基于变分水平集的图像分割模型

基于传统的变分水平集方法的图像分割,水平集函数必须周期性地重新初始化使之保持为符号距离函数,这存在如何选择重新初始化的时间和方式的难题.Li模型通过在能量泛函中引入一个内部约束能量,去除了水平集函数在演化过程中需重新初始化的难题.通过对Li模型的分析,提出了一个新的变分水平集的分割模型.该模型通过在能量泛函中加入一个较简单的内部约束能量,同样可以实现水平集演化过程中的无需重新初始化.并且通过对边缘停止函数的重新定义,引入了新的外部能量,使得本文模型对噪声图像的分割更具鲁棒性.实验表明无论是在收敛速度上,还是在对噪声图像的分割质量上,本文模型和Li模型相比都具有一定的优势.

New Model Based on Variational Level Set for Image Segmentation

In the traditional variational level set method for image segmentation, the evolving level set function needs periodical re-initialization to keep it close to a signed distance function during the evolution. It remains many serious problems such as when and how to apply the re-initialization. Li presented a new variational formulation that forces the level set function to be close to a signed distance function by adding an internal energy into the energy functional, and therefore completely eliminates the need of the expensive re-initialization procedure. We present a new image segmentation model based on variational level set method. It also completely eliminates the need of the re-initialization by adding a new and simple internal energy into the energy functional. In addition, a new external energy by redefining the edge stopping function is introduced, which makes the proposed model more robust to noisy image segmentation. The experimental results show that, compared with Li model, our model has some superiority in the convergence speed andsegmentation quality for noisy image.