基于简化Mumford-Shah模型的活动轮廓边缘检测模型

Active Contour Model for Edge Detection Based on Simplified Mumford-Shah Functional

在Chan-Vese活动轮廓模型(C-V法)的基础上,提出了一种新的边缘检测模型.在该模型中,图像被定义为两个同质区域的组合,图像边缘检测问题转化为基于Mumford-Shah泛函的能量函数最小化问题.本文在分片常数优化逼近中,添加了图像梯度信息,通过调节该项的权重因子,可以得到基于不同灰度强度的图像边缘图.该方法采用了水平集数值技术,因此活动轮廓具备了拓扑变化的能力,并能克服C-V模型检测不出离灰度均值较远的边缘的问题,实验表明了其有效性.

An improved active contour model for edge detection based on Chan and Vese active contour model is proposed. The basic idea is to evolve a curve under constraints from a given image, which is defined as a union of two homogeneous regions representing the object and background respectively. The edge can be detected by seeking a global minimum of an energy function based on the Mumford-Shah functional. The constant term in this model is modified by combining the image gradient information in piecewise constant optimal approximations. This different constant term can be obtained by adjusting the weighting factor that acts on the image gradient term in constant function, and different edge map based on different intensity of image can be obtained. This method is capable of handling changes in the topology of the evolving contour, and can avoid the problem arise in the C-V model that cannot detect the edges whose values are far from the mean intensity value of image. Effectiveness of this method is demonstrated in numerical experiments.