基于高阶正则与非光滑数据拟合项的图像边缘检测模型

Image Edge Detection Model Based on Higher Order Regular and Nonsmooth Data Fitting Terms

在现代科技社会中,随着数字图像处理技术的高速发展,图像分割和物体边缘检测被广泛应用于医学领域,军事领域,公共防卫领域,计算机视觉领域及农业气象领域.在本文中,基于经典的Chan-Vese (CV)模型,介绍一个含有L1范数数据拟合项和二阶正则项(TV2)的分段常数图像边缘检测模型.新模型利用一个高阶正则函数对目标函数进行惩罚,将其作为新目标函数的一个约束,使得该模型能够分割和检测低对比度,并且含有外加噪声的图像.理论上,我们在大胆合理的假设下,给出该模型的部分收敛性分析.计算方面,我们通过研究新模型的理论可解性,关于该模型的数值实现方面,应用ADMM算法对该模型进行数值求解,从而设计一种新的求解方式,并用灰度图像和真实图像做大量的数值实验,并和原始CV模型进行对比,得出的实验结果表明,该模型的许多优点在各领域具有广泛应用价值.

In the modern science and technology society, with the rapid development of digital image processing technology, image segmentation, and object edge detection are widely used in the medical, military, public defense,computer vision, and agricultural meteorology field. In this study, based on the classical Chan-Vese(CV) model, a piecewise constant image edge detection model with L1 norm data fitting term and TV2 second-order regular term is introduced. The new model uses a high-order regular function to penalize the objective function as a constraint on the new objective function, so that the model enabling to segment and detect images with low contrast and containing additional noise. Theoretically, we give reasonable assumptions, and a partial convergence analysis of the model is carried out. In terms of computation load, we study the theoretical solvability of the new model. Compulationally, for the numerical implementation of the model, the model is numerically solved by ADMM algorithm, and a new solution method is designed. A large number of numerical experiments were carried out with grayscale images and real images, and compared with the original CV model. The experimental results show that many advantages of the model with wide applications.