Luminita A. Vese and Stanley J. Osher proposed a model that can decompose a given image into a cartoon and a texture component efficiently, but the decomposition is not completely. The cartoon part contains some texture information and its edge are easy to be fuzzy. By using the method of half-quadratic regularization in the model of vese and osher, a model is proposed that combines extracting texture with detecting contour, and discusses three forms of edge regularization. The numerical experiments show that the new model C makes image decomposition and edge extraction be in progress at the same time. It can keep the cartoon image better smoothness and meanwhile, can protect the edge detail information effectively. Thus the image is decomposed completely and the extraction of the edge information is more accurate.%Luminita A.Vese和Stanley J.Osher提出的卡通一纹理图像分解模型,能将一幅自然图像中的卡通部分和纹理部分分开,但是分解不完全,卡通部分还含有一些纹理信息且边缘容易被模糊.在Vese和Osher卡通一纹理分解模型的基础上,运用半二次规整化方法,得到联合图像分解与边缘检测的新模型.并讨论了其中边缘正则项的三种形式.数值实验表明新模型C使得卡通—纹理分解与边缘提取同时进行,在保持卡通图像较好光滑性的同时,能有效地保护边缘细节的信息,使得图像分解更彻底,提取的边缘信息更准确.
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