On logarithmic retinae
Daniel Raviv, D Orser, James Sacra Albus · 1992
This paper suggests several iconic image "warpings", or remappings, which facilitate computationally inexpensive measurements of moving 3-D points relative to a camera.Assuming translational motion of the camera, where the optical axis coincides with the direction of motion, and a stationary scene, points in 3-D space that lie on a particular 3-D surface produce a constant value for some nonlinear function of the opti- cal flow.This function need not be computed after the image is formed, but rather can be implemented by hardware at the retinal level, Le., via non-linear variable-resolution (usually logarithmic) retina.Four sets of different surfaces are introduced and there is one optical-flow-based constant value for each surface.We call these values "invari- ants".An invariant, which is a scalar, describes a 3-D surface.For each invariant a logarithmic retina is defined which will cause optical flow on these surfaces to have identical values.The process of image remapping, called "normalization", is defined for four 1-D parameterizations of space: range, depth, looming and clearance.For each invariant a camera-retina imaging OKxlel utilizing spherical projection and foveal peripheral resolu- '::,»^3 f{3, wo'if'is^::*.