Euclidean group invariant computation of stochastic completion fields using shiftable-twistable functions

We describe a method for computing the likelihood that a completion joining two contour fragments passes through any given position and orientation in the image plane. Like computations in primary visual cortex ( and unlike all previous models of contour completion), the output of our computation is invariant under rotations and translations of the input pattern. This is achieved by representing the input, output, and intermediate states of the computation in a basis of shiftable-twistable functions.