摘要
将Ambrosio和Tortorelli提出的Mumford-Shah椭圆泛函逼近模型推广到彩色图像情形.推广模型将彩色图像建模为黎曼流形上的嵌入曲面,据此将刻画不同颜色通道间方向梯度差异的物理量———向量积项引入能量泛函中目标的正则化部分,进而建立了新的能量泛函.从理论上证明了新能量泛函的Gamma收敛性,推导了最优化能量泛函所满足的欧拉-拉格朗日方程.利用最速下降法,提出了推广模型的一种有限差分方法.理论分析和实验结果都表明:传统的直接将灰度图像的Mumford-Shah模型推广到向量图像情形,往往存在孤立对待每个通道的问题,而该文推广模型能够精细刻画各通道之间的相关性和相互影响,在图像恢复和分割效果上都大大优于传统的直接推广的模型.
This paper focuses on Mumford-Shah model based approaches for color images restoration and segmentation. The extension of the elliptic functional proposed by Ambrosio and Tortorelli for color image is studied and analyzed. In the generalization model, image is considered as embedded surface in Riemannian manifold. A new physical quantity in the form of vector product, which describes the differences of the gradient between different channels, is introduced into the regularization term of the ＂obiect＂, then a new energy functional is proposed. The authors give a detailed proof of Gamma convergence result of the generalization energy functional, and Euler-Lagrange equation for optimizing the new energy functional is also proved. Utilizing the steepest descent method and half-point scheme, a finite difference algorithm is proposed. Experimental results and theoretic analysis show that the straightforward generalization Mumford-Shah model for vector-valued image will deal with different channels as the same way, while the generalization model which is in Riemannian manifold framework provides a new mechanism to align different channels together, and to measure the cross correlation of orientation between different channels, also the generalization model has better performance than the direct extension model.
出处
《计算机学报》
EI
CSCD
北大核心
2006年第2期286-295,共10页
Chinese Journal of Computers
基金
高等学校博士学科点专项科研基金项目(20020288024)
南京理工大学青年学者基金(NJUST200401)资助~~
作者简介
肖亮，男，1976年生，博士，讲师，主要研究方向为变分偏微分方程在图像处理中的应用、模式识别、运动估计与跟踪、虚拟现实与系统仿真．E-mail：xixiaoliang@163．com.
吴慧中，女，I942年生，教授，博士生导师，研究领域为虚拟现实、计算机图形图像理论．
韦志辉，男，1963年生，博士，教授，博士生导师，主要研究领域为变分偏微分方程在图像处理中的应用、小波分析、模式识别．
