一种改进的无需水平集重新初始化的C-V主动轮廓模型

摘要

重新初始化是使水平集函数保持符号距离函数的必要步骤.虽然它保证了水平集函数的稳定收敛,但是它也降低了曲线演化的速度.本文主要在该方面针对Chan-Vese提出的水平集图像分割模型进行了改进,提出了无需重新初始化的C-V模型.该模型将水平集函数与距离函数的偏差作为能量函数引入C-V模型,以此来约束水平集函数成为距离函数,提高了C-V模型的演化速度.同时该模型能够用一般的分段常数函数来定义初始水平集函数,即水平集函数不必初始化为符号距离函数.这样,对于不规则形状的初始轮廓,节省了初始化过程所消耗的时间.实验结果表明,本文所提出的模型不仅提高了C-V模型的演化速度,而且实现了水平集函数初始化的灵活性.%We propose a novel improved C-V model without re-initialization to segment objects in an image. We introduce the deviation of level set function from the signed distance function into the C-V model (i.e., active contours without edges) to keep approximately the level set function as a signed distance function during the curve evolution. Therefore, in our model, the time-consuming re-initialization procedure is not necessary and it thus speeds up the curve evolution and the segmentation. Moreover, the level set function can be flexibly initialized with a piecewise constant function rather than a signed distance function in practice. Thereby the consuming time to compute a signed distance function from an initial curve in irregular shape is saved. The numerical algorithm of our model is implemented using the finite difference scheme.