The recognition of graphical patterns invariant to geometrical transformation of the models

In case that a pattern recognition system is used for images recognition (in robot vision, handwritten recognition etc.), the system must have the capacity to identify an object indifferently of its size or position in the image. The problem of the invariance of recognition can be approached in some fundamental modes. One may apply the similarity criterion used in associative recall. The original pattern is replaced by a mathematical transform that assures some invariance (e.g. the value of two-dimensional Fourier transformation is translation invariant, the value of Mellin transformation is scale invariant). In a different approach the original pattern is represented through a set of features, each of them being coded indifferently of the position, orientation or position of the pattern. Generally speaking, it is easy to obtain invariance in relation with one transformation group, but is difficult to obtain simultaneous invariance at rotation, translation and scale. In this paper we analyze some methods to achieve invariant recognition of images, particularly for digit images. A great number of experiments are due and the conclusions are underplayed in the paper.