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Image segmentation is an important task in the domain of computer vision andmedical imaging. In natural and medical images, intensity inhomogeneity, i.e.the varying image intensity, occurs often and it poses considerable challengesfor image segmentation. In this paper, we propose an efficient variationalmethod for segmenting images with intensity inhomogeneity. The method isinspired by previous works on two-stage segmentation and variational Retinex.Our method consists of two stages. In the first stage, we decouple the imageinto reflection and illumination parts by solving a convex energy minimizationmodel with either total variation or tight-frame regularisation. In the secondstage, we segment the original image by thresholding on the reflection part,and the inhomogeneous intensity is estimated by the smoothly varyingillumination part. We adopt a primal dual algorithm to solve the convex modelin the first stage, and the convergence is guaranteed. Numerical experimentsclearly show that our method is robust and efficient to segment both naturaland medical images.

Total Variation and Tight Frame Image Segmentation with Intensity Inhomogeneity