This paper presents a region-based active contour method for the segmentation of intensity inhomogeneous images using an energy functional based on local and global fitted images. A square image fitted model is defined by using both local and global fitted differences. Moreover, local and global signed pressure force functions are introduced in the solution of the energy functional to stabilize the gradient descent flow. In the final gradient descent solution, the local fitted term helps extract regions with intensity inhomogeneity, whereas the global fitted term targets homogeneous regions. A Gaussian kernel is applied to regularize the contour at each step, which not only smoothes it but also avoids the computationally expensive re-initialization. Intensity inhomogeneous images contain undesired smooth intensity variations (bias field) that alter the results of intensity-based segmentation methods. The bias field is approximated with a Gaussian distribution and the bias of intensity inhomogeneous regions is corrected by dividing the original image by the approximated bias field. In this paper, a two-phase model is first derived and then extended to a four-phase model to segment brain magnetic resonance (MR) images into the desired regions of interest. Experimental results with both synthetic and real brain MR images are used for a quantitative and qualitative comparison with state-of-the-art active contour methods to show the advantages of the proposed segmentation technique in practical terms.
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