图像分割中的偏微分方程模型解的存在性分析

Analysis on Existence of PDE's Solution for Image Segmentation

该文研究一类基于水平集的偏微分方程图像分割模型的解的存在性问题,使用偏微分方程理论和图像处理中的偏微分方程粘性解理论,从理论上解决了模型的解的存在性问题和唯一性问题,为解决数值计算的迭代收敛性问题提供了理论依据,从而使图像分割模型在实际应用中具有比较强的稳定性。

This paper investigates the existence and uniqueness of one type of partial differential equation's(PDE) solution for image segmentation based on level set method.The theory of PDE and the theory of viscosity solutions for image processing are used to solve the problems of existence and uniqueness of viscosity solutions.This work supports the theoretical basis to solve the convergence problem for iteration of numerical computation.In practice,the result ensures the better stability for image segmentation mo...