改进的Ambrosio-Tortorelli模型及其图像分割应用

Improved Ambrosio-Tortorelli Model and Its Applicationin Image Segmentation

针对Ambrosio-Tortorelli模型在图像分割应用中边缘检测能力不足的问题,在确保模型解的存在性等良好性质前提下,对模型的边缘惩罚项进行改进,提出了一种新的图像边缘测度的逼近形式-改进的Ambrosio-Tortorelli模型.采用变分法,梯度下降法和有限差分法等方法设计了有效的数值求解算法,并进行数值实验.实验结果表明,改进的Ambrosio-Tortorelli模型具有更合理的衰减特性,能够在一定程度上提高弱边缘检测能力.

Aiming at the problem of insufficient edge detection ability of Ambrosio-Tortorelli model in image segmentation application,under the premise of ensuring the existence of model solutions and other good properties,the edge penalty term of the model is improved,and a new approximation form of image edge measurement,an Improved Ambrosio-Tortorelli model,is proposed.Variational method,gradient descent method and finite difference method are used to design effective numerical solution algorithms and carry out numerical experiments.Experimental results show that the Improved Ambrosio-Tortorelli model has more reasonable attenuation characteristics,which can improve the weak edge detection ability to a certain extent.