Abstract
An improved Mumford-Shah functional for coupled edge-preserving regularization and image segmentation is presented. A nonlinear smooth constraint function is introduced that can induce edge-preserving regularization thus also facilitate the coupled image segmentation. The formulation of the functional is considered from the level set perspective, so that explicit boundary contours and edge-preserving regularization are both addressed naturally. To reduce computational cost, a modified additive operator splitting (AOS) algorithm is developed to address diffusion equations defined on irregular domains and multi-initial scheme is used to speed up the convergence rate. Experimental results by our approach are provided and compared with that of Mumford-Shah functional and other edge-preserving approach, and the results show the effectiveness of the proposed method.
Highlights
Mumford-Shah (MS) functional is an important variational model in image analysis
To reduce the computational cost, a modified additive operator splitting (AOS) algorithm is developed to address the diffusion equations defined on irregular domains
By introducing Markov random field (MRF) line process, the above restoration is expressed as the minimization problem [2]: Some approaches solve the weak formulation of the MS functional [9,10,11]
Summary
Mumford-Shah (MS) functional is an important variational model in image analysis. It minimizes a functional involving a piecewise smooth representation of an image and penalizing the Hausdorff measure of the set of discontinuities, resulting in simultaneous linear restoration and segmentation [1, 2]. The situation becomes worse for poor-quality images with artifacts and low contrast, making the coupled segmentation unreliable To address this problem, many improvements on MS model from nonlinear diffusion perspective are developed. In [4], an edge-preserving regularization model based on the half-quadratic theorem is proposed, where the diffusion is nonlinear both in intensity and edges These approaches solving weak formulation concentrate rather on image restoration than image segmentation. In this paper, inspired by the nonlinear diffusion theory and level set method, an improved Mumford-Shah functional is presented from both the theoretical and numerical aspects. Different from existing edge-preserving approaches that solve the weak formulation of the problem, we formulate the proposed functional from the level set perspective so that nonlinear edgepreserving regularization and explicit boundary contours are both addressed naturally.
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