Improved Mumford-Shah Functional for Coupled Edge-Preserving Regularization and Image Segmentation
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Improved Mumford-Shah Functional for Coupled Edge-Preserving Regularization and Image Segmentation Zhang Hongmei1, 2 and Wan Mingxi1, 2 1 The
Key Laboratory of Biomedical Information Engineering, Ministry of Education, 710049 Xi’an, China of Biomedical Engineering, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China
2 Department
Received 11 October 2005; Revised 16 January 2006; Accepted 18 February 2006 Recommended for Publication by Moon Gi Kang 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 MumfordShah functional and other edge-preserving approach, and the results show the effectiveness of the proposed method. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.
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INTRODUCTION
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]. However, the MS functional is based on Bayesian linear restoration, so the resultant linear diffusion not only smoothes all structures in an equal amount but also dislocates them more and more with the increasing scale that may blur true boundaries [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. However, due to the unknown discontinuities set of lower dimension, most approaches solve the weak formulation of the improved functional. In [3], the smooth constraint and the data fidelity are defined by the norm functions instead of quadratic functions in the MS functional. The resultant diffusion is modulated by the magnitude of the gradient that can deblur the edges. 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. But these approaches solving weak formulation concentrate rather on image restoration than image segmentation. Therefore, exact boundary locations cannot be explicitly yielded. To solve the MS functional in such a way that image segmentation can be explicitly yielded, level set and curve evolution fo
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