图像分割中分段光滑Mumford-Shah模型的水平集算法

图像分割和轮廓提取在计算机视觉和模式识别中具有重要意义，基于主动轮廓模型的图像分割和轮廓提取是目前研究热点，分析了Mumford—Shah模型的主动轮廓新的视觉机制；并推导了简化的分段光滑水平集模型,通过构造具有柔性距离函数，对迭代步骤中水平集函数重新初始化，结合本质上无振荡格式(ENO scheme)和预测校正格式，提出了一种新的有限差分算法，该算法不但能提取多个具有不同凹凸拓扑结构和灰度差异物体的轮廓，而且能保持分割后物体的灰度特性。最后给出了若干算例，算例表明，该水平集算法具有数值稳定性，不会出现振荡现象。

A New Level Set Method of Piece-Wise Smooth Mumford-Shah Model for Image Segmentation

Image segmentation and contour detection is important for computer vision and pattern recognition, and the active contour for image segmentation is treated as the most popular study hotspots. A detailed analysis of Mumford-Shah model is given with emphasis on its active contour mechanism, and then a piece-wise smooth level set model is discussed. By constructing the new soft distance function to reinitialize the level set function during the iterations, and by combining the essentially non-oscillatory scheme and the predict-revised scheme, a new finite difference algorithm is proposed. This algorithm not only can detect multiple objects with various shapes of topology including convex and concave objects, but also has the ability to preserve the gray property of the multiple objects. Finally, some examples are given and it is shown that the new algorithm is stable and oscillation does not appear.