In this paper, we focus on the Image Registration problem. Mathematically, this problem consists of minimizing an energy which is composed of a regularization term and a similarity term. The similarity term, which depends on image intensities, has to be chosen according to the nature of image grey-level dependencies. Its adequacy always depends on the validity of some assumptions about these dependencies. But, in medical applications, there are many situations where these assumptions are not confirmed. In particular, intensity variations caused by observed pathologies may not be consistent with assumptions. Such variations may distort registration constraints and cause registration errors. In order to cope with this problem, we propose a new approach which takes into account possible inconsistencies in the computation of registration constraints. This approach is described from two different points of view. First, we formulate a new minimization problem with an extra unknown which measures the degree of inconsistency on each pixel. Then, we show that this problem is equivalent to another one which can be related to usual ones. We also outline several ways to generalize our approach and propose an algorithm to solve numerically problems. Finally, we illustrate on synthetic data some characteristics of the algorithmwhen dealing with inconsistent image differences.