In this chapter we propose a novel variational formulation for brain MRI segmentation. The originality of our approach is on the use of J-divergence (symmetrized Kullback-Leibler divergence) to measure the dissimilarity between local and global regions. In addition, a three-phase model is proposed to perform the segmentation task. The voxel intensity value of all regions is assumed to follow Gaussian distribution. It is introduced to ensure the robustness of the algorithm when an image is corrupted by noise. J-divergence is then used to measure the “distance” between the local and global region probability density functions. The proposed method yields promising results on synthetic and real brain MR images.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
6 References
Zhu C, Jiang T. 2003. Multicontext fuzzy clustering for separation of brain tissues in magenetic resonance images. NeuroImage 18685-696.
Pham DL, Prince JL. 1999. Adaptive fuzzy segmentation of magnetic resonance images. IEEE Trans Med Imaging 18(9):737-752.
Xu C, Pham DL, Prince JL. 2000. Medical image segmentation using deformable models. In Handbook of medical imaging, Vol. 2: Medical image processing and analysis. pp. 129-174. Bellingham, WA: SPIE Press.
Kass M, Witkin A, Terzopoulos D. 1987. Snakes: active contour models. In Proceedings of the IEEE international conference on computer vision, pp. 259-268. Washington, DC: IEEE Computer Society.
Osher S, Sethian JA. 1988. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79(1):12-49.
Malladi R, Sethian JA, Vemuri BC. 1995. Shape modeling with front propagation: a level set approach. IEEE Trans Pattern Anal Machine Intell 17(2):158-175.
Caselles V, Catte F, Coll T, Dibos F. 1993. A geometric model for active contours. Num Math 66:1-31.
Caselles V, Kimmel R, Sapiro G. 1997. Geodesic active contours. Int J Comput Vision 22(1)61-72.
Chan TF, Vese LA. 2001. Active contours without edges. IEEE Trans Image Process 10(2)266-277.
Hibbard LS. 2004. Region segmentation using information divergence measures. Med Image Anal 8(3):233-244.
Paragios N. 2000. Geodesic active regions and level set methods: contributions and applications in artifical vision, PhD dissertation, University of Nice, Sophia Antipolis, France.
Paragios N, Deriche R. 2000. Coupled geodesic active regions for image segmentation: a level set approach. In Proceedings of the European conference on computer vision (ECCV), pp. 224-240. New York: Springer.
Paragios N, Deriche R. 2002. Geodesic active regions and level set methods for supervised texture segmentation. Int J Comput Vision 46(3):223-247.
Gibou F, Fedkiw R. 2003. A Fast hybrid k-means level set algorithm for segmentation. Int J Comput Visio50(3):271-293.
Besson SJ, Barlaud M. 2003. DREAM2S: Deformable regions driven by an eulerian accurate minimization method for image and video segmentation. Int J Comput Vision 53(1):45-70.
Zhu S, Yuille A. 1996. Region competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation. IEEE Trans Pattern Anal Machine Intell 18(9):884-900.
Kadir T, Brady M. 2003. Unsupervised non-parametric region segmentation using level sets. In Proceedings of the IEEE international conference on computer vision, pp. 1267-1274. Washington, DC: IEEE Computer Society.
Heiler M, Schnorr C. 2003. Natural image statistics for natural image segmentation. In Pro- ceedings of the IEEE international conference on computer vision, Vol. 2, pp. 1259-1266. Washington, DC: IEEE Computer Society.
Heiler M, Schnorr C. 2005. Natural image statistics for natural image segmentation. Int J Comput Vision 63(1):5-19.
Goldenberg R, Kimmel R, Rivlin E, Rudzsky M. 2002. Cortex segmentation: a fast variational geometric approach. IEEE Trans Med Imaging 21:1544-1551.
Han X, Xu C, Prince JL. 2003. A topology preserving level set method for geometric deformable models. IEEE Trans Pattern Anal Machine Intell 25(6):755-768.
Han X, Pham D, Tosun D, Rettmann ME, Xu C, Prince JL. 2004. CRUISE: cortical reconstruction using implicit surface evolution. NeuroImage 23(3):997-1012.
Zeng X, Staib L, Schultz R, Duncan J. 1999. Segmentation and measurement of the cortex from 3D MR images using coupled surfaces propagation. IEEE Trans Med Imaging 18(10):927-937.
Chakraborty A, Staib LH, Duncan JS. 1996. Deformable boundary finding in medical images by integrating gradient and region information. IEEE Trans Med Imaging 15(6):859-870.
Van Leemput K, Maes F, Vandermeulen D, Suetens P. 2003. A unifying framework for partial volume segmentation of brain MR images. IEEE Trans Med Imaging 22(1):105-119.
Rajapakes J, Frugges F. 1998. Segmentation of MR images with intensity inhomogeneities. Image Vision Comput 16(3):165-180.
Vese LA, Chan TF. 2002. A multiphase level set framework for image segmentation using the Mumford and Shah model. Int J Comput Vision 50(3):271-293.
Kim J, Fisher III JW, Yezzi A, Cetin M, Willsky AS. 2005. A nonparametric statistical method for image segmentation using information theory and curve evolution. IEEE Trans Image Process 14(10):1486-1502.
Lenglet C, Rousson M, Deriche R. 2004. Segmentation of 3D probability density fields by surface evolution: application to diffusion mr images. In Proceedings of the international conference on medical image computing and computer-assisted intervention (MICCAI 2004). Lecture notes in computer science, Vol. 3216, pp. 18-25. Berlin: Springer.
Sussman M, Smereka P, Osher S. 1994. A level set approach for computing solutions to incom- pressible two-phase flow. J Comput Phys 199:146-159.
Stejskal EO, Tanner JE. 1965. Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J Chem Phys 42:288-292.
Li C, Xu C, Gui C, Fox MD. 2005. Level set evolution without re-initialization: a new varia- tional formulation. In IEEE international conference on computer vision and pattern recognition (CVPR), pp. 430-436. Washington, DC: IEEE Computer Society.
Aubert G, Barlaud M, Faugeras O, Jehan-Besson S. 2003. Image segmentation using active contours: calculus of variations or shape gradients? SIAM J Appl Math 63(6):2128-2154.
Sethian JA. 1999. Level set methods and fast marching methods: evolving interfaces in computa- tional geometry, fluid mechanics, computer vision and materials science. Cambridge: Cambridge UP.
Tai X, Chan T. 2004. A survey on multiple level set methods with applications for identifying piecewise constant functions. Int J Num Anal Model 1(1):25-47.
Wang Z, Vemuri BC. 2004. Tensor field segmentation using region based active contour model. In Proceedings of the European conference on computer vision (ECCV), Vol. 4, pp. 304-315. Washington, DC: IEEE Computer Society.
Yezzi A, Tsai A, Willsky A. 1999. A statistical approach to curve evolution for image segmentation. MIT LIDS Technical Report.
Zhu W, Jiang T, Li X. 2005. Local region based medical image segmentation using J-divergence measures. In Proceedings of the 27th annual international conference on engineering in medicine and biology, pp. 7174-7177. Washington, DC: IEEE Computer Society.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Zhu, W., Jiang, T., Li, X. (2007). Segmentation Of Brain Mr Images Using J-Divergence Based Active Contour Models. In: Deformable Models. Topics in Biomedical Engineering. International Book Series. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68343-0_11
Download citation
DOI: https://doi.org/10.1007/978-0-387-68343-0_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-31204-0
Online ISBN: 978-0-387-68343-0
eBook Packages: EngineeringEngineering (R0)