基于Mumford-Shah模型和G空间的图像结构纹理分解

Image Cartoon-Texture Decomposition Using Mumford-Shah Model and G-Space

构造了一个变分问题来实现图像的纹理结构分解。其中结构成分用分段光滑的函数(即Mumford-Shah模型)刻画,纹理部分用振荡函数(G空间)来描述。由于Mumford-Shah模型将结构成分显式地描述为分段光滑函数,在非结构边缘点处的梯度采用L2范数约束,故相对于全变差(Total variation,TV,梯度的L1范数)的分解方式,很好地克服TV带来的阶梯效应;G空间本身定义的纹理函数的振荡特性保证了分解的结构成分中含有更少的纹理信息。实验表明,无论相对于经典的TV-L2分解还是TV-G分解,本文方法均体现出了很好的分解性能。

The cartoon-texture decomposition is presented by a variational problem. The cartoon component is described by piecewise smooth functions （Mumford-Shah model, or M-S model）, while the texture is characterized by oscillating functions in G space. Since M-S model explicitly requires the piecewise smoothness of the structure （i. e. cartoon component） and applies L^2 norm of the gradients at the non-edge pixels, it can avoid the staircase effect coming from the total variation （TV） model. Furthermore, the oscillating characteristics of texture defined in the G space ensure that there is less texture information in the resultant cartoon component. Experimental results show that the proposed method can achieve better result than the classical TV-L^2and the recent TV-G methods.