I was writing a program that would input data for HTMs from my computer screen. (It's harder than you'd think.) I tried applying lens effects, but eventually settled for multiple desktop-captures of varying sizes centered at... wherever I put the center:
Either way, if those inputs were given to columns and the same spatial algorithms were applied, it would effect the input differently depending on the center location.
I had a similar thought for audio. When reading in a FFT, the amplitude is important, but the exact location of the height in a FFT graph isn't necessarily important:
In that case, computing local spatial algorithms in the horizontal dimension, but fast global spatial algorithms in the vertical dimension, would include the total amplitude as neurons activated, but would discard unnecessary positional information. Actually, it would allow very loud single frequency sounds to more successfully inhibit quieter local frequencies.
So I'm curious: is this something that biology does naturally? I remember the rods in the eyes are spaced so that they should give more of a fisheye input, but I'm not sure how the inhibition and other spatial algorithms are calculated biologically in the eye. Also, are there other applications for partial or abnormal spatial topologies?