WESD-Weighted spectral distance for measuring shape dissimilarity

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 35, Issue 9, 2013, Pages 2284-2297

  Konukoglu, Ender ^a   Glocker, Ben ^b   Criminisi, Antonio ^b   Pohl, Kilian M ^c  

^a MASSACHUSETTS GENERAL HOSPITAL   (United States)

^b MICROSOFT RESEARCH   (United Kingdom)

^c UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

label maps; Laplace operator; Laplace spectrum; medical images; segmentations; Shape distance; spectral distance

Indexed keywords

LABEL MAPS; LAPLACE OPERATOR; LAPLACE SPECTRA; SEGMENTATIONS; SHAPE DISTANCES; SPECTRAL DISTANCES;

EXPERIMENTS; LAPLACE TRANSFORMS; MEDICAL IMAGING;

EIGENVALUES AND EIGENFUNCTIONS;

ALGORITHM; ANATOMY AND HISTOLOGY; ANIMAL; AUTOMATED PATTERN RECOGNITION; BRAIN; CARDIAC IMAGING; COMPUTER SIMULATION; HUMAN; IMAGE PROCESSING; NUCLEAR MAGNETIC RESONANCE IMAGING; PROCEDURES; ARTICLE; HISTOLOGY; METHODOLOGY;

ALGORITHMS; ANIMALS; BRAIN; CARDIAC IMAGING TECHNIQUES; COMPUTER SIMULATION; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; MAGNETIC RESONANCE IMAGING; PATTERN RECOGNITION, AUTOMATED;

EID: 84880902916     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2012.275     Document Type: Article

References (43)

