图像分割中偏微分方程解的存在性研究

The theory of image segmentation in the existence of partial differential equation model

本文对图像分割中基于水平集的偏微分方程模型解的存在性进行研究,主要采用偏微分方程理论以及图像处理中偏微分方程粘性解理论。对模型的解的存在性和唯一性问题在理论上进行解决,进而解决数值计算中存在的迭代收敛性问题,为其提供理论依据,确保实际应用中图像分割模型具有一定的稳定性。

In this paper, the image segmentation based on level set in the existence of the solution of the partial differential equation model for research, mainly USES the theory of partial differential equations and the theory of the viscosity solution of partial differential equations in image processing. Existence and uniqueness of solutions of the model in theory to solve the problem, and solve problems in iterative convergence of numerical calculation, providing theoretical basis, to ensure that the image segmentation model in practical application has certain stability.