Abstract
Despite many research efforts, accurate extraction of structures of interest still remains a difficult issue in many medical imaging applications. This is particularly the case for magnetic resonance (MR) images where image quality depends highly on the acquisition protocol. In this paper, we propose a variational region based algorithm that is able to deal with spatial perturbations of the image intensity directly. Image segmentation is obtained by using a Γ-Convergence approximation for a multi-scale piecewise smooth model. This model overcomes the limitations of global region models while avoiding the high sensitivity of local approaches. The proposed model is implemented efficiently using recursive Gaussian convolutions. Numerical experiments on 2-dimensional human liver MR images show that our model compares favorably to existing methods.
Chapter PDF
Similar content being viewed by others
Keywords
- Image Segmentation
- Piecewise Smooth
- Convergence Approximation
- Liver Segmentation
- Liver Magnetic Resonance Image
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Ambrosio, L., Tortorelli, V.: Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence. Communications on Pure and Applied Mathematics 43, 999–1036 (1990)
An, J., Chen, Y.: Region based image segmentation using a modified Mumford-Shah algorithm. In: Proc. Scale Space Varional Methods in Computer Vision, pp. 733–742 (2007)
Baldo, S.: Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids. Annals of Institute Henri Poincare 7, 67–90 (1990)
Chan, T., Vese, L.: Active contours without edges. IEEE Transaction on Image Processing 10, 266–277 (2001)
Esedoglu, S., Tsai, R.: Threshold dynamics for the piecewise constant Mumford-Shah fuctional. Computational and Applied Mathematics Report. 04-63 UCLA (2004)
Li, C., Kao, C., Gore, J., Ding, Z.: Implicit active contours driven by local binary fitting energy. In: Proc. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE Computer Society Press, Los Alamitos (2007)
Lie, J., Lysaker, M., Tai, X.: A binary level set model and some aplications to Mumford-Shah segmentation. Computational and Applied Mathematics Report. vol. 31 (2004)
Modica, L.: The gradient theory of phase transitions and the minimal interface criterion. Archive for Rational Mechanics and Analysis 98, 123–142 (1987)
Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics 42, 577–685 (1989)
Osher, S., Fedkiw, R.: Level set methods and dynamic implicit surfaces. Springer, New York (2003)
Piovano, J., Rousson, M., Papadopoulo, T.: Efficient segmentation of piecewise smooth images. In: Proc. Scale Space Varional Methods in Computer Vision, pp. 709–720 (2007)
Shen, J.: Γ-Convergence approximation to piecewise constant Mumford-Shah segmentation. In: Blanc-Talon, J., Philips, W., Popescu, D.C., Scheunders, P. (eds.) ACIVS 2005. LNCS, vol. 3708, pp. 499–506. Springer, Heidelberg (2005)
Wang, M., Zhou, S.: Phase field: A variational method for structural topology optimization. Computer Modeling in Engineering & Science 6, 547–566 (2004)
Hou, Z.: A review on MR image intensity inhomogeneity correction. International Journal of Biomedical Imaging, 1–11 (2006)
Zhang, Y., Brady, M., Smith, S.: Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm. IEEE Transactions on Medical Imaging 20, 45–57 (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
An, J., Rousson, M., Xu, C. (2007). Γ-Convergence Approximation to Piecewise Smooth Medical Image Segmentation. In: Ayache, N., Ourselin, S., Maeder, A. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2007. MICCAI 2007. Lecture Notes in Computer Science, vol 4792. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75759-7_60
Download citation
DOI: https://doi.org/10.1007/978-3-540-75759-7_60
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75758-0
Online ISBN: 978-3-540-75759-7
eBook Packages: Computer ScienceComputer Science (R0)