A Variational Framework for Joint Image

Abstract

In this paper we propose a new symmetrical framework that solves image denoising, edge detection and non--rigid image registration simultaneously. This framework is based on the Ambrosio--Tortorelli approximation of the Mumford--Shah model. The optimization of a global functional leads to decomposing the image into a piecewise--smooth representative, which is the denoised intensity function, and a phase field, which is the approximation of the edge-set. At the same time, the method seeks to register two images based on the segmentation results. The key idea is that the edge set of one image should be transformed to match the edge set of the other. The symmetric non--rigid transformations are estimated simultaneously in two directions. One consistency functional is designed to constrain each transformation to be the inverse of the other. The optimization process is guided by a generalized gradient flow to guarantee smooth relaxation. A multi--scale implementation scheme is applied to ensure the e#ciency of the algorithm. We have performed preliminary medical evaluation on T1 and T2 MRI data, where the experiments show encouraging results