Brownian Warps for Non-Rigid Registration

A Brownian motion model in the group of diffeomorphisms has been introduced as inducing a least committed prior on warps. This prior is source-destination symmetric, fulfills a natural semi-group property for warps, and with probability 1 creates invertible warps. Using this as a least committed prior, we formulate a Partial Differential Equation for obtaining the maximally likely warp given matching constraints derived from the images. We solve for the free boundary conditions, and the bias toward smaller areas in the finite domain setting. Furthermore, we demonstrate the technique on 2D images, and show that the obtained warps are also in practice source-destination symmetric and in an example on X-ray spine registration provides extrapolations from landmark point superior to those of spline solutions.