Forward and Inverse Model for the Intensity Dependent Spread Filter
S. Najand, D. Blough and G. Healey

Cornsweet and Yellott invented the nonlinear intensity-dependent spread (IDS) filter based on the human vision system. They showed that this filter shares certain characteristics with the human visual system such as Mach bands, Weber's law, and Ricco's law, which account for the bandpass characteristic, brightness constancy, and tradeoff between sensitivity and resolution. Up to now, because of its nonlinearity and mathematical complexity, the study of its response has been limited to simple images such as step edges or sinusoidal gratings. Also, no good inverse models have been introduced to allow this filter possibly to be used for image compression. We provide a more complete model for the IDS filter and its inverse and show that for the common circularly symmetric spread functions the bandpass characteristic of the IDS filter can be modeled as spatial summation of a spatially varying high-pass filter and that the high-pass filter can be modeled as the Laplacian of a low-pass filter. We then show that the image can be recovered by inverting the effects of the Laplacian, followed by a deblurring stage and then by computing the reciprocal of the result.
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