Anisotropic laplace-beltrami operators for shape analysis

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 8928, Issue , 2015, Pages 299-312

  Andreux, Mathieu ^a   Rodolá, Emanuele ^b   Aubry, Mathieu ^c   Cremers, Daniel ^b  

^a ECOLE POLYTECHNIQUE   (France)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^c UNIVERSITÉ PARIS EST   (France)

Author keywords

Anisotropic diffusion; Curvature; Laplace Beltrami operator; Non rigid matching; Segmentation; Shape analysis

Indexed keywords

ANISOTROPY; COMPUTER VISION; DIFFUSION; IMAGE SEGMENTATION; LAPLACE TRANSFORMS; OPTICAL ANISOTROPY;

ANISOTROPIC DIFFUSION; CURVATURE; LAPLACE-BELTRAMI OPERATOR; NONRIGID MATCHING; SHAPE ANALYSIS;

MATHEMATICAL OPERATORS;

EID: 84925391507     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-319-16220-1_21     Document Type: Conference Paper

References (25)

1. Aubry, M., Schlickewei, U., Cremers, D.: The wave kernel signature: A quantum mechanical approach to shape analysis. In: ICCVWorkshops, pp. 1626–1633 (2011)
2. Black, M.J., Sapiro, G., Marimont, D.H., Heeger, D.: Robust anisotropic diffusion. Trans. Img. Proc. 7(3), 421–432 (1998)
3. Boucher, M., Evans, A., Siddiqi, K.: Anisotropic Diffusion of Tensor Fields for Fold Shape Analysis on Surfaces. In: Székely, G., Hahn, H.K. (eds.) IPMI 2011. LNCS, vol. 6801, pp. 271–282. Springer, Heidelberg (2011)
4. Bronstein, A.M., Bronstein, M.M., Castellani, U., Dubrovina, A., Guibas, L.J., Horaud, R.P., Kimmel, R., Knossow, D., von Lavante, E., Mateus, D., Ovsjanikov, M., Sharma, A.: Shrec 2010: robust correspondence benchmark. In: Proc. EUROGRAPHICS Workshop on 3D Object Retrieval, EG 3DOR 2010 (2010)
5. Bronstein, A., Bronstein, M., Kimmel, R.: Numerical Geometry of Non-Rigid Shapes, 1st edn. Springer Publishing Company, Incorporated (2008)
6. Clarenz, U., Diewald, U., Rumpf, M.: Anisotropic geometric diffusion in surface processing. In: Proc. of the Conference on Visualization 2000, VIS 2000, pp. 397–405 (2000)
7. Cohen-Steiner, D., Morvan, J.M.: Restricted delaunay triangulations and normal cycle. In: Proc. of the Nineteenth Annual Symposium on Computational Geometry, SCG 2003, pp. 312–321 (2003)
8. Desbrun, M., Meyer, M., Schröder, P., Barr, A.H.: Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proc. of the 26th Annual Conference on Computer Graphics and Interactive Techniques. pp. 317–324. SIGGRAPH’99 (1999)
9. Fillard, P., Arsigny, V., Ayache, N., Pennec, X.: A Riemannian Framework for the Processing of Tensor-Valued Images. In: Fogh Olsen, O., Florack, L.M.J., Kuijper, A. (eds.) DSSCV 2005. LNCS, vol. 3753, pp. 112–123. Springer, Heidelberg (2005)
10. de Goes, F., Liu, B., Budninskiy, M., Tong, Y., Desbrun, M.: Discrete 2-tensorfields on triangulations. Computer Graphics Forum 33(5) (2014)
11. Kim, K., Tompkin, J., Theobalt, C.: Curvature-aware regularization on Riemannian submanifolds. In: Proc. of the IEEE International Conference on Computer Vision, ICCV 2013, pp. 881–888 (2013)
12. Kovnatsky, A., Raviv, D., Bronstein, M.M., Bronstein, A.M., Kimmel, R.: Geometric and photometric data fusion in non-rigid shape analysis. Numerical Mathematics: Theory, Methods and Applications (NM-TMA) 6(1), 199–222 (2013)
13. Litman, R., Bronstein, A.: Learning spectral descriptors for deformable shape correspondence. IEEE Transactions on Pattern Analysis and Machine Intelligence 36(1), 171–180 (2014)
14. Litman, R., Bronstein, A.M., Bronstein, M.M.: Diffusion-geometric maximally stable component detection in deformable shapes. Computers & Graphics 35(3), 549–560 (2011)
15. Meyer, M., Desbrun, M., Schröder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. Visualization and Mathematics III, pp. 35–57 (2003)
16. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990)
17. Peyré, G.: Toolbox graph - a toolbox to process graph and triangulated meshes. (2008) https://www.ceremade.dauphine.fr∼peyre/matlab/graph/content.html
18. Pinkall, U., Polthier, K.: Computing discrete minimal surfaces and their conjugates. Experimental Mathematics 2(1), 15–36 (1993)
19. Pokrass, J., Bronstein, A.M., Bronstein, M.M., Sprechmann, P., Sapiro, G.: Sparse modeling of intrinsic correspondences. Computer Graphics Forum 32(2pt. 4), 459–468 (2013)
20. Reuter, M., Biasotti, S., Giorgi, D., Patané, G., Spagnuolo, M.: Discrete laplacebeltrami operators for shape analysis and segmentation. Computers & Graphics 33(3), 381–390 (2009)
21. Rodolà, E., Rota Buló, S., Cremers, D.: Robust region detection via consensus segmentation of deformable shapes. Computer Graphics Forum 33(5) (2014)
22. Rodolà, E., Rota Buló, S., Windheuser, T., Vestner, M., Cremers, D.: Dense nonrigid shape correspondence using random forests. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2014)
23. Rustamov, R.M.: Laplace-beltrami eigenfunctions for deformation invariant shape representation. In: Proc. of the Fifth Eurographics Symposium on Geometry Processing, SGP 2007, pp. 225–233 (2007)
24. Sun, J., Ovsjanikov, M., Guibas, L.: A concise and provably informative multiscale signature based on heat diffusion. In: Proc. of the Symposium on Geometry Processing, SGP 2009, pp. 1383–1392 (2009)
25. Tasdizen, T., Whitaker, R., Burchard, P., Osher, S.: Geometric surface smoothing via anisotropic diffusion of normals. In: Proc. of the Conference on Visualization 2002, VIS 2002, pp. 125–132 (2002)