Abstract

Previous work has shown that the theory of intensity-dependent spread functions (IDS) predicts many phenomena in human vision. However, IDS, being a nonlinear system, is difficult to work with. Theoretical results applicable primarily to inputs composed of regions of constant intensity are presented. In these cases, the work here shows that the output reduces to a sum of convolutions. The convolutions have several useful geometric interpretations, and they explicitly show how IDS adjusts its resolution according to local intensities. If the input contains only two intensities, e.g., bars, disks, or square waves, it is proved that the output is a constant plus the convolution of the input and a parameterized bandpass filter. For a Gaussian spread function this becomes the difference-of-Gaussians filter but with scale factors that adjust automatically to the input intensities. Bounds on the step output are set, and it is proved that IDS is a stable system. All results are exact.

© 1992 Optical Society of America

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