo, G. M. 2004. Automatic 3D modeling of textured cultural heritage objects. Trans. Image Process. 13, 3, 335--369. Google ScholarDigital Library
- Arya, S., Mount, D. M., Netanyahu, N. S., Silverman, R., and Wu, A. Y. 1998. An optimal algorithm for approximate nearest neighbor searching fixed dimensions. J. ACM 45, 6, 891--923. Google ScholarDigital Library
- Assfalg, J., Bertini, M., and Delbimbo, A. P. P. 2007. Content-Based retrieval of 3D objects using spin image signatures. Trans. Multimedia 9, 3, 589--599. Google ScholarDigital Library
- Bay, H., Tuytelaars, T., and Van Gool, L. 2006. SURF: Speeded up robust features. In Proceedings of the European Conference on Computer Vision (ECCV'06). 404--417. Google ScholarDigital Library
- Behmo, R., Paragios, N., and Prinet, V. 2008. Graph commute times for image representation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'08).Google Scholar
- Belkin, M. and Niyogi, P. 2003. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15, 6, 1373--1396. Google ScholarDigital Library
- Belkin, M., Sun, J., and Wang, Y. 2009. Constructing Laplace operator from point clouds in Rd. In Proceedings of the Symposium on Discrete Algorithms. 1031--1040. Google ScholarDigital Library
- Belongie, S., Malik, J., and Puzicha, J. 2002. Shape matching and object recognition using shape contexts. Trans. Patt. Anal. Mach. Intell. 24, 4, 509--522. Google ScholarDigital Library
- Ben-Chen, M., Weber, O., and Gotsman, C. 2008. Characterizing shape using conformal factors. In Proceedings of the 3DOR Conference. Google ScholarDigital Library
- Bérard, P., Besson, G., and Gallot, S. 1994. Embedding riemannian manifolds by their heat kernel. Geom. Function. Anal. 4, 4, 373--398.Google ScholarCross Ref
- Biasotti, S., Marini, S., Mortara, M., and Patané, G. 2003. An overview on properties and efficacy of topological skeletons in shape modeling. In Proceedings of the IEEE International Conference on Shape Modeling and Applications (SMI'03). 245--254. Google ScholarDigital Library
- Bobenko, A. I. and Springborn, B. A. 2007. A discrete Laplace--Beltrami operator for simplicial surfaces. Discr. Comput. Geom. 38, 4, 740--756. Google ScholarDigital Library
- Borg, I. and Groenen, P. 1997. Modern Multidimensional Scaling -- Theory and Applications. Springer.Google Scholar
- Bronstein, A. M. and Bronstein, M. M. 2010a. Affine-Invariant spatially-sensitive vocabularies. In Proceedings of the European Conference on Computer Vision (ECCV'10).Google Scholar
- Bronstein, A. M., Bronstein, M. M., Bustos, B., Castelani, U., Crisani, M., Falcidieno, B., Guibas, L. J., Sipiran, I., Kokkinos, I., Murino, V., Ovsjanikov, M., Patané, G., Spagnuolo, M., and Sun, J. 2010a. SHREC 2010: Robust feature detection and description benchmark. In Proceedings of the 3DOR Conference.Google Scholar
- Bronstein, A. M., Bronstein, M. M., Carmon, Y., and Kimmel, R. 2009. Partial similarity of shapes using a statistical significance measure. Trans. Comput. Vis. Appl. 1, 0, 105--114.Google ScholarCross Ref
- Bronstein, A. M., Bronstein, M. M., Castellani, U., Falcidieno, B., Fusiello, A., Godil, A., Guibas, L. J., Kokkinos, I., Lian, Z., Ovsjanikov, M., Patané, G., Spagnuolo, M., and Toldo, R. 2010b. SHREC 2010: Robust large-scale shape retrieval benchmark. In Proceedings of the 3DOR Conference.Google Scholar
- Bronstein, A. M., Bronstein, M. M., and Kimmel, R. 2006a. Efficient computation of isometry-invariant distances between surfaces. SIAM J. Sci. Comput. 28, 5, 1812--1836.Google ScholarCross Ref
- Bronstein, A. M., Bronstein, M. M., and Kimmel, R. 2006b. Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching. Proc. Nat. Acad. Sci. 103, 5, 1168--1172.Google ScholarCross Ref
- Bronstein, A. M., Bronstein, M. M., and Kimmel, R. 2008. Numerical Geometry of Non-Rigid Shapes. Springer. Google ScholarDigital Library
