Abstract
One of the major goals of computer vision is the development of flexible and efficient methods for shape representation. This paper proposes an approach for shape matching and retrieval based on scale-invariant heat kernel (HK). The approach uses a novel descriptor based on the histograms of the scale-invariant HK for a number of critical points on the shape at different time scales. We propose an improved method to introduce scale-invariance of HK to avoid noise-sensitive operations in the original method. A collaborative classification (CC) scheme is then employed for object classification. For comparison we compare our approach to well-known approaches on a standard benchmark dataset: the SHREC 2011. The results have indeed confirmed the high performance of the proposed approach on the shape retrieval problem.
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Raviv, D., et al.: Affine-invariant diffusion geometry for the analysis of deformable 3D shapes. In: Proc. Computer Vision and Pattern Recognition, CVPR (2011)
Kazhdan, M., et al.: Rotation invariant spherical harmonic representation of 3D shape descriptors. In: Proc. SGP, pp. 156–164 (2003)
Elad, A., Kimmel, R.: Bending invariant representations for surfaces. In: Proc. CVPR, pp. 168–174 (2001)
Bronstein, A.M., Bronstein, M.M., Bruckstein, A.M., Kimmel, R.: Analysis of two-dimensional non-rigid shapes. IJCV (2008)
Reuter, M., et al.: Discrete Laplace-Beltrami operators for shape analysis and segmentation. Computers and Graphics 33(3), 381–390 (2009)
Reuter, M., Wolter, F.E., Peinecke, N.: Laplace-Beltrami spectra as Shape-DNA of surfaces and solids. Computer-Aided Design 38(4), 342–366 (2006)
Bronstein, M., Kokkinos, I.: Scale-invariant heat kernel signatures for non-rigid shape recognition. In: IEEE Computer vision and pattern recognition (CVPR), pp. 1704–1711 (2010)
Sun, J., Ovsjanikov, M., Guibas, L.: A concise and provably informative multi-scale signature based on heat diffusion. In: SGP 2009: Proceedings of the Symposium on Geometry Processing, pp. 1383–1392 (2009)
Fang, Y., Sun, M., Ramani, K.: Temperature Distribution Descriptor for Robust 3D Shape Retrieval. In, NORDIA 2011 (2011) (CVPRW)
Johnson, A., Hebert, M.: Using spin images for efficient object recognition in cluttered 3 d scenes. Trans. PAMI 21(5), 433–449 (1999)
Toldo, R., Castellani, U., Fusiello, A.: Visual vocabulary signature for 3D object retrieval and partial matching. In: Proc. Eurographics Workshop on 3D Object Retrieval (2009)
Ben-Chen, M., Weber, O., Gotsman, C.: Characterizing shape using conformal factors. In: Proc. Eurographics Workshop on Shape Retrieval (2008)
Lian, Z., et al.: SHREC 2011 Track: Shape Retrieval on Non-rigid 3D Watertight Meshes. In: Proceedings of the Eurographics/ACM SIGGRAPH Symposium on 3D Object Retrieval (2011)
Grinspun, E., Gingold, Y., Reisman, J., Zorin, D.: Computing discrete shape operators on general meshes. [Eurographics (2006) Best Paper, 3rd Place]. Eurographics (Computer Graphics Forum) 25(3), 547–556 (2006)
Wardetzky, M., Mathur, S., Kalberer, F., Grinspun, E.: Discrete Laplace operators: no free lunch. In: Conf. Comp. Grap. and Interactive Techniques (2008)
Shilane, P., Min, P., Kazhdan, M., Funkhouser, T.: The princeton shape benchmark. In: Proc. SMI 2004, pp. 167–178 (2004)
Bronstein, A.M., Bronstein, M.M., Ovsjanikov, M., Guibas, L.J.: Shape Google: geometric words and expressions for invariant shape retrieval. ACM Trans. Graphics (TOG) 30(1), 1–20 (2011)
Abdelrahman, M., El-Melegy, M.T., Farag, A.A.: Heat Kernels for Non-Rigid Shape Retrieval: Sparse Representation and Efficient Classification. In: CRV, pp. 153–160 (2012)
Reuter, M.: Hierarchical shape segmentation and registration via topological features of laplace-beltrami eigenfunctions. Proc. IJCV 89(2), 287–308 (2010)
Zhang, L., Yang, M., Feng, X.: Sparse Representation or Collaborative Representation: Which Helps Face Recognition? In: ICCV (2011)
Yang, M., Zhang, L., Zhang, D., Wang, S.: Relaxed Collaborative Representation for Pattern Classification. In: CVPR (2012)
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Abdelrahman, M., El-Melegy, M., Farag, A. (2012). 3D Object Classification Using Scale Invariant Heat Kernels with Collaborative Classification. In: Fusiello, A., Murino, V., Cucchiara, R. (eds) Computer Vision – ECCV 2012. Workshops and Demonstrations. ECCV 2012. Lecture Notes in Computer Science, vol 7583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33863-2_3
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DOI: https://doi.org/10.1007/978-3-642-33863-2_3
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