Many applications, as in computer vision or medicine, aim at identifying the similarities between several images or signals. Thereafter, it is possible to detect objects, to follow them, or to overlap different pictures. In every case, the algorithmic procedures that treat the images use a selection of keypoints that they try to match by pairs. The most popular algorithm nowadays is SIFT, that performs keypoint selection, descriptor calculation, and provides a criterion for global descriptor matching. We considered changing the classical descriptor, which resulted in a shift testing problem that we solved in the minimax frame. Then, we gave a rigorous statistical formulation for the global descriptor matching problem and studied it in some special cases.