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Photometric Heat Kernel Signatures

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6667))

Abstract

In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local heat kernel signature shape descriptors. Our construction is based on the definition of a diffusion process on the shape manifold embedded into a high-dimensional space where the embedding coordinates represent the photometric information. Experimental results show that such data fusion is useful in coping with different challenges of shape analysis where pure geometric and pure photometric methods fail.

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References

  1. Amores, J., Sebe, N., Radeva, P.: Context-based object-class recognition and retrieval by generalized correlograms. Trans. PAMI 29(10), 1818–1833 (2007)

    Article  Google Scholar 

  2. Arya, S., Mount, D.M., Netanyahu, N.S., Silverman, R., Wu, A.Y.: An optimal algorithm for approximate nearest neighbor searching. J. ACM 45, 891–923 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Assfalg, J., Bertini, M., Bimbo, A.D., Pala, P.: Content-based retrieval of 3-d objects using spin image signatures. IEEE Transactions on Multimedia 9(3), 589–599 (2007)

    Article  Google Scholar 

  4. Belkin, M., Sun, J., Wang, Y.: Constructing Laplace operator from point clouds in Rd. In: Proc. Symp. Discrete Algorithms, pp. 1031–1040 (2009)

    Google Scholar 

  5. Belkin, M., Sun, J., Wang, Y.: Discrete Laplace operator on meshed surfaces. In: Proc. Symp. Computational Geometry, pp. 278–287 (2009)

    Google Scholar 

  6. 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., Toldo, R.: Shrec 2010: robust large-scale shape retrieval benchmark. In: Proc. 3DOR (2010)

    Google Scholar 

  7. Bronstein, A.M., Bronstein, M.M., Ovsjanikov, M., Guibas, L.J.: Shape google: a computer vision approach to invariant shape retrieval. In: Proc. NORDIA (2009)

    Google Scholar 

  8. Bronstein, M.M., Bronstein, A.M.: Shape recognition with spectral distances. Trans. PAMI (2010) (to appear)

    Google Scholar 

  9. Bronstein, M.M., Kokkinos, I.: Scale-invariant heat kernel signatures for non-rigid shape recognition. In: Proc. CVPR (2010)

    Google Scholar 

  10. Chum, O., Philbin, J., Sivic, J., Isard, M., Zisserman, A.: Total recall: Automatic query expansion with a generative feature model for object retrieval. In: Proc. ICCV (2007)

    Google Scholar 

  11. Coifman, R.R., Lafon, S.: Diffusion maps. Applied and Computational Harmonic Analysis 21, 5–30 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Gelfand, N., Mitra, N.J., Guibas, L.J., Pottmann, H.: Robust global registration. In: Proc. SGP (2005)

    Google Scholar 

  13. Jones, P.W., Maggioni, M., Schul, R.: Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels. PNAS 105(6), 1803 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. Kazhdan, M., Funkhouser, T., Rusinkiewicz, S.: Rotation invariant spherical harmonic representation of 3D shape descriptors. In: Proc. SGP, pp. 156–164 (2003)

    Google Scholar 

  15. Kimmel, R., Malladi, R., Sochen, N.: Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images. IJCV 39(2), 111–129 (2000)

    Article  MATH  Google Scholar 

  16. Lévy, B.: Laplace-Beltrami eigenfunctions towards an algorithm that understands geometry. In: Proc. Shape Modeling and Applications (2006)

    Google Scholar 

  17. Ling, H., Jacobs, D.W.: Deformation invariant image matching. In: ICCV, pp. 1466–1473 (2005)

    Google Scholar 

  18. Lowe, D.: Distinctive image features from scale-invariant keypoint. IJCV (2004)

    Google Scholar 

  19. Mahmoudi, M., Sapiro, G.: Three-dimensional point cloud recognition via distributions of geometric distances. Graphical Models 71(1), 22–31 (2009)

    Article  Google Scholar 

  20. Ohbuchi, R., Osada, K., Furuya, T., Banno, T.: Salient local visual features for shape-based 3d model retrieval, pp. 93–102 (June 2008)

    Google Scholar 

  21. Osada, R., Funkhouser, T., Chazelle, B., Dobkin, D.: Shape distributions. TOG 21(4), 807–832 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  22. Pan, X., Zhang, Y., Zhang, S., Ye, X.: Radius-normal histogram and hybrid strategy for 3d shape retrieval, pp. 372–377 (June 2005)

    Google Scholar 

  23. Reuter, M., Wolter, F.-E., Peinecke, N.: Laplace-spectra as fingerprints for shape matching. In: Proc. ACM Symp. Solid and Physical Modeling, pp. 101–106 (2005)

    Google Scholar 

  24. Rustamov, R.M.: Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Proc. SGP, pp. 225–233 (2007)

    Google Scholar 

  25. Sivic, J., Zisserman, A.: Video google: A text retrieval approach to object matching in videos. In: Proc. CVPR (2003)

    Google Scholar 

  26. Sun, J., Ovsjanikov, M., Guibas, L.J.: A concise and provably informative multi-scale signature based on heat diffusion. In: Proc. SGP (2009)

    Google Scholar 

  27. Thangudu, K.: Practicality of Laplace operator (2009)

    Google Scholar 

  28. Thorstensen, N., Keriven, R.: Non-rigid shape matching using geometry and photometry. In: Proc. CVPR (2009)

    Google Scholar 

  29. Tomasi, C., Manduchi, R.: Bilateral fitering for gray and color images. In: Proc. ICCV, pp. 839–846 (1998)

    Google Scholar 

  30. Vranic, D.V., Saupe, D., Richter, J.: Tools for 3D-object retrieval: Karhunen-Loeve transform and spherical harmonics. In: Proc. Workshop Multimedia Signal Processing, pp. 293–298 (2001)

    Google Scholar 

  31. Wardetzky, M., Mathur, S., Kälberer, F., Grinspun, E.: Discrete Laplace operators: no free lunch. In: Conf. Computer Graphics and Interactive Techniques (2008)

    Google Scholar 

  32. Wu, C., Clipp, B., Li, X., Frahm, J.-M., Pollefeys, M.: 3d model matching with viewpoint-invariant patches (vip), pp. 1–8 (June 2008)

    Google Scholar 

  33. Wyngaerd, J.V.: Combining texture and shape for automatic crude patch registration, pp. 179–186 (October 2003)

    Google Scholar 

  34. Xu, G.: Convergence of discrete Laplace-Beltrami operators over surfaces. Technical report, Institute of Computational Mathematics and Scientific/Engineering Computing, China (2004)

    Google Scholar 

  35. Yoon, K.-J., Prados, E., Sturm, P.: Joint estimation of shape and reflectance using multiple images with known illumination conditions (2010)

    Google Scholar 

  36. Zaharescu, A., Boyer, E., Horaud, R.P.: Transformesh: a topology-adaptive mesh-based approach to surface evolution (November 2007)

    Google Scholar 

  37. Zaharescu, A., Boyer, E., Varanasi, K.: R Horaud. Surface feature detection and description with applications to mesh matching. In: Proc. CVPR (2009)

    Google Scholar 

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© 2012 Springer-Verlag Berlin Heidelberg

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Kovnatsky, A., Bronstein, M.M., Bronstein, A.M., Kimmel, R. (2012). Photometric Heat Kernel Signatures. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2011. Lecture Notes in Computer Science, vol 6667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24785-9_52

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  • DOI: https://doi.org/10.1007/978-3-642-24785-9_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24784-2

  • Online ISBN: 978-3-642-24785-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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