A framework for comparing different image segmentation methods and its use in studying equivalences between level set and fuzzy connectedness frameworks

Computer Vision and Image Understanding

Volumn 115, Issue 6, 2011, Pages 721-734

  Ciesielski, Krzysztof Chris ^a,b   Udupa, Jayaram K ^b  

^a WEST VIRGINIA UNIVERSITY   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Algorithm equivalence; Convergence; Delineation; Fuzzy connectedness; Level sets; Medical images; Segmentation

Indexed keywords

CONVERGENCE; DELINEATION; FUZZY CONNECTEDNESS; LEVEL SETS; MEDICAL IMAGES; SEGMENTATION;

ALGORITHMS; EQUIVALENCE CLASSES; FUZZY SYSTEMS; IMAGE RESOLUTION; IMAGE SEGMENTATION; MATHEMATICAL MODELS; MEDICAL IMAGING;

CONVERGENCE OF NUMERICAL METHODS;

EID: 79954596629     PISSN: 10773142     EISSN: 1090235X     Source Type: Journal    
DOI: 10.1016/j.cviu.2011.01.003     Document Type: Article

References (54)

1. L. Ambrosio, and V.M. Tortorelli Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence Communications on Pure and Applied Mathematics 43 1990 999 1036
2. L. Ambrosio, and V.M. Tortorelli On the approximation of free discontinuity problems Bollettino Della Unione Matematica Italiana 6-B 1992 105 123
3. G. Aubert, and L. Blanc-Féraud Some remarks on the equivalence between 2D and 3D classical snakes and geodesic active contours International Journal of Computer Vision 34 1 1999 19 28 (Pubitemid 30507188)
4. G. Aubert, and P. Kornprobst Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations Applied Mathematical Sciences vol. 147 2006 Springer
5. S. Beucher, The watershed transformation applied to image segmentation, in: 10th Pfefferkorn Conference on Signal and Image Processing in Microscopy and Microanalysis, 1992, pp. 299-314.
6. B. Bourdin, and A. Chambolle Implementation of an adaptive finite-element approximation of the Mumford-Shah functional Numerische Mathematik 85 4 2000 609 646
7. Y. Boykov, and G. Funka-Lea Graph cuts and efficient N-D image segmentation International Journal of Computer Vision 70 2 2006 109 131 (Pubitemid 44127252)
8. Y. Boykov, V. Kolmogorov, Computing geodesics and minimal surfaces via graph cuts, in: Proceedings of the International Conference on Computer Vision, I: 2633, Nice, France, 2003.
9. Y. Boykov, O. Veksler, and R. Zabih Fast approximate energy minimization via graph cuts IEEE Transactions on Pattern Analysis and Machine Intelligence 23 11 2001 1222 1239 (Pubitemid 33137959)
10. A. Braides Γ-Convergence for Beginners 2002 Oxford University Press Oxford
11. Martin Burger, Growth fronts of first-order Hamilton-Jacobi equations, Report 02-8, 2002, see < www.sfb013.uni-linz.ac.at/%7Esfb/reports/2002/ps- files/sfb02-08.ps.gzSFB >.
12. A. Chakraborty, L. Staib, and J. Duncan Deformable boundary finding in medical images by integrating gradient and region information IEEE Transactions on Medical Imaging 15 6 1996 859 870 (Pubitemid 126773987)
13. A. Chambolle Image segmentation by variational methods: Mumford and Shah functional and the discrete approximations SIAM Journal of Applied Mathematics 55 3 1995 827 863
14. T. Chan, and J. Shen Image processing and analysis: variational, PDE, wavelet, and stochastic methods Society of Industrial and Applied Mathematics 2005
15. T.F. Chan, and L.A. Vese Active contours without edges IEEE Transaction on Image Processing 10 2001 266 277 (Pubitemid 32254596)
16. K.C. Ciesielski, J.K. Udupa, P.K. Saha, and Y. Zhuge Iterative relative fuzzy connectedness for multiple objects, allowing multiple seeds Computer Vision and Image Understanding 107 3 2007 160 182 (Pubitemid 47179912)
17. K.C. Ciesielski, and J.K. Udupa Affinity functions in fuzzy connectedness based image segmentation I: equivalence of affinities Computer Vision and Image Understanding 114 2010 146 154
18. K.C. Ciesielski, and J.K. Udupa Affinity functions in fuzzy connectedness based image segmentation II: defining and recognizing truly novel affinities Computer Vision and Image Understanding 114 2010 155 166
19. K.C. Ciesielski, J.K. Udupa, Region-based segmentation: fuzzy connectedness, graph cut and related algorithms, in: Thomas M. Deserno (né Lehmann) (Ed.), Recent Advances in Biomedical Image Processing and Analysis, Springer, 2011, pp. 251-278.
20. D.L. Collins, A.P. Zijdenbos, V. Kollokian, J.G. Sled, N.J. Kabani, C.J. Holmes, and A.C. Evans Design and construction of a realistic digital brain phantom IEEE Transactions on Medical Imaging 17 3 1998 463 468 (Pubitemid 128747700)
21. T. Cootes, C. Taylor, and D. Cooper Active shape models-their training and application Computer Vision and Image Understanding 61 1995 38 59
22. T. Cootes, G. Edwards, and C. Taylor Active appearance models IEEE Transactions on Pattern Analysis and Machine Intelligence 23 6 2001 681 685 (Pubitemid 32585279)
23. M.G. Crandall, and P.L. Lions Viscosity solutions of Hamilton-Jacobi equations Transactions of the American Mathematical Society 277 1983 1 42