- Bronstein, A. M., Bronstein, M. M., and Kimmel, R. 2010c. The video genome. arXiv 1003.5320v1.Google Scholar
- Bronstein, A. M., Bronstein, M. M., Kimmel, R., Mahmoudi, M., and Sapiro, G. 2010d. A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching. Int. J. Comput. Vis. 89, 2-3, 266--286. Google ScholarDigital Library
- Bronstein, M. M. and Bronstein, A. M. 2009. On a relation between shape recognition algorithms based on distributions of distances. Tech. rep. CIS-2009-14, Department of Computer Science, Technion, Israel.Google Scholar
- Bronstein, M. M. and Bronstein, A. M. 2010b. Shape recognition with spectral distances. Trans. Patt. Anal. Mach. Intell. To appear. Google ScholarDigital Library
- Bronstein, M. M., Bronstein, A. M., Kimmel, R. and Yavneh, I. 2006. Multigrid multidimensional scaling. Numer. Linear Alg. Appl. 13, 149--171.Google ScholarCross Ref
- Bronstein, M. M., Bronstein, A. M., Michel, F., and Paragios, N. 2010e. Data fusion through cross-modality metric learning using similarity-sensitive hashing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'10).Google Scholar
- Bronstein, M. M. and Kokkinos, I. 2010. Scale-Invariant heat kernel signatures for non-rigid shape recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'10).Google Scholar
- Bustos, B., Keim, D. A., Saupe, D., Schreck, T., and Vranic, D. V. 2005. Feature-Based similarity search in 3D object databases. ACM Comput. Surv. 37, 4, 387. Google ScholarDigital Library
- Castellani, U., Cristani, M., Fantoni, S., and Murino, V. 2008. Sparse points matching by combining 3D mesh saliency with statistical descriptors. Comput. Graph. Forum 27, 643--652.Google ScholarCross Ref
- Chazal, F., Cohen-Steiner, D., Guibas, L. J., Mémoli, F., and Oudot, S. Y. 2009a. Gromov-Hausdorff stable signatures for shapes using persistence. Comput. Graph. Forum 28, 5, 1393--1403. Google ScholarDigital Library
- Chazal, F., Guibas, L. J., Oudot, S. Y., and Skraba, P. 2009b. Analysis of scalar fields over point cloud data. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'09). 1021--1030. Google ScholarDigital Library
- Chen, D., Ouhyoung, M., Tian, X., and Shen, Y. 2003. On visual similarity based 3D model retrieval. Comput. Graph. Forum 22, 3, 223--232.Google ScholarCross Ref
- Chum, O., Philbin, J., Sivic, J., Isard, M., and Zisserman, A. 2007. Total recall: Automatic query expansion with a generative feature model for object retrieval. In Proceedings of the IEEE International Conference on Computer Vision (ICCV'07).Google Scholar
- Clarenz, U., Rumpf, M., and Telea, A. 2004. Robust feature detection and local classification for surfaces based on moment analysis. Trans. Visualiz. Comput. Graph. 10, 5, 516--524. Google ScholarDigital Library
- Coifman, R. R. and Lafon, S. 2006. Diffusion maps. Appl. Comput. Harmon. Anal. 21, 5--30.Google ScholarCross Ref
- Dalal, N. and Triggs, B. 2005. Histograms of oriented gradients for human detection. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'05). Google ScholarDigital Library
- Dubrovina, A. and Kimmel, R. 2010. Matching shapes by eigen-decomposition of the Laplace-Beltrami operator. In Proceedings of the 3DPVT Conference.Google Scholar
- Edelsbrunner, H., Letscher, D., and Zomorodian, A. 2000. Topological persistence and simplification. In Proceedings of the IEEE Conference on Foundations of Computer Science. 454--463. Google ScholarDigital Library
- Elad, A. and Kimmel, R. 2001. Bending invariant representations for surfaces. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'01). 168--174.Google Scholar
- Elad, A. and Kimmel, R. 2003. On bending invariant signatures for surfaces. Trans. Patt. Anal. Mach. Intell. 25, 10, 1285--1295. Google ScholarDigital Library
- Floater, M. S. and Hormann, K. 2005. Surface parameterization: A tutorial and survey. Adv. Multiresolut. Geom. Model. 1.Google Scholar
