多层Mumford-Shah向量值图像分割、去噪与重建模型

Hierarchical Mumford-Shah Model for Vector-valued Image Segmentation, Denoising and Reconstruction

针对多层Mumford-Shah图像分割、去噪与重建模型不能进行彩色等向量值图像处理的问题,提出了多层Mumford-Shah向量值图像分割、去噪与重建模型和求解该模型泛函最小值的水平集逐层迭代算法．该模型是Mumford- Shah“最小分割问题”的向量值图像“多层”实现模型．实验结果表明,该方法不仅能够同时进行具有T型图像边缘或更复杂拓扑结构图像边缘的向量值图像分割、去噪与重建,而且比Tsai A等人提出的多层求解轮廓和Chan T等人提出的多相水平集方法更简单有效．

A novel hierarchical Mumford-Shah functional model is addressed to simultaneously segment, denoise and reconstruct the data within a given vector-valued image such as a color image, and to handle important image features such as triple points and other multiple junctions, which can be seen as a hierarchical case of the Mumford-Shah minimal partition problem for vector-valued images. At the same time, a new iterative tier-by-tier algorithm based on techniques of level set is proposed to minimize the functional, which is more effective and more simply than existing algorithms such as the hierarchical approach proposed by Tsai A et al. and the multiphase level set methods proposed by Chan T et al.