Contour evolution scheme for variational image segmentation and smoothing

IET Image Processing

Volumn 1, Issue 3, 2007, Pages 287-294

  Mahmoodi, S ^a   Sharif, B S ^a  

^a NEWCASTLE UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CONTOUR MEASUREMENT; EDGE DETECTION; FOURIER SERIES; IMAGE ANALYSIS; IMAGE ENHANCEMENT; SIGNAL TO NOISE RATIO;

CONTOUR LENGTH MINIMIZATION; IMAGE CONTOUR SEGMENTATION; LEGENDRE'S SERIES;

IMAGE SEGMENTATION;

EID: 34548391862     PISSN: 17519659     EISSN: None     Source Type: Journal    
DOI: 10.1049/iet-ipr:20050188     Document Type: Article

References (26)

1. Kass, M., Witkin, A., and Terzopoulos, D.: ' Snakes: active contour models ', Int. J. Comput. Vis., 1987, 1, p. 321-331 10.1007/BF00133570 0920-5691
2. Mumford, D., and Shah, J.: ' Optimal approximations by piecewise smooth functions and associated variational problems ', Commun. Pure Appl. Math., 1989, 42, (4), p. 577-688
3. Tsai, A., Yezzi, A., and Willsky, A.S.: ' Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation and magnification ', IEEE Trans. Image Process., 2001, 10, (8), p. 1169-1186 10.1109/83.935033 1057-7149
4. Chan, T.F., and Vese, L.A.: ' Active contours without edges ', IEEE Trans. Image Process., 2001, 10, (2), p. pp. 266-277 1057-7149
5. Hintermuller, M., and Ring, W.: ' An inexact-CG-type active contour approach for the minimization of the Mumford-Shah Functional ', J. Math. Imaging Vis., 2004, 20, p. 19-42, 10.1023/B:JMIV.0000011317.13643.3a 0924-9907
6. Dervieux, A., and Thomasset, F.: ' A finite element method for the simulation of Rayleigh-Taylor instability ', Approximation methods for Navier-Stokes problems, lecture notes in mathematics, (Springer, 1979), 771, p. 145-158
7. Dervieux, A., and Thomasset, F.: ' Multifluid incompressible flows by a finite element method ', Lect. Notes Phys., 1981, 11, p. 158-163
8. Osher, S., and Sethian, J.: ' Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations ', J. Comput. Phys., 1988, 79, p. 12-49 0021-9991
9. Sethian, J.A.: ' Levet set methods: evolving interfaces in geometry, fluid mechanics, computer vision and material science ', (Cambridge University Press, 1996)
10. Caselles, V., Kimmel, R., and Sapiro, G.: ' Geodesic active contours ', Proc. 5th Int. Conf. on Computer Vision, IEEE Computer Society Press, 1995, p. 694-699
11. Caselles, V., Kimmel, R., and Saprio, G.: ' Geodesic active contours ', Int. J. Comput. Vis., 1997, 22, (1), p. 61-79 10.1023/A:1007979827043 0920-5691
12. Sapiro, G.: ' Geometric partial differential equations and image analysis ', (Cambridge University Press, 2001)
13. Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., and Yezzi, A.: ' Gradient flows and geometric active contour models ', Fifth Int. Conf. on Computer Vision (ICCV'95), 1995, p. 810-815
14. Yezzi, A., Kichenassamy, S., Kumar, A., Olver, P., and Tannenbaum, A.: ' A geometric snake model for segmentation of medical imagery ', IEEE Trans. Med. Imaging, 1997, 16, (12), p. 199-209 0278-0062
15. Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., and Yezzi, A.: ' Conformal curvature flows: from phase transitions to active vision ', Arch. Ration. Mech. and Anal., 1996, 134, (3), p. 275-301
16. Aubert, G., and Kornprobst, P.: ' Mathematical problems in image processing: partial differential equations and calculus of variations ', (Springer-Verlag, New York, 2002)
17. Morel, J.L., and Solimini, S.: ' Variational methods in image segmentation ', (Birkhauser, Boston, 1995)
18. Mumford, D., and Shah, J.: ' Boundary detection by minimizing functionals ', Proc. Int. Conf. on Computer Vision and Pattern Recognition, 1985, p. 22-26
19. Vese, L.A., and Chan, T.F.: ' A multiphase level set framework for image segmentation using the Mumford and Shah model ', Int. J. Comput. Vis., 2002, 50, (3), p. 271-293 10.1023/A:1020874308076 0920-5691
20. Chan, T.F., Sandberg, B.Y., and Vese, L.A.: ' Active contours without edges for vector-valued images ', J. Vis. Commun. Image Represent., 2000, 11, p. 130-141 10.1006/jvci.1999.0442 1047-3203
21. Chan, T.F., and Vese, L.A.: ' Levels et algorithm for minimising the Mumford-Shah functional in image processing ', Proc. IEEE Workshop on Variational and Level Set Methods in Computer Vision, 2001, p. 161-168
22. Vese, L.A.: ' Multiphase object detection and image segmentation ', Osher, S., Paragios, N., Geometrical level set methods in imaging, vision, and graphics, (Springer Verlag, 2003), p. 175-194
23. Gelfand, I.M., and Fomin, S.V.: ' Calculus of variations ', (Prentice-Hall Inc., New Jersey, 1963)
24. Mahmoodi, S., and Sharif, B.S.: ' Signal segmentation and denoising algorithm based on energy optimization ', Signal Process., 2005, 85, (9), p. 1845-1851 10.1016/j.sigpro.2005.03.016 0165-1684
25. Mahmoodi, S., and Sharif, B.S.: ' Noise reduction, smoothing and time interval segmentation of noisy signals using an energy optimisation method ', IEE Proc., Vis. Image Signal Process., 2006, 153, (2), p. 101-108 10.1049/ip-vis:20045205 1350-245X
26. Kreyszig, E.: ' Advanced engineering mathematics ', (John Wiley, 1999)