Frame based segmentation for medical images

Communications in Mathematical Sciences

Volumn 9, Issue 2, 2011, Pages 551-559

  Dong, Bin ^a   Chien, Aichi ^b   Shen, Zuowei ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Image segmentation; Level set method; Sparse approximation; Tight frames

Indexed keywords

EID: 78650483922     PISSN: 15396746     EISSN: None     Source Type: Journal    
DOI: 10.4310/cms.2011.v9.n2.a10     Document Type: Article

References (38)

1. J. Cai, S. Osher, and Z. Shen, Split Bregman methods and frame based image restoration, Multiscale Modeling and Simulation: A SIAM Interdisc. J., 8(2), 337-369, 2009.
2. T. Chan and L. Vese, An active contour model without edges, Scale-Space Theo. in Comput. Vis., 141-151, 1999.
3. T. Chan and L. Vese, Active contours without edges, IEEE Trans. Imag. Proc., 10(2), 266-277, 2001.
4. T. Chan, S. Esedoglu, and M. Nikolova, Algorithms for finding global minimizers of image segmentation and denoising models, ALG., 66(5), 1632-1648.
5. X. Bresson, S. Esedoglu, P. Vandergheynst, J. Thiran, and S. Osher, Fast global minimization of the active contour/snake model, J. Math. Imag. and Vis., 28(2), 151-167, 2007.
6. T. McInerney and D. Terzopoulos, Deformable models in medical image analysis: a survey, Med. Imag. Anal., 1(2), 91-108, 1996.
7. M.E. Leventon, W.E.L. Grimson, and O. Faugeras, Statistical shape influence in geodesic active contours, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2000, 1, 316-323, 2002.
8. Z. Tu, K. Narr, P. Dollar, I. Dinov, P. Thompson, and A. Toga, Brain anatomical structure segmentation by hybrid discriminative/generative models, IEEE Trans. Med. Imag., 27(4), 495-508, 2008.
9. J. Yang, L. Staib, and J. Duncan, Neighbor-constrained segmentation with 3d deformable models, Lecture Notes in Computer Science, 198-209, 2003.
10. C. Li, C. Kao, J. Gore, and Z. Ding, Minimization of region-scalable fitting energy for image segmentation, IEEE Trans. Imag. Proc., 17(10), 1940-1949, 2008.
11. L. Vese and T. Chan, A multiphase level set framework for image segmentation using the Mumford and Shah model, Int. J. Comput. Vis., 50(3), 271-293, 2002.
12. S. Pizer, P. Fletcher, S. Joshi, A. Thall, J. Chen, Y. Fridman, D. Fritsch, A. Gash, J. Glotzer, and M. Jiroutek, Deformable m-reps for 3d medical image segmentation, Int. J. Comput. Vis., 55(2), 85-106, 2003.
13. A. Tsai, A. Yezzi, W. Wells, C. Tempany, D. Tucker, A. Fan, W. Grimson, and A. Willsky, A shape-based approach to the segmentation of medical imagery using level sets, IEEE Trans. Med. Imag., 22(2), 137-154, 2003.
14. N. Flasque, M. Desvignes, J. Constans, and M. Revenu, Acquisition, segmentation and tracking of the cerebral vascular tree on 3D magnetic resonance angiography images, Med. Imag. Anal., 5(3), 173-183, 2001.
15. D. Nain, A. Yezzi, and G. Turk, Vessel segmentation using a shape driven flow, Lecture Notes in Computer Science, 51-59, 2004.
16. C. Kirbas and F. Quek, A review of vessel extraction techniques and algorithms, ACM Comput. Surv., 36(2), 81-121, 2004.
17. Y. Chen, H. Tagare, S. Thiruvenkadam, F. Huang, D. Wilson, K. Gopinath, R. Briggs, and E. Geiser, Using prior shapes in geometric active contours in a variational framework, Int. J. Comput. Vis., 50(3), 315-328, 2002.
18. I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Lecture Notes, SIAM, nr., 61, 1992.
19. d): the analysis of the analysis operator, J. Func. Anal., 148(2), 408-447, 1997.
20. I. Daubechies, B. Han, A. Ron, and Z. Shen, Framelets: Mra-based constructions of wavelet frames, Appl. Comput. Har. Anal., 14, 1-46, Jan 2003.
21. Z. Shen, Wavelet frames and image restorations, Proceedings of the International Congress of Mathematicians, Hyderabad, India, 2010.
22. B. Dong and Z. Shen, MRA based wavelet frames and applications, IAS Lecture Notes Series, Summer Program on The Mathematics of Image Processing, Park City Mathematics Institute, 2010.
23. R. Coifman and D. Donoho, Translation-invariant de-noising, Lecture Notes in Statistics, New York, Springer Verlag, 125-125, 1995.
24. E. Candes and D. Donoho, New tight frames of curvelets and optimal representations of objects with C2 singularities, Commun. Pure Appl. Math., 56, 219-266, 2004.
25. C. Chaux, P. Combettes, J. Pesquet, and V. Wajs, A variational formulation for frame-based inverse problems, Inv. Prob., 23, 1495-1518, 2007.
26. I. Daubechies, G. Teschke, and L. Vese, Iteratively solving linear inverse problems under general convex constraints, Inv. Prob. Imag., 1(1), 29, 2007.
27. M. Elad, J. Starck, P. Querre, and D. Donoho, Simultaneous cartoon and texture image in-painting using morphological component analysis (MCA), Appl. Comput. Har. Anal.., 19, 3, 340-358, 2005.
28. M. Fadili, J. Starck, and F. Murtagh, Inpainting and zooming using sparse representations, Comput. J., 52(1), 64, 2009.
29. A. Chai and Z. Shen, Deconvolution: A wavelet frame approach, Numer. Math., 106(4), 529-587, 2007.
30. M. Unser, Texture classification and segmentation using wavelet frames, IEEE Trans. Imag. Proc., 4(11), 1549-1560, 1995.
31. S. Arivazhagan and L. Ganesan, Texture segmentation using wavelet transform, Patt. Recog. Lett., 24(16), 3197-3203, 2003.
32. R. Kimmel, Fast edge integration, Geometric Level Set Methods in Imaging Vision and Graphics, 59-77, 2003.
33. R. Kimmel and A. Bruckstein, Regularized laplacian zero crossings as optimal edge integrators, Int. J. Comput. Vis., 53(3), 225-243, 2003.
34. V. Caselles, R. Kimmel, and G. Sapiro, Geodesic active contours, Int. J. Comput. Vis., 22, 61-79, 1997.
35. W. Fleming and R. Rishel, An integral formula for total gradient variation, Arch. der Math., 11(1), 218-222, 1960.
36. T. Goldstein, X. Bresson, and S. Osher, Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction, UCLA CAM report, 09-06, 2009.
37. T. Goldstein and S. Osher, The split Bregman algorithm for L1 regularized problems, SIAM J. Imag. Sci., 2(2), 323-343, 2009.
38. A. Chien, M. Castro, S. Tateshima, J. Sayre, J. Cebral, and F. Vinuela, Quantitative hemody-namic analysis of brain aneurysms at different locations, Amer. J. Neuroradiology, 30(8), 1507-1512, 2009.