- Freund, Y. and Schapire, R. E. 1995. A decision-theoretic generalization of on-line learning and an application to boosting. In Proceedings of the European Conference on Computational Learning Theory. Google ScholarDigital Library
- Funkhouser, T., Min, P., Kazhdan, M., Chen, J., Halderman, A., Dobkin, D., and Jacobs, D. 2003. A search engine for 3D models. ACM Trans. Graph. 22, 1, 83--105. Google ScholarDigital Library
- Gebal, K., Baerentzen, J. A., Aanaes, H., and Larsen, R. 2009. Shape analysis using the auto diffusion function. Comput. Graph. Forum 28, 5, 1405--1413. Google ScholarDigital Library
- Gelfand, N., Mitra, N. J., Guibas, L. J., and Pottmann, H. 2005. Robust global registration. In Proceedings of the Symposium on Geometry Processing (SGP'05). Google ScholarDigital Library
- Glomb, P. 2009. Detection of interest points on 3D data: Extending the harris operator. In Proceedings of the Conference on Computer Recognition Systems 3. Advances in Soft Computing, Vol. 57. Springer, 103--111.Google Scholar
- Grauman, K. and Darrell, T. 2005. Efficient image matching with distributions of local invariant features. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'05), Vol. 2. Google ScholarDigital Library
- Gromov, M. 1981. Structures Metriques Pour les Varietes Rieman- niennes. Number 1 in Textes Mathematiques.Google Scholar
- Harris, C. and Stephens, M. 1988. A combined corner and edge detection. In Proceedings of the 4th Alvey Vision Conference. 147--151.Google Scholar
- Hilaga, M., Shinagawa, Y., Kohmura, T., and Kunii, T. 2001. Topology matching for fully automatic similarity estimation of 3D shapes. In Proceedings of the Conference on Computer Graphics and Interactive Techniques. 203--212. Google ScholarDigital Library
- Hsu, E. P. 2002. Stochastic Analysis on Manifolds. American Mathematical Society.Google Scholar
- Itti, L., Koch, C., and Niebur, E. 1998. A model of saliency-based visual attention for rapid scene analysis. Trans. Patt. Anal. Mach. Intell. 20, 11. Google ScholarDigital Library
- Jain, P., Kulis, B., and Grauman, K. 2008. Fast image search for learned metrics. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recongnition (CVPR'08).Google Scholar
- Jiantao, P., Yi, L., Guyu, X., Hongbin, Z., Weibin, L., and Uehara, Y. 2004. 3D model retrieval based on 2D slice similarity measurements. In Proceedings of the 3DPVT Conference. 95--101. Google ScholarDigital Library
- Johnson, A. E. and Hebert, M. 1999. Using spin images for efficient object recognition in cluttered 3D scenes. Trans. Patt. Anal. Mach. Intell. 21, 5, 433--449. Google ScholarDigital Library
- Jones, P. W., Maggioni, M., and Schul, R. 2008. Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels. Proc. Nat. Acad. Sci. 105, 6, 1803.Google ScholarCross Ref
- Kazhdan, M., Funkhouser, T., and Rusinkiewicz, S. 2003. Rotation invariant spherical harmonic representation of 3D shape descriptors. In Proceedings of the Symposium on Geometry Processing (SGP'03). 156--164. Google ScholarDigital Library
- Kazhdan, M., Funkhouser, T., and Rusinkiewicz, S. 2004. Symmetry descriptors and 3D shape matching. In Proceedings of the Symposium on Geometry Processing (SGP'04). 115--123. Google ScholarDigital Library
- Kimmel, R., Zhang, C., Bronstein, A. M., and Bronstein, M. M. 2010. Are MSER features really interesting? IEEE Trans. Patt. Anal. Mach. Intell. submitted. Google ScholarDigital Library
- Kolomenkin, M., Shimshoni, I., and Tal, A. 2009. On edge detection on surfaces,. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'09).Google Scholar
- Lafon, S. 2004. Diffusion maps and geometric harmonics. Ph.D. thesis, Yale University.Google Scholar
- Lazebnik, S., Schmid, C., and Ponce, J. 2006. Beyond bags of features: Spatial pyramid matching for recognizing natural scene categories. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'06). Google ScholarDigital Library
