This paper deals with the roles of assumption, mathematical models, and experimental control in Pattern Recognition. In order to base the discussion on actual examples, three studies are first described. The first one presents filtering of bird singings via their sonograms. The second and the third ones deal with morphological operators on the unit circle, which are successively applied to hue gradient and top hats in color images, and to directional irregularities in wood textures. The discussion holds on the necessity to bring implicit assumptions to light, to evaluate the consistency of the mathematical formalism with respect to these assumptions, and finally to control experimentally the domain of pertinence of the proposed approach.