Multiscale approach for variational problem joint diffeomorphic image registration and intensity correction: theory and application

Image registration matches the features of two images by minimizing the intensity difference, so that useful and complementary information can be extracted from the mapping. However, in real life problems, images may be affected by the imaging environment, such as varying illumination and noise during the process of imaging acquisition. This may lead to the local intensity distortion, which makes it meaningless to minimize the intensity difference in the traditional registration framework. To address this problem, we propose a variational model for joint image registration and intensity correction. Based on this model, a related greedy matching problem is solved by introducing a multiscale approach for joint image registration and intensity correction. An alternating direction method (ADM) is proposed to solve each multiscale step, and the convergence of the ADM method is proved. For the numerical implementation, a coarse-to-fine strategy is further proposed to accelerate the numerical algorithm, and the convergence of the proposed coarse-to-fine strategy is also established. Some numerical tests are performed to validate the efficiency of the proposed algorithm.