Pre-image as karcher mean using diffusion maps: Application to shape and image denoising

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

Volumn 5567 LNCS, Issue , 2009, Pages 721-732

  Thorstensen, Nicolas ^a   Segonne, Florent ^a   Keriven, Renaud ^a  

^a UNIVERSITÉ PARIS EST   (France)

Author keywords

[No Author keywords available]

Indexed keywords

2D IMAGES; 2D SHAPE; 3-D SHAPE; DE-NOISING; DIFFUSION MAPS; IMAGE DE-NOISING; IMAGE METHOD; IMAGE MODELING; MANIFOLD LEARNING; NON-LINEAR; SAMPLE POINT; STATISTICAL LEARNING TECHNIQUES;

COMPUTER VISION; INTERPOLATION; LEARNING ALGORITHMS;

THREE DIMENSIONAL;

EID: 69049102394     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-02256-2_60     Document Type: Conference Paper

References (24)

1. Dambreville, S., Rathi, Y., Tannenbaum, A.: Statistical shape analysis using kernel PCA. In: IS&T/SPIE Symposium on Electronic Imaging (2006)
2. Arias, P., Randall, G., Sapiro, G.: Connecting the out-of-sample and pre-image problems in kernel methods. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June 18-23 (2007)
3. Kwok, J.T., Tsang, I.W.: The pre-image problem in kernel methods. IEEE Transaction in Neural Network 15(6), 1517-1525 (2004)
4. Carreira-Perpiñan, M.A., Lu, Z.: The Laplacian Eigenmaps Latent Variable Model. JMLR W&P 2, 59-66 (2007)
5. Roweis, S., Saul, L.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323-2326 (2000)
6. Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319-2323 (2000)
7. Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation 15(6), 1373-1396 (2003)
8. Coifman, R., Lafon, S., Lee, A., Maggioni, M., Nadler, B.,Warner, F., Zucker, S.: Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps. PNAS 102(21), 7426-7431 (2005)
9. Hein, M., Audibert, J.Y., von Luxburg, U.: From graphs to manifolds - weak and strong pointwise consistency of graph Laplacians. Journal of Machine Learning Research, ArXiv Preprint (forthcoming) (2006)
10. Lafon, S., Keller, Y., Coifman, R.R.: Data fusion and multicue data matching by diffusion maps. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(11), 1784-1797 (2006)
11. Leventon, M., Grimson, E., Faugeras, O.: Statistical shape influence in geodesic active contours. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 316-323 (2000)
12. Cremers, D., Kohlberger, T., Schnörr, C.: Nonlinear shape statistics in mumford shah based segmentation. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2351, pp. 93-108. Springer, Heidelberg (2002)
13. Lu, Z., Carreira-Perpinan, M., Sminchisescu, C.: People tracking with the laplacian eigenmaps latent variable model. In: Platt, J., Koller, D., Singer, Y., Roweis, S. (eds.) Advances in Neural Information Processing Systems, vol. 20, pp. 1705-1712. MIT Press, Cambridge (2008)
14. Pennec, X.: Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements. Journal of Mathematical Imaging and Vision 25(1), 127-154 (2006); a preliminary appeared as INRIA RR-5093 (January 2004)
15. Davis, B., Fletcher, P., Bullitt, E., Joshi, S.: Population shape regression from random design data. In: ICCV, vol. 1 (2007)
16. Karcher, H.: Riemannian center of mass and mollifier smoothing. Comm. Pure Appl. Math. (30), 509-541 (1977)
17. Etyngier, P., Segonne, F., Keriven, R.: Shape priors using manifold learning techniques. In: 11th IEEE International Conference on Computer Vision, Rio de Janeiro, Brazil (October 2007)
18. Lafon, S., Lee, A.B.: Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(9), 1393-1403 (2006)
19. Bengio, Y., Paiement, J.F., Vincent, P., Delalleau, O., Le Roux, N., Ouimet, M.: Out-ofsample extensions for lle, isomap, mds, eigenmaps, and spectral clustering. In: Thrun, S., Saul, L.K., Schölkopf, B. (eds.) Advances in Neural Information Processing Systems, vol. 16. MIT Press, Cambridge (2004)
20. Baker, C.T.H., Baker, C.T.H.: Numerical analysis of volterra functional and integral equations. In: Duff, I.S., Watson, G.A. (eds.) The state of the art in numerical analysis, pp. 193-222. University Press (1996)
21. Etyngier, P., Keriven, R., Segonne, F.: Projection onto a shape manifold for image segmentation with prior. In: 14th IEEE International Conference on Image Processing, San Antonio, Texas, US (September 2007)
22. Charpiat, G., Faugeras, O., Keriven, R.: Approximations of shape metrics and application to shape warping and empirical shape statistics. Foundations of Computational Mathematics 5(1), 1-58 (2005)
23. Solem, J.: Geodesic curves for analysis of continuous implicit shapes. In: International Conference on Pattern Recognition, vol. 1, pp. 43-46 (2006)
24. Rousson, M., Paragios, N.: Shape priors for level set representations. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2351, pp. 78-92. Springer, Heidelberg (2002)