The exhaustive search of multiple matches in an overlapping area of two multimodal remote sensing images and the accurate localization of found matches are inherent steps to an efficient registration of these two images. A supervised approach based on convolutional neural networks can address this challenge by producing a similarity map, identifying potential matches within a preset search area and estimating a covariation matrix of their location errors. The training is based on a specially designed loss function to enforce the translational and rotational invariance of the similarity map. Using synthetic samples from anisotropic fractal Brownian motion (afBm) models of different orientation, we made the experimental finding that this loss function is biased with respect to orientation. This bias problem is then addressed by beneficially adding pure afBm data to the learning process.