We present two new algorithms for multimodal, dense matching of two images using a variational approach. These algorithms complete and generalise our previous work by treating the case of semi-local energy functionals. In brief, they are derived from the maximization of two statistical criteria (mutual information and correlation ratio) estimated from corresponding regions around each pixel (or voxel in the 3D case). As a second contribution, we present a result of existence and uniqueness of the solution of the abstract evolution problems associated to these algorithms, as well as those of the corresponding global ones (the proofs could not be reproduced here but can be found in [10]). This is important since it shows the well-posedness of the problems to solve. We finish by showing some applications of our methods to one synthetic and four real examples.