Computational Models of Visual Hyperacuity

The process of visual hyperacuity is described and analyzed in the terms of informative theory. It is shown that in principle, the detection and representation of both luminance and edge features can be performed with a precision commensurate with human abilities. Algorithms are formulated in accord with the different representational methods, and are implemented as distinct computer models, which are tested with vernier acuity tasks. The results indicate that edge information, encoded either in the manner proposed by Marr and his col1eagucs (as zero-crossings in the Laplacian of a Gaussian convolved with the image) or when encoded as a simple filtered difference allows finer spatial localization than does the centroid of the intensity distribution. In particular it is shown that to judge changes of relative positions with a precision of 0.1 sec arc in two and three dimensions, it is sufficient to represent the displacement of an edge by the difference of two Laplacian-Gaussian filters rather than by the difference between interpolated zero-crossings in them. This method entails no loss of relative position information (sign), allows recovery of the magnitude of the change, and provides significant economies of computation.