A Locally Statistical Active Contour Model for Image Segmentation with Intensity Inhomogeneity

Kaihua Zhang^a, Lei Zhang^a, Kin-Man Lam^b and David Zhang^a

^aDept. of Computing, The Hong Kong Polytechnic University, Hong Kong, China

^bDepartment of Electronic and Information Engineering, The Hong Kong Polytechnic University

Abstract ˇŞ It is often a very challenging task to accurately segment images with intensity inhomogeneity, because most of the widely used algorithms are region-based and depend on the intensity homogeneity of the interested object. A novel locally statistical active contour model (ACM) for image segmentation in the presence of intensity inhomogeneity is presented in this paper. The inhomogeneous objects are modeled as Gaussian distributions of different means and variances, and a moving window is used to map the original image into another domain, where the intensity distributions of inhomogeneous objects are still Gaussian but are better separated. The means of the Gaussian distributions in the transformed domain can be adaptively estimated by multiplying a bias field with the original signal within the window. A statistical energy functional is then defined for each local region, which combines the bias field, the level set function, and the constant approximating the true signal of the corresponding object. The proposed ACM can be directly applied to simultaneous segmentation and bias correction for 3T and 7T MR images. It is robust to the initialization of the level set function, thereby allowing automatic applications. Experiments on both synthetic and real images demonstrate the superiority of our proposed algorithm to state-of-the-art and representative methods.

MATLAB CODES:

2-phase model LSACM_2PH_v0.zip

4-phase model LSACM_4PH_v0.zip

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Some experimental results by our method in our paper:

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1. Segmentation for two synthetic images and two real vessel images with intensity inhomogeneity (Figure 2 in paper).

2. Segmentation for a synthetic image and two real MR images with severe intensity inhomogeneity. (Figure 3 in paper).

References:

[1] K. Zhang, L. Zhang, K. Lam, and D. Zhang, A Locally Statistical Active Contour Model for Image Segmentation with Intensity Inhomogeneity. Submitted.

Our former related work

[2] K. Zhang, L. Zhang, H. Song and W. Zhou, ˇ°Active contours with selective local or global segmentation: a new formulation and level set method,ˇ± Image and Vision Computing, vol. 28, issue 4, pp. 668-676, April 2010.Paper Source code Website

[3] K. Zhang, H. Song, and L. Zhang, ˇ°Active contours driven by local image fitting energy,ˇ± Pattern recognition, vol.43, no.4, pp.1199-1206, 2010.Paper Source code

[4] K. Zhang, L. Zhang and S. Zhang, ˇ°A VARIATIONAL MULTIPHASE LEVEL SET APPROACH TO SIMULTANEOUS SEGMENTATION AND BIAS CORRECTION,ˇ± ICIP 2010.Paper Source code

Other main related work

[5] T. Chan and L. Vese, ˇ°Active contours without edges,ˇ± IEEE Trans. Image Process, vol. 10, no. 2, pp. 266¨C277, Feb. 2001.

[6] X. Bresson, S. Esedoglu, P. Vandergheynst, J. Thiran, S. Osher, ˇ°Fast Global Minimization of the Active Contours/Snakes Model,ˇ± J.Math Imaging Vis., vol. 28, pp. 151¨C167, 2007.

[7] C. Darolti, A. Mertins, C. Bodensteiner, and U. Hofmann, ˇ°Local Region Descriptors for Active Contours Evolution,ˇ± IEEE Trans. Image Process., vol. 17, no. 12, pp. 2275-2288, Dec. 2008.

[8] S. Lankton, A. Tannenbaum, ˇ°Localizing Region-Based Active Contours,ˇ± IEEE Trans. Image Process., vol. 17, no. 11, pp. 2029-2039, Nov. 2008.

[9] C. Li, C. Kao, J. Gore, and Z. Ding, ˇ°Implicit Active Contours Driven by Local Binary Fitting Energy,ˇ±  Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1¨C7, 2007.

[10] C. Li, R. Huang, Z. Ding, C. Gatenby, D. Metaxas, and J. C. Gore, ˇ°A Level Set Method for Image Segmentation in the Presence of Intensity Inhomogeneities with Application to MRI,ˇ± IEEE Trans. Image Process., vol. 20, no. 7, pp. 2007-2016, Jul. 2011.