- Leibe, B., Leonardis, A., and Schiele, B. 2004. Combined object categorization and segmentation with an implicit shape model. In Proceedings of the Workshop Statistical Learning in Computer Vision. 17--32.Google Scholar
- Lévy, B. 2006. Laplace-Beltrami eigenfunctions towards an algorithm that “understands” geometry. In Proceedings of the Conference on Shape Modeling and Applications. Google ScholarDigital Library
- Li, Y., Zha, H., and Qui, H. 2006. Shape topics: A compact representation and new algorithm for 3D partial shape retrieval. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'06). Google ScholarDigital Library
- Lian, Z., Godil, A., and Sun, X. 2010a. Visual similarity based 3D shape retrieval using bag-of-features. In Proceedings of the IEEE International Conference on Shape Modeling and Applications (SMI'10). Google ScholarDigital Library
- Lian, Z., Rosin, P. L., and Sun, X. 2010b. Rectilinearity of 3D meshes. Int. J. Comput. Vis. To appear. Google ScholarDigital Library
- Lipman, Y. and Funkhouser, T. 2009. Mobius voting for surface correspondence. ACM Trans. Graph. 28, 3. Google ScholarDigital Library
- Lowe, D. 2004. Distinctive image features from scale-invariant key-point. Int. J. Comput. Vis. 60, 2, 91--110. Google ScholarDigital Library
- Mahmoudi, M. and Sapiro, G. 2009. Three-Dimensional point cloud recognition via distributions of geometric distances. Graph. Models 71, 1, 22--31. Google ScholarDigital Library
- Marszaek, M. and Schmid, C. 2006. Spatial weighting for bag- of-features. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'06). Google ScholarDigital Library
- Matas, J., Chum, O., Urban, M., and Pajdla, T. 2004. Robust wide-baseline stereo from maximally stable extremal regions. Image Vis. Comput. 22, 10, 761--767.Google ScholarCross Ref
- Mateus, D., Horaud, R. P., Knossow, D., Cuzzolin, F., and Boyer, E. 2008. Articulated shape matching using laplacian eigen-functions and unsupervised point registration. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'08).Google Scholar
- Mémoli, F. 2007. On the use of Gromov-Hausdorff distances for shape comparison. In Point Based Graphics.Google Scholar
- Mémoli, F. 2009. Spectral Gromov-Wasserstein distances for shape matching. In Proceedings of the Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment (NORDIA'09).Google ScholarCross Ref
- Mémoli, F. and Sapiro, G. 2005. A theoretical and computational framework for isometry invariant recognition of point cloud data. Found. Comput. Math. 5, 313--346.Google ScholarDigital Library
- Meyer, M., Desbrun, M., Schroder, P., and Barr, A. H. 2003. Discrete differential-geometry operators for triangulated 2-manifolds. Visualiz. Math. III, 35--57.Google ScholarCross Ref
- Min, P., Kazhdan, M., and Funkhouser, T. 2004. A comparison of text and shape matching for retrieval of online 3D models. Res. Adv. Technol. Digital Librar., 209--220.Google Scholar
- Mitra, N., Bronstein, A. M., and Bronstein, M. M. 2010. Intrinsic regularity detection in 3D geometry. In Proceedings of the European Conference on Computer Vision (ECCV'10). Google ScholarDigital Library
- Mitra, N. J., Guibas, L. J., Giesen, J., and Pauly, M. 2006. Probabilistic fingerprints for shapes. In Proceedings of the Symposium on Geometry Processing (SGP'06). Google ScholarDigital Library
- Napoléon, T., Adamek, T., Schmitt, F., and O'Connor, N. E. 2007. Multi-View 3D retrieval using silhouette intersection and multi-scale contour representation. In Proceedings of the Conference on Shape Modeling and Applications.Google Scholar
- Novotni, M. and Klein, R. 2003. 3D Zernike descriptors for content based shape retrieval. In Proceedings of the ACM Symposium on Solid Modeling and Applications. 216--225. Google ScholarDigital Library