24. A.X. Falcão, J. Stolfi, and R.A. Lotufo The image foresting transform: theory, algorithms, and applications IEEE Transactions on Pattern Analysis and Machine Intelligence 26 1 2004 19 29
25. C. Imielinska, D. Metaxas, J.K. Udupa, Y. Jin, T. Chen, Hybrid segmentation of anatomical data, in: Proceedings of MICCAI, 2001, pp. 1048-1057. (Pubitemid 33352514)
26. Y. Giga Surface Evolution Equations. A Level set Approach Monographs in Mathematics vol. 99 2006 Birghäuser Verlag
27. M. Kass, A. Witkin, and D. Terzopoulos Snakes: active contour models International Journal of Computer Vision 1 1987 321 331
28. A.S. Kechris Classical Descriptive Set Theory 1994 Springer-Verlag
29. R. Kimmel Fast edge integration S. Osher, N. Paragios, Geometric Level Set Method in Imaging, Vision and Graphics 2006 Springer
30. O. Ley Lower-bound gradient estimates for first-order Hamilton-Jacobi equations and applications to the regularity of propagating fronts Advanced Differential Equations 6 5 2001 547 576
31. R. Malladi, J.A. Sethian, and B.C. Vemuri Shape modeling with front propagation: a level set approach IEEE Transactions on Pattern Analysis and Machine Intelligence 17 2 1995 158 175
32. A. Mansouri, A. Mitiche, and C. Vázquez Multiregional competition: a level set extension of region competition to multiple region image partitioning Computer Vision and Image Understanding 101 2006 137 150 (Pubitemid 41767423)
33. T. McInerney, and D. Terzopoulos Deformable models in medical image analysis: a survey Medical Image Analysis 1 2 1996 91 108 (Pubitemid 126421958)
34. P.A.V. Miranda, and A.X. Falcão Links between image segmentation based on optimum-path forest and minimum cut in graph Journal of Mathematical Imaging and Vision 35 2009 128 142
35. D. Morgenthaler, and A. Rosenfeld Multidimensional edge detection by hypersurface fitting IEEE Transactions on Pattern Analysis and Machine Intelligence 3 1981 482 486 (Pubitemid 11522289)
36. D. Mumford, and J. Shah Optimal approximations by piecewise smooth functions and associated variational problems Communications on Pure and Applied Mathematics 42 1989 577 685
37. L. Najman, and M. Schmitt Watershed for a continuous function Signal Processing 38 1 1994 99 112
38. S. Osher, and R. Fedkiw Level Set Method and Dynamic Implicit Surfaces 2003 Springer
39. S. Osher, N. Paragios, Geometric Level Set Methods in Imaging, Vision, and Graphics 2006 Springer
40. P.K. Saha, and J.K. Udupa Relative fuzzy connectedness among multiple objects: theory, algorithms, and applications in image segmentation Computer Vision and Image Understanding 82 1 2001 42 56 (Pubitemid 32405220)
41. P.K. Saha, J.K. Udupa, and D. Odhner Scale-based fuzzy connectedness image segmentation: theory, algorithms, and validation Computer Vision and Image Understanding 77 2000 145 174 (Pubitemid 30557365)
42. E. Schechter Handbook of Analysis and Its Foundations 1997 Academic Press
43. J.A. Sethian Curvature and evolution of fronts Communications in Mathematical Physics 101 1985 487 499
44. J.A. Sethian Fast Marching Methods and Level Sets Methods. Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science 1999 Cambridge University Press
45. L. Shafarenko, M. Petrou, and J. Kittler Automatic watershed segmentation of randomly textured color images IEEE Transactions on Image Processing 6 1997 1530 1544 (Pubitemid 127768422)
46. Y. Shi, W.C. Karl, A fast implementation of the level set method without solving partial differential equations, Technical Report ECE-2005-02, ECE Department, Boston University, January 2005.
47. Y. Shi, W.C. Karl, A fast level set method without solving PDEs, acoustics, speech, and signal processing, in: Proceedings ICASSP'05, 2005.
48. M. Trivedi, and J. Bezdek Low-level segmentation of aerial images with fuzzy clustering IEEE Transactions on Systems, Man, and Cybernetics 16 4 1986 589 598 (Pubitemid 16629868)
49. J.K. Udupa, and P.K. Saha Fuzzy connectedness in image segmentation Proceedings of the IEEE 91 10 2003 1649 1669
50. J.K. Udupa, P.K. Saha, and R.A. Lotufo Relative fuzzy connectedness and object definition: theory, algorithms, and applications in image segmentation IEEE Transactions on Pattern Analysis and Machine Intelligence 24 2002 1485 1500 (Pubitemid 35421791)
51. J.K. Udupa, and S. Samarasekera Fuzzy connectedness and object definition: theory, algorithms, and applications in image segmentation Graphical Models and Image Processing 58 3 1996 246 261 (Pubitemid 126381825)
52. L.A. Vese, and T.F. Chan A multiphase level set framework for image segmentation using the Mumford and Shah model Journal of Computer Vision 50 3 2002 271 293 (Pubitemid 35377416)
53. L. Vincent, and P. Soile Watersheds in digital spaces: an efficient algorithm based on immersion simulations IEEE Transactions on Pattern Analysis and Machine Intelligence 13 6 1991 583 598 (Pubitemid 21675616)
54. National Library of Medicine Insight Segmentation and Registration Toolkit, ITK, program "ShapeDetectionLevelSetFilter," < http://www.itk.org/HTML/ShapeDetectionLevelSet.htm >.