1. D. Zhang and G. Lu, "Review of Shape Representation and Description Techniques,"Pattern Recognition, vol. 37, no. 1, pp. 1-19, 2004. (Pubitemid 37425254)
2. N. Iyer, S. Jayanti, K. Lou, Y. Kalyanaraman, and K. Ramani, "Three-Dimensional Shape Searching: State-of-the-Art Review and Future Trends,"Computer-Aided Design, vol. 37, pp. 509-30, 2005. (Pubitemid 40415193)
3. M. Reuter, F.-E. Wolter, and N. Peinecke, "Laplace-Beltrami Spectra as 'Shape-DNA' of Surfaces and Solids,"Computer-Aided Design, vol. 38, pp. 342-366, 2006.
4. B. Lévy, "Laplace-Beltrami Eigenfunctions towards an Algorithm that 'Understands' Geometry,"Proc. IEEE Conf. Shape Modeling and Applications, 2006.
5. R.M. Rustamov, "Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representations,"Proc. Eurographics Symp. Geometry Processing, 2007.
6. J. Sun, M. Ovsjanikov, and L. Guibas, "A Concise and Provably Informative Multi-Scale Signature Based on Heat Diffusion,"Proc. Eurographics Symp. Geometry Processing, 2009.
7. M. Reuter, F.-E. Wolter, M. Shenton, and M. Niethammer, "Laplace-Beltrami Eigenvalues and Topological Features of Eigenfunctions for Statistical Shape Analysis,"Computer-Aided Design, vol. 41, pp. 739-755, 2009.
8. M.M. Bronstein and A.M. Bronstein, "Shape Recognition with Spectral Distances,"IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 33, no. 5, pp. 1065-1071, May 2011.
9. H. Weyl, "Das Asymptotische Verteilungsgesetz der Eigenwerte Linearer Partieller Differentialgleichungen,"Mathematische Annalen, vol. 71, pp. 441-479, 1912.
10. M. Kac, "Can One Hear the Shape of a Drum?"The Am. Math. Monthly, vol. 73, no. 7, pp. 1-23, 1966.
11. R. Courant and D. Hilbert, Method of Mathematical Physics, vol. 1. Interscience Publishers, 1966.
12. V. Jain and H. Zhang, "Robust 3D Shape Correspondence in the Spectral Domain,"Proc. Int'l Conf. Shape Modeling and Applications, 2006.
13. A.M. Bronstein, M. Bronstein, M. Mahmoudi, R. Kimmel, and G. Sapiro, "A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-Rigid Shape Matching,"Int'l J. Computer Vision, vol. 89, no. 2/3, pp. 266-286, 2010.
14. F. Mémoli, "A Spectral Notion of Gromov-Wasserstein Distance and Related Methods,"Applied and Computational Harmonic Analysis, vol. 30, no. 3, pp. 363-401, 2010.
15. M. Ovsjanikov, A.M. Bronstein, M.M. Bronstein, and L.J. Guibas, "Shape Google: A Computer Vision Approach to Invariant Shape Retrieval,"Proc. IEEE Int'l Conf. Computer Vision Workshops, pp. 320-327, 2009.
16. M. Bronstein, "Scale-Invariant Heat Kernel Signatures for Non-Rigid Shape Recognition,"Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2010.
17. R. Lai, Y. Shi, K. Scheibel, S. Fears, R. Woods, A. Toga, and T. Chan, "Metric-Induced Optimal Embedding for Intrinsic 3D Shape Analysis,"Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2010.
18. S. Gnutzmann, U. Smilansky, and N. Sondergaard, "Resolving Isospectral 'Drums' by Counting Nodal Domains,"J. Physics A: Math. and General, vol. 38, no. 41, pp. 8921-8933, 2005. (Pubitemid 41392832)
19. S. Gnutzmann, P. Karageorge, and U. Smilansky, "Can One Count the Shape of a Drum?"Physical Rev. Letters, vol. 97, no. 9, 2006.
20. R. Lai, Y. Shi, I. Dinov, T. Chan, and A. Toga, "Laplace-Beltrami Nodal Counts: A New Signature for 3D Shape Analysis,"Proc. Int'l Symp. Biomedical Imaging, 2009.
21. A. Pleijel, "A Study of Certain Green's Functions with Applications in the Theory of Vibrating Membranes,"Arkiv för Matematik, vol. 2, no. 6, pp. 553-569, 1954.
22. H. McKean and I. Singer, "Curvature and the Eigenvalues of the Laplacian,"J. Differential Geometry, vol. 1, pp. 43-69, 1967.
23. L. Smith, "The Asymptotics of the Heat Equation for a Boundary Value Problem,"Inventiones Math., vol. 63, pp. 467-493, 1981.
24. M. Protter, "Can One Hear the Shape of a Drum? Revisited,"SIAM Rev., vol. 29, no. 2, pp. 185-197, June 1987. (Pubitemid 17582925)
25. D. Vassilevich, "Heat Kernel Expansion: User's Manual,"Physics Reports, vol. 388, no. 5/6, pp. 279-360, 2003. (Pubitemid 37394272)
26. G. Jurman, R. Visintainer, and C. Furlanello, "An Introduction to Spectral Distances in Networks (Extended Version),"preprint in ArXiv, Oct. 2010.
27. Z. Lian, A. Godil, B. Bustos, M. Daoudi, J. Hermans, S. Kawamura, Y. Kurita, G. Lavoué, H.V. Nguyen, R. Ohbuchi, Y. Ohkita, Y. Ohishi, F. Porikli, M. Reuter, I. Sipiran, D. Smeets, P. Suetens, H. Tabia, and D. Vandermeulen, "SHREC '11 Track: Shape Retrieval on Non-Rigid 3D Watertight Meshes,"Proc. Eurographics/ACM Siggraph Symp. 3D Object Retrieval, 2011.
28. C. Gordon, D. Webb, and S. Wolpert, "Isospectral Plane Domains and Surfaces via Riemannian Orbifolds,"Inventiones Math., vol. 110, no. 1, pp. 1-22, 1992.
29. M. Niethammer, M. Reuter, F.-E. Wolter, S. Bouix, N. Peinecke, M.-S. Koo, and M.E. Shenton, "Global Medical Shape Analysis Using the Laplace-Beltrami Spectrum,"Proc. 10th Int'l Conf. Medical Image Computing and Computer Assisted Intervention, 2007.
30. E. Whittaker and G. Watson, A Course of Modern Analysis. Cambridge Math. Library, 1996.
31. L. Evans, Partial Differential Equations. Am. Math. Soc., 1998.
32. W.F. Ames, Numerical Methods for Partial Differential Equations. Academic Press, 1977.
33. W.E. Arnoldi, "The Principle of Minimized Iterations in the Solution of the Matrix Eigenvalue Problem,"Quarterly of Applied Math., vol. 9, no. 17, pp. 17-29, 1954.
34. A. Bronstein, A.B.M.M. Bronstein, and R. Kimmel, "Analysis of Two-Dimensional Non-Rigid Shapes,"Int'l J. Computer Vision, vol. 78, no. 1, pp. 67-77, 2008.
35. A. Bronstein, M. Bronstein, and R. Kimmel, Numerical Geometry of Non-Rigid Shapes. Springer, 2008.
36. J. Tenenbaum, V. de Silva, and J. Langford, "A Global Geometric Framework for Nonlinear Dimensionality Reduction,"Science, vol. 290, no. 5500, pp. 2319-2323, 2000. (Pubitemid 32041577)
37. Z. Lian, A. Godil, X. Sun, and H. Zhang, "Non-Rigid 3D Shape Retrieval Using Multidimensional Scaling and Bag-of-Features,"Proc. 17th IEEE Int'l Conf. Image Processing, pp. 3181-3184, 2010.
38. C. Maes, T. Fabry, J. Keustermans, D. Smeets, P. Suetens, and D. Vandermuelen, "Feature Detection on 3D Face Surfaces for Pose Normalisation and Recognition,"Proc. Fourth IEEE Int'l Conf. Biometrics: Theory, Applications and Systems, 2010.
39. D. Smeets, T. Fabry, J. Hermans, D. Vandermuelen, and P. Suetens, "Isometric Deformation Modelling for Object Recognition,"Proc. 13th Int'l Conf. Computer Analysis of Images and Patterns, pp. 757-765, 2009.
40. F.L. Bookstein, P.D. Sampson, A.P. Streissguth, and P.D. Connor, "Geometric Morphometrics of Corpus Callosum and Subcortical Structures in the Fetal-Alcohol-Affected Brain,"Teratology, vol. 64, pp. 4-32, July 2001.
41. D. Shattuck, M. Mirza, V. Adisetiyo, C. Hojatkashani, G. Salamon, K. Narr, R. Poldrack, R. Bilder, and A. Toga, "Construction of a 3D Probabilistic Atlas of Human Cortical Structures,"NeuroImage, vol. 39, no. 3, pp. 1064-80, 2008.
42. T. Mansi, I. Voigt, B. Leonardi, X. Pennec, S. Durrleman, M. Sermesant, H. Delingette, A. Taylor, Y. Boudjemline, G. Pongiglione, and N. Ayache, "A Statistical Model for Quantification and Prediction of Cardiac Remodeling: Application to Tetralogy of Fallot,"IEEE Trans. Medical Imaging, vol. 30, no. 9, pp. 1605-1616, Sept. 2011.
43. E. Bernardis, E. Konukoglu, Y. Ou, D.N. Metaxas, B. Desjardins, and K.M. Pohl, "Temporal Shape Analysis via the Spectral Signature,"Proc. 15th Int'l Conf. Medical Image Computing and Computer Assisted Intervention, 2012.