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Digital Processing of Quantum-Limited Images Conjecture on the Relationship between Spatial and Temporal Visual Processes Why do Stabilized Images Disappear? A Simple Model for Filling-In, Contrast, Contrast Constancy and Assimilation |
Conjecture on the Relationship between Spatial and Temporal Visual Processes There are many striking similarities between spatial and temporal phenomena in vision. For example, the spatial and temporal contrast sensitivity curves have very similar shapes and both change in the same way with mean luminance. The relationships between threshold luminance and stimulus size (Ricco's Law) and threshold luminance and stimulus duration (Bloch's Law) bear a striking resemblance over many changes in conditions. Here is a conjecture: Given any model that explains a phenomenon related to spatia-1 interactions, the same model will also explain the related set of temporal phenomena if only one modification is made to the spatial model, namely that the fact that signals in neural substrates must travel with finite velocities is taken into account. This works for the lateral inhibition model for the spatial CSF. Make a model in which each input pixel spreads its signals in an excitatory way over its near neighbors (or maybe only itself) and in an inhibitory way over cells farther way, the farther the weaker the interaction. This will yield a band-pass CSF. Then add to the model the feature that these spreading signals travel at some finite velocity and so arrive later at farther points, and a band-pass shaped temporal CSF will result. This also works for the Intensity-Dependent Spread model that Jack Yellott and I published. Steve Reuman, in his dissertation at UC Irvine, showed that the temporal CSF becomes band-pass, that Bloch's Law follows from Ricco's Law, and also a number of other interesting relationships. It is also clear that after images, both positive and negative, will necessarily result if spatial spreading of signals takes time. (No other assumptions are needed at all to get after-images, although very likely more are actually needed to provide a full explanation of real after-images.) I think I can prove that this conjecture is true for any linear system, although I don't have the time to do it right. The conjecture does hold for Intensity-Dependent Spread, which is fundamentally non-linear, but I don't know how to prove it for non-linear systems in general. Maybe you do. Note: (Dennis Baylor showed that the temporal CSF for a single cone isolated from all interactions with neighbors, has a band-pass shape, so it cannot be claimed that finite propagation velocity is the entire explanation for its shape.) |
