<p>Existing studies have addressed the variational problem for joint image registration and unilateral intensity correction only when the floating image exhibits intensity inhomogeneity, but do not consider the scenario where the target image also suffers from intensity inhomogeneity. To address this problem, we propose a variational model for image registration and bilateral intensity correction. Simultaneously, we develop a coarse-to-fine multiscale algorithm, powered by the alternating direction minimization (ADM) method, and prove the convergence of ADM. Furthermore, numerical experiments are conducted and the results show that the intensity corrections of the target image and the floating image are solved at the same time and a high registration accuracy is achieved.</p>