An Improved Algorithm for the Piecewise-Smooth Mumford and Shah Model in Image Segmentation
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An Improved Algorithm for the Piecewise-Smooth Mumford and Shah Model in Image Segmentation Yingjie Zhang School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an Shaanxi, 710049, China Received 8 September 2005; Revised 18 January 2006; Accepted 22 January 2006 Recommended for Publication by Yue Wang An improved algorithm for the piecewise-smooth Mumford and Shah functional is presented. Compared to the previous work of Chan and Vese, and Choi et al., extensions of the key functions u± are replaced by updating the level set function based on an artificial image that is composed of the diffused image and the original image. The low convergence problem of the classical algorithm is efficiently solved in the proposed approach. The resulting algorithm has also been demonstrated by several cases. Copyright © 2006 Yingjie Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Image segmentation is one of the fundamental tasks of computer vision. Its goal is to partition a given image into regions that contain distinct objects. Active contours or “snakes” can be used to segment objects automatically. This framework has been used successfully by Kass et al. [1] to extract boundaries and edges. One potential problem with this approach is that the initial curve has to surround the objects to be detected, and interior contours can not be detected automatically. An algorithm to overcome this difficulty was first introduced by Osher and Sethian [2]. Chan and Vese [3] used a limiting version of Mumford and Shah (MS) [4] function, where the image was modeled as a piece-constant function. After that, they [5] extended the model to segment image using a particular multiphase level set formulation. However, the MS model in piecewise-constant case cannot detect objects successfully from noisy images. To overcome the drawback, Chan and Vese [6] showed how the piecewise-smooth MS segmentation problem could be solved using the level set method, and they had given the piecewise-smooth optimal approximations of a given image. Although the piecewisesmooth MS model works better, it requires the initial curve to be close to the boundaries, or the convergence of the curve to object boundary will be too slow, and for highly noisy images, it will almost collapse. Le and Vese [7] addressed the segmentation problem of images corrupted with additive or multiplicative noise by decomposing the images into three components, such as a piecewise-constant component,
a smooth component and noise. Motivated by the Chan and Vese approach, Lie et al. [8] proposed a variant of a PDEbased level set method, they solved the segmentation problem in a different way, that is, by introducing a piecewiseconstant level set function. Instead of using the zero level of a function to represent the interface between subdomains, the interface is represented implicitly by the discontinu
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