Generalized gradients: Priors on minimization flows

International Journal of Computer Vision

Volumn 73, Issue 3, 2007, Pages 325-344

  Charpiat, G ^a   Maurel, P ^a   Pons, J P ^b   Keriven, R ^c   Faugeras, O ^b  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b INRIA   (France)

^c UNIVERSITÉ PARIS EST   (France)

Author keywords

Active contours; Generalized gradient; Gradient descent; Hausdorff distance; Inner product; Landmarks; Minimization flow; Rigidification; Semi local rigidification; Shape; Shape warping; Sobolev; Spatial coherence

Indexed keywords

DEFORMATION; NUMERICAL METHODS; OPTIMIZATION; PROBABILITY; PROBLEM SOLVING; SENSITIVITY ANALYSIS;

ACTIVE CONTOURS; GENERALIZED GRADIENT; GRADIENT DESCENT; HAUSDORFF DISTANCE; INNER PRODUCTS; LANDMARKS; MINIMIZATION FLOW; RIGIDIFICATION; SEMI LOCAL RIGIDIFICATION; SHAPE WARPING;

CONTOUR MEASUREMENT;

EID: 33846890000     PISSN: 09205691     EISSN: 15731405     Source Type: Journal    
DOI: 10.1007/s11263-006-9966-2     Document Type: Article

References (36)

1. Akhiezer, N.I. and Glazman, I.M. 1981. Theory of Linear Operators in Hilbert Space. Pitman.
2. Bertalmío, M., Cheng, L.T., Osher, S., and Sapiro, G. 2001. Variational problems and partial differential equations on implicit surfaces. Journal of Computational Physics, 174(2):759-780.
3. Bertalmio, M., Sapiro, G., Cheng, L.T., and Osher, S. 2001. Variational problems and PDE's on implicit surfaces. In IEEE Workshop on Variational and Level Set Methods, (Ed.), Vancouver, Canada, pp. 186-193,
4. Bonnans, J.F., Gilbert, J.C., Lemarechal, C., and Sagastizabal, C.A. 2002. Numerical Optimization: Theoretical and Practical Aspects. Springer-Verlag.
5. Boykov, Y. and Kolmogorov, V. 2003. Computing geodesics and minimal surfaces via graph cuts. In International Conference on Computer Vision, vol. 1, pp. 26-33.
6. Caselles, V., Kimmel, R., and Sapiro, G. 1997. Geodesic active contours. The International Journal of Computer Vision, 22(1):61-79.
7. Charpiat, G., Faugeras, O., and Keriven, R. 2005. Approximations of shape metrics and application to shape warping and empirical shape statistics. Foundations of Computational Mathematics, 5(1): 1-58.
8. Charpiat, G.,Keriven, R., Pons, J.P., and Faugeras, O. 2005. Designing spatially coherent minimizing flows for variational problems based on active contours. In 10th International Conference on Computer Vision, Beijing, China.
9. Dervieux, A. and Thomasset, F. 1979. A finite element method for the simulation of Rayleigh-Taylor instability. Lecture Notes in Mathematics, 771:145-159.
10. DoCarmo, M.P. 1976. Differential Geometry of Curves and Surfaces. Prentice-Hall.
11. Duan, Y., Yang, L., Qin, H., and Samaras, D. 2004. Shape reconstruction from 3D and 2D data using PDE-based deformable surfaces. In European Conference on Computer Vision, vol. 3, pp. 238-251.
12. Faugeras, O. and Keriven, R. 1998. Variational principles, surface evolution, PDE's, level set methods and the stereo problem. IEEE Transactions on Image Processing, 7(3):336-344.
13. Goldlücke, B. and Magnor, M. 2004. Space-time isosurface evolution for temporally coherent 3D reconstruction. In International Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 350-355.
14. Goldlücke, B. and Magnor, M. 2004. Weighted minimal hypersurfaces and their applications in computer vision. In European Conference on Computer Vision, vol. 2, pp. 366-378.
15. Jin, H., Soatto, S., and Yezzi, A.J. 2003. Multi-view stereo beyond Lambert. In International Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 171-178.
16. Kass, M., Witkin, A., and Terzopoulos, D. 1987. Snakes: Active contour models. The International Journal of Computer Vision, 1(4):321-331.
17. Kolmogorov, V. and Zabih, R. 2002. Multi-camera scene reconstruction via graph cuts. In European Conference on Computer Vision, vol. 3, pp. 82-96.
18. Kolmogorov, V. and Zabih, R. 2004. What energy functions can be minimized via graph cuts? IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(2):147-159.
19. Maurel, P., Keriven, R., and Faugeras, O. 2006. Reconciling landmarks and level sets. In International Conference on Pattern Recognition.
20. Michor, P.W. and Mumford, D. 2005. Riemannian geometries of space of plane curves. Preprint.
21. Osher, S. and Fedkiw, R. 2002. The Level Set Method and Dynamic Implicit Surfaces. Springer-Verlag.
22. Osher, S. and Paragios, N. (Eds.) 2003. Geometric Level Set Methods in Imaging, Vision and Graphics. Springer Verlag.
23. Osher, S. and Sethian, J.A. 1988. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79(1):12-49.
24. Overgaard, N.C. and Solem, J.E. 2005. An analysis of variational alignment of curves in images. In International Conference on Scale Space and PDE Methods in Computer Vision, pp. 480-491.
25. Paragios, N. and Deriche, R. 2005. Geodesic active regions and level set methods for motion estimation and tracking. Computer Vision and Image Understanding, 97(3):259-282.
26. Peng, D., Merriman, B., Osher, S., Znao, H.-K., and Kang, M. 1999. A PDE-based fast local level set method. Journal of Computational Physics, 155(2):410-438.
27. Pons, J.-P., Hermosillo, G., Keriven, R., and Faugeras, O. 2003. How to deal with point correspondences and tangential velocities in the level set framework. In International Conference on Computer Vision, vol. 2, pp. 894-899.
28. Rudin, W. 1966. Real and Complex Analysis. McGraw-Hill.
29. Sethian, J.A. 1999. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Sciences. Cambridge Monograph on Applied and Computational Mathematics. Cambridge University Press.
30. Solem, J.E. and Overgaard, N.C. 2005. A geometric formulation of gradient descent for variational problems with moving surfaces. In International Conference on Scale Space and PDE Methods in Computer Vision, pp. 419-430.
31. Sundaramoorthi, G., Yezzi, A.J., and Mennucci, A. 2005. Sobolev active contours. In IEEE Workshop on Variational and Level Set Methods, Beijing, China, pp. 109-120.
32. Trouvé, A. 1998. Diffeomorphisms groups and pattern matching in image analysis. The International Journal of Computer Vision, 28(3):213-221,
33. Yezzi, A.J. and Mennucci, A.C.G. 2005. Metrics in the space of curves. Preprint.
34. Yezzi, A.J. and Soatto, S. 2003. Deformotion: Deforming motion, shape average and the joint registration and approximation of structures in images. The International Journal of Computer Vision, 53(2): 153-167.
35. Younes, L. 1998. Computable elastic distances between shapes. SIAM Journal of Applied Mathematics, 58(2):565-586.
36. Zhao, H.-K., Osher, S., Merriman, B., and Kang, M. 2000. Implicit and non-parametric shape reconstruction from unorganized points using a variational level set method. Computer Vision and Image Understanding, 80(3):295-314.