The external world is visually perceived through the projections on the retina. The image on the retina is continuously shifted, rotated, resized, compressed, stretched due to the movements of the object in front of the eye and the eye itself, constant micro-changes in posture and due to tremor. Similar points are present in the problems associated with machine vision and robotics. In general, this leads to the problem of such a description of the image, which would be invariant to its affine transformations on the plane. Such a description is presented in the article. It is generally accepted that the basis for the recognition and organization of purposeful behavior is the existence of a kind of “internal” model of the external world. This leads to the problem of describing the body and set of bodies. The article presents a description of the body, invariant to its affine transformations in space. The “internal” model of the environment can arise only through the medium projections of the medium onto the retina of the eyes. Hence the task of restoring a three-dimensional image from its flat projections. The main issue here is the problem of establishing the correspondence between the points of images on different projections. The article describes the mechanism of recovery of the body from the projections, within which the problem of pointwise correspondence between the projections is also solved.

mathematical modeling in biology, recognition of visual images, models of stereo perception

Mathematical problems and theory of numerical methods