Pattern Recognition by the Method of Isoclines: I. A Mathematical Model for the Visual Integrative Process

摘要

A theoretical model for the visual integrative process is advanced that is based upon microelectrode studies of the animal visual cortex by Hubel and Wiesel, Jung, and others. In this theoretical model the cortical columns of directionsensing elements found by Hubel and Weisel are interpreted as sets of isoclines making up the visual field. The form of a visual image corresponds to a family of contours ('orbits' or 'paths', in the terminology of differential equations) that pass through those isoclines stimulated by the corresponding retinal regions. A contour of an image is thus approximated in the visual cortex as an isoclinic polygonal arc. Hubel and Wiesel's microelectrode studies are thus strongly suggestive of a differential equation interpretation of the visual integrative process. The invariance of the visual integrative process under rigid motions (translation and rotation) and perspective that is required by the psychological phenomenon of Gestalt enables us to specify the particular form of the differential equations involved. (Author)