- Osada, R., Funkhouser, T., Chazelle, B., and Dobkin, D. 2002. Shape distributions. ACM Trans. Graph. 21, 4, 807--832. Google ScholarDigital Library
- Ovsjanikov, M., Bronstein, A. M., Bronstein, M. M., and Guibas, L. J. 2009. Shape Google: A computer vision approach to invariant shape retrieval. In Proceedings of the Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment (NORDIA'09).Google Scholar
- Ovsjanikov, M., Sun, J., and Guibas, L. J. 2008. Global intrinsic symmetries of shapes. Comput. Graph. Forum. 27, 1341--1348. Google ScholarDigital Library
- Paquet, E., Rioux, M., Murching, A., Naveen, T., and Tabatabai, A. 2000. Description of shape information for 2-D and 3-D objects. Signal Process. Image Comm. 16, 1-2, 103--122.Google ScholarCross Ref
- Patané, G. and Falcidieno, B. 2010. Multi-Scale feature spaces for shape analysis and processing. In Proceedings of the IEEE International Conference on Shape Modeling and Applications (SMI'10). Google ScholarDigital Library
- Pauly, M., Keiser, R., and Gross, M. 2003. Multi-Scale feature extraction on point-sampled surfaces. Comput. Graph. Forum 22, 281--289.Google ScholarCross Ref
- Pinkall, U. and Polthier, K. 1993. Computing discrete minimal surfaces and their conjugates. Exper. Math. 2, 1, 15--36.Google ScholarCross Ref
- Raviv, D., Bronstein, A. M., Bronstein, M. M., and Kimmel, R. 2007. Symmetries of non-rigid shapes. In Proceedings of the NRTL'07 Conference.Google Scholar
- Raviv, D., Bronstein, A. M., Bronstein, M. M., Kimmel, R., and Sapiro, G. 2010a. Diffusion symmetries of non-rigid shapes. In Proceedings of the 3DPVT Conference.Google Scholar
- Raviv, D., Bronstein, M. M., Bronstein, A. M., and Kimmel, R. 2010b. Volumetric heat kernel signatures. In Proceedings of the ACM Multimedia Workshop on 3D Object Retrieval. Google ScholarDigital Library
- Reuter, M., Biasotti, S., Giorgi, D., Patané, G., and Spagnuolo, M. 2009. Discrete Laplace--Beltrami operators for shape analysis and segmentation. Comput. Graph. 33, 3, 381--390. Google ScholarDigital Library
- Reuter, M., Wolter, F.-E., and Peinecke, N. 2005. Laplace-Spectra as fingerprints for shape matching. In Proceedings of the ACM Symposium on Solid and Physical Modeling. 101--106. Google ScholarDigital Library
- Reuter, M., Wolter, F.-E., and Peinecke, N. 2006. Laplace-Beltrami spectra as “shape-DNA” of surfaces and solids. Comput. Aid. Des. 38, 342--366. Google ScholarDigital Library
- Rubner, Y., Tomasi, C., and Guibas, L. J. 2000. The earth mover's distance as a metric for image retrieval. Int. J. Comput. Vis. 40, 2, 99--121. Google ScholarDigital Library
- Rustamov, R. M. 2007. Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In Proceedings of the Symposium on Geometry Processing (SGP'07). 225--233. Google ScholarDigital Library
- Shakhnarovich, G. 2005. Learning task-specific similarity. Ph.D. thesis, MIT. Google ScholarDigital Library
- Shilane, P. and Funkhauser, T. 2006. Selecting distinctive 3D shape descriptors for similarity retrieval. In Proceedings of the Conference on Shape Modelling and Applications. Google ScholarDigital Library
- Shilane, P., Min, P., Kazhdan, M., and Funkhouser, T. 2004. The Princeton shape benchmark. In Proceedings of the the IEEE International Conference on Shape Modeling and Applications (SMI'04). 167--178. Google ScholarDigital Library
- Sipiran, I. and Bustos, B. 2010. A robust 3D interest points detector based on Harris operator. In Proceedings of the Eurographics Workshop on 3D Object Retrieval. 7--14. Google ScholarDigital Library
- Sivic, J. and Zisserman, A. 2003. Video Google: A text retrieval approach to object matching in videos. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'03). Google ScholarDigital Library
- Strecha, C., Bronstein, A. M., Bronstein, M. M., and Fua, P. 2010. LDA-hash: Improved matching with smaller descriptors. IEEE Trans. Patt. Anal. Mach. Intell. submitted. Google ScholarDigital Library
