A network model for generating differential symmetry axes of shapes via receptive fields

Some symmetries (e.g. bilateral, rotational, translational) only describe quite specialized shapes, but differential symmetry axes (e.g. Blum, J. Theoret. Biol. 38, 205-287, 1973; Brady and Asada, Int. J. Robotics Res. 3, 36-61, 1984) describe more general shapes. Such axes are of interest in part because they form the 'backbone' of generalized cylinder and other shape representations used in shape recognition (e.g. Marr, Vision, W. H. Freeman and Co., NY, 1982; Biederman, Psychol. Rev. 94, 115-147, 1987). However, despite the popularity of these representations as psychological models, algorithms from machine vision for computing them have strong limitations as psychological models. This paper presents two versions of a network model, one of which is more plausible as a psychological model because it derives symmetry axes from the activations of idealized visual receptive fields.