Multiscale flat norm signatures for shapes and images

Applied Mathematical Sciences

Volumn 4, Issue 13-16, 2010, Pages 667-680

  Vixie, Kevin R ^a   Clawson, Keith ^a   Asaki, Thomas J ^a   Sandine, Gary ^b   Morgan, Simon P ^b   Price, Brandon ^c  

^a WASHINGTON STATE UNIVERSITY   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

^c Walla Walla College   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77953337236     PISSN: None     EISSN: 1312885X     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. W. Allard. Total variation regularization for image denoising; I. Geometric Theory. SIAM Journal on Mathematical Analysis, 39:1150-1190, 2007.
2. W. Allard. Total variation regularization for image denoising; II. Examples. submitted, 2008.
3. W. Allard. Total variation regularization for image denoising; III. Examples. Submitted, 2008.
4. S. Alliney. A property of the minimum vectors of a regularizing functional defined by means of the absolute norm. IEEE Trans. Signal Process., 45:913-917, 1997.
5. Y. Boykov, O. Veksler, and R. Zabih. Fast approximate energy minimization via graph cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(11):1222-1239, 2001.
6. T. Chan and S. Esedoglu. Aspects of total variation regularized L1 function approximation. SIAM J. Appl. Math., 65(5):1817-1837, 2005.
7. J. Darbon and M. Sigelle. A fast and exact algorithm for total variation minimization. In 2nd Iberian Conference on Pattern Recognition and Image Analysis, volume 3522, pages 351-359. Springer, 2005.
8. L. Evans and R. Gariepy. Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, 1992. ISBN 0-8493-7157-0.
9. H. Federer. Geometric Measure Theory. Classics in Mathematics. Springer-Verlag, 1969.
10. D. Goldfarb and W. Yin. Parametric maximum flow algorithms for fast total variation minimization. Technical report, CAAM TR07-09, Rice University, 2007.
11. V. Kolmogorov and R. Zabih. What Energy Functions Can Be Minimized via Graph Cuts? IEEE transactions on pattern analysis and machine intelligence, pages 147-159, 2004.
12. F. Morgan. Geometric Measure Theory: A Beginner's Guide. Academic Press, 4th edition, 2008.
13. 1TV computes the flat norm for boundaries. Abstract and Applied Analysis, 2007:Article ID 45153, 14 pages, 2007. doi:10.1155/2007/45153.
14. M. Nikolova. Minimizers of cost-functions involving nonsmooth datafidelity terms. SIAM J. Numer. Anal., 40:965-994, 2003.
15. L. Rudin, S. Osher, and E. Fatemi. Nonlinear total variation based noise removal algorithms. Physica D, 60(1-4):259-268, November 1992.
16. K. Vixie. Some properties of minimizers for the Chan-Esedog̈lu L1TV functional. arXiv.org, Oct 2007.