A linear Euclidean distance transform algorithm based on the linear-time Legendre transform

Proceedings - 2nd Canadian Conference on Computer and Robot Vision, CRV 2005

Volumn , Issue , 2005, Pages 262-267

  Lucet, Y ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BINARY IMAGES; COMPUTER VISION;

CONVEX ANALYSIS; DIMENSION REDUCTION; EUCLIDEAN DISTANCE TRANSFORMS; EXACT EUCLIDEAN DISTANCE; LEGENDRE TRANSFORMS; LEGENDRE-FENCHEL TRANSFORMS; LINEAR TIME COMPLEXITY; SQUARED EUCLIDEAN DISTANCE;

MATHEMATICAL TRANSFORMATIONS;

EID: 84938566904     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CRV.2005.7     Document Type: Conference Paper

References (28)

1. E. Aurell, S.-g. N. Gurbatov, and S.-g. I. Simdyankin. Numerical proof of self-similarity in burgers' turbulence. Technical Report http://arxiv.org/abs/patt-sol/9602005, arXiv.org, 1996.
2. J. Bec, Frisch, U., and K. Khanin. Kicked burger turbulence. J. Fluid Mech., 416:239-267, 2000.
3. Y. Brenier. Un algorithme rapide pour le calcul de transform eé de Legendre-Fenchel discrètes. C. R. Acad. Sci. Paris Sér. I Math., 308:587-589, 1989.
4. L. Corrias. Fast Legendre-Fenchel transform and applications to Hamilton-Jacobi equations and conservation laws. SIAM J. Numer. Anal., 33(4):1534-1558, Aug. 1996.
5. O. Cuisenaire. Distance Transformations: Fast Algorithms and Applications to Medical Image Processing. PhD thesis, Université Catholique de Louvain, Louvain-la-Neuve, Belgium, Oct. 1999.
6. L. Deniau and J. Blanc-Talon. Fractal analysis with hausdorff distance under affine transformations. Technical report, ETCA-CREA-SP, 1995.
7. H. Edelsbrunner. Algorithms in Combinatorial Geometry. EATC Monographs on Theoretical Computer Science. Springer-Verlag, 1987.
8. P. F. Felzenszwalb and D. P. Huttenlocher. Distance transforms of sampled functions. Technical Report TR2004-1963, Cornell Computing and Information Science, Sept. 2004.
9. U. Frisch and J. Bec. Burgulence. In A. M. Lesieur and e. F. David, editors, Les Houches 2000: New Trends in Turbulence, pages 341-383. Springer EDP-Sciences, 2001.
10. U. Frisch, J. Bec, and B. Villone. Singularities and the distribution of density in the burgers/adhesion model. Physica D, 152-153:620-635, 2001.
11. M. Gavrilova and M. H. Alsuwaiyel. Two algorithms for computing the euclidean distance transform. Technical Report 2000-661-13, Computer Science Technical Reports, University of Calgary, 2000.
12. S. N. Gurbatov, S. I. Simdyankin, E. Aurell, U. Frisch, and G. Tth. On the decay of burgers turbulence. J. Fluid Mech., 344:339-374, 1997.
13. S. N. Gurbatov and A. V. Troussov. The decay of multiscale signals-deterministic model of the burgers turbulence. Technical report, arxiv.org, 2000.
14. T. Hisakado, K. Okumura, V. Vukadinovic, and L. Trajkovic. Characterization of a simple communication network using legendre transform. In Proc. IEEE Int. Symp. Circuits and Systems, volume 3, pages 738-741, May 2003.
15. J. ichiro Toriwaki and K. Mori. Distance transformation and skeletonization of 3d pictures and their applications to medical images. In R. K. E. G. Bertrand, A. Imiya, editor, Digital and Image Geometry: Advanced Lectures, volume 2243/2001 of Lecture Notes in Computer Science, pages 412-429. Springer-Verlag Heidelberg, 2001.
16. B. Koopen. Contact of bodies in 2D-space: Implementing the discrete legendre transform. AI master's thesis, Intelligent Autonomous Systems Group, University of Amsterdam, Feb. 2002.
17. Y. Lucet. A fast computational algorithm for the Legendre-Fenchel transform. Computational Optimization and Applications, 6(1):27-57, July 1996.
18. Y. Lucet. Faster than the fast Legendre transform, the lineartime Legendre transform. Numer. Algorithms, 16(2):171-185, Jan. 1997.
19. P. Maragos. Differential morphology and image processing. IEEE Transactions on Image Processing, 5(6):922-927, June 1996.
20. P. Maragos. Differential morphology. In S. K. Mitra and G. L. Sicuranza, editors, Nonlinear Image Processing, Academic Press Series in Communications, Networking, and Multimedia, chapter 10, pages 289-329. Academic Press, 2001.
21. A. Noullez, S. N. Gurbatov, E. Aurell, and S. I. Simdyankin. The global picture of self-similar and not self-similar decay in burgers turbulence. Technical Report nlin.CD/0409022, arXiv.org eprint archive, Sept. 2004.
22. A. Noullez and M. Vergassola. A fast Legendre transform algorithm and applications to the adhesion model. Journal of Scientific Computing, 9(3):259-281, 1994.
23. F. P. Preparata and M. I. Shamos. Computational Geometry. Texts and monographs in computer science. Springer-Verlag, third edition, 1990.
24. R. T. Rockafellar and R. J.-B. Wets. Variational analysis. Springer-Verlag, Berlin, 1998.
25. A. Rosenfeld and J. L. Pfaltz. Sequential operations in digital picture processing. J. ACM, 13(4):471-494, 1966.
26. Z.-S. She, E. Aurell, and U. Frisch. The inviscid burgers equation with initial data of brownian type. Comm. Math. Phys., 148(3):623-641, 1992.
27. F. Y. Shih and Y.-T. Wu. Fast euclidean distance transformation in two scans using a 3 x 3 neighborhood. Comput. Vis. Image Underst., 93(2):195-205, 2004.
28. M. Vergassola, B. Dubrulle, U. Frisch, and N. A. Burger's equation, devil's staircases and the mass distribution function for large-scale structures. Astronomy and Astrophysics, 289:325-356, 1994.