- Sumner, R. and Popovic, J. 2004. Deformation transfer for triangle meshes. In Proceedings of the Conference on Computer Graphics and Interactive Techniques. 399--405. Google ScholarDigital Library
- Sun, J., Ovsjanikov, M., and Guibas, L. J. 2009. A concise and provably informative multi-scale signature based on heat diffusion. In Proceedings of the Symposium on Geometry Processing (SGP'09). Google ScholarDigital Library
- Sundar, H., Silver, D., Gagvani, N., and Dickinson, S. 2003. Skeleton based shape matching and retrieval. In Proceedings of the IEEE Conference on Shape Modeling and Applications (SMI'03). Vol. 130. Google ScholarDigital Library
- Tal, A., Elad, M., and Ar, S. 2001. Content based retrieval of VRML objects - An iterative and interactive approach. In Proceedings of the Eurographics Workshop on Multimedia. Google ScholarDigital Library
- Tangelder, J. W. H. and Veltkamp, R. C. 2008. A survey of content based 3D shape retrieval methods. Multimedia Tools Appl. 39, 3, 441--471. Google ScholarDigital Library
- Thorstensen, N. and Keriven, R. 2009. Non-Rigid shape matching using geometry and photometry. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'09).Google Scholar
- Tola, E., Lepetit, V., and Fua, P. 2008. A fast local descriptor for dense matching. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'08).Google Scholar
- Toldo, R., Castellani, U., and Fusiello, A. 2009. Visual vocabulary signature for 3D object retrieval and partial matching. In Proceedings of the 3DOR Conference. Google ScholarDigital Library
- Torralba, A., Fergus, R., and Weiss, Y. 2008. Small codes and large image databases for recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'08).Google Scholar
- Torresani, L., Kolmogorov, V., and Rother, C. 2008. Feature correspondence via graph matching: Models and global optimization. In Proceedings of the European Conference on Computer Vision (ECCV'08). 596--609. Google ScholarDigital Library
- Tung, T. and Schmitt, F. 2005. The augmented multiresolution Reeb graph approach for content-based retrieval of 3D shapes. Int. J. Shape Model. 11, 1, 91--120.Google ScholarCross Ref
- Vaxman, A., Ben-Chen, M., and Gotsman, C. 2010. A multi-resolution approach to heat kernels on discrete surfaces. ACM Trans. Graph. 29, 4. Google ScholarDigital Library
- Veltkamp, R. C. and Hagedoorn, M. 2001. State of the art in shape matching. In Principles of Visual Information Retrieval. Google ScholarDigital Library
- Wang, C., Bronstein, M. M., and Paragios, N. 2010. Discrete minimum-distortion correspondence problems in non-rigid shape analysis. Res. rep. 7333, INRIA.Google Scholar
- Wardetzky, M., Mathur, S., Kalberer, F., and Grinspun, E. 2008. Discrete Laplace operators: No free lunch. In Conference on Computer Graphics and Interactive Techniques.Google Scholar
- Zaharescu, A., Boyer, E., Varanasi, K., and Horaud, R. 2009. Surface feature detection and description with applications to mesh matching. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'09).Google Scholar
- Zeng, Y., Wang, C., Wang, Y., Gu, X., Samaras, D., and Paragios, N. 2010. Dense non-rigid surface registration using high-order graph matching. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'10).Google Scholar
- Zhang, C. and Chen, T. 2001. Efficient feature extraction for 2D/3D objects in mesh representation. In Proceedings of the IEEE International Conference on Image Processing (ICIP'01). Vol. 3.Google Scholar
- Zhang, H. 2004. Discrete combinatorial Laplacian operators for digital geometry processing. In Proceedings of the Conference on Geometric Design. 575--592.Google Scholar
Index Terms
- Shape google: Geometric words and expressions for invariant shape retrieval
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