Sobolev gradients and joint variational image segmentation, denoising and deblurring

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 7246, Issue , 2009, Pages

  Jung, Miyoun ^a   Chung, Ginmo ^b   Sundaramoorthi, Ganesh ^a   Vese, Luminita A ^a   Yuille, Alan L ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b YALE UNIVERSITY   (United States)

Author keywords

Functional minimization; Gradient descent; Image restoration; Image segmentation; Implicit representation; Sobolev gradients

Indexed keywords

FUNCTIONAL MINIMIZATION; GRADIENT DESCENT; IMAGE RESTORATION; IMPLICIT REPRESENTATION; SOBOLEV GRADIENTS;

DIGITAL IMAGE STORAGE; IMAGE RECONSTRUCTION; RESTORATION;

IMAGE SEGMENTATION;

EID: 65649122291     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.806067     Document Type: Conference Paper

References (19)

1. L. Bar and G. Sapiro, "Generalized Newton method for energy formulations in image processing", IMA preprint series 2195, 2008.
2. L. Bar, N. Sochen, and N. Kiryati, "Semi-blind image restoration via Mumford-Shah regularization", IEEE TIP 15(2): 483-493, 2006. (Pubitemid 43126173)
3. T. Chan and L. Vese, "An active contour model without edges", LNCS 1682: 141-151, 1999.
4. T.F. Chan and L.A. Vese, "Active contours without edges", IEEE TIP 10(2): 266-177, 2001.
5. J. Chung, "A unifying framework for piecewise-constant image segmentation and deblurring", Ph.D. Thesis, UCLA, 2007.
6. J. Chung and L. Vese, "Energy Minimization Based Segmentation and Denoising Using a Multilayer Level Set Approach", LNCS 3757: 439-455, 2005. (Pubitemid 43722950)
7. J. Chung and L. Vese, "Image segmentation using a multilayer level-set approach", to appear in Computing and Visualization in Science, 2009.
8. G. Charpiat, P. Maurel, J.-P. Pons, R. Keriven, O. Faugeras, "Generalized Gradients: Priors on Minimization Flows", IJCV 73(3): 325-344, 2007. (Pubitemid 46227278)
9. G. Dogan, P. Morin and R. Nochetto, "A Variational Shape Optimization Approach for Image Segmentation with a Mumford-Shah Functional", SIAM Journal on Scientific Computing 30(6): 3028-3049, 2008.
10. D. Kim, A. Tsai, M. Cetin and A. Willsky, "A curve evolution based variational approach to simultaneous image restoration and segmentation", Proc. IEEE ICIP, Vol. 1: 109-112, 2002. (Pubitemid 35438303)
11. C. Li, C.-Y. Kao, J.C. Gore, Z. Ding, "Implicit Active Contours Driven by Local Binary Fitting Energy", CVPR 2007. (Pubitemid 47529909)
12. D. Mumford and J. Shah, "Optimal approximations by piecewise smooth functions and associated variational problems", Commun. Pure Appl. Math., 42(5): 577-685, 1989.
13. J.W. Neuberger, "Sobolev gradients and differential equations", Springer Lecture notes in Mathematics, Vol. 1670, 1997.
14. S. Osher, R. Fedkiw, "Level set methods and dynamic implicit surfaces", Springer, New York, 2003.
15. R.J. Renka, "A simple explanation of the Sobolev gradient method", 2006 (http://www.cse.unt.edu/renka/papers/sobolev.pdf).
16. W.B. Richardson, "Sobolev gradient preconditioning for image processing PDEs", Commun Numer. Methods in Engineering, 24(6): 493-504, 2008.
17. L. Rudin and S. Osher, "Total variation based image restoration with free local constraints", Proc. IEEE ICIP, Vol. I: 31-35, 1994. Austin, TX.
18. J.A. Sethian, "Level Set Methods and Fast Marching Methods Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science", Cambridge University Press, 1999.
19. G. Sundaramoorthi, A. Yezzi, and A. C. Mennucci, "Sobolev active contours", IJCV 73(3):345-366, 2007. (Pubitemid 46227279)