Large deformation diffeomorphisms with application to optic flow

Using standard statistical assumptions we derive a stochastic differential equation generating flows of diffeomorphisms. These stochastic processes provide a generative model for non-rigid registration and image warping problems. We give a mathematically rigorous derivation of the renormalized Brownian density in context of maximum a posteriori estimation of the underlying Brownian motions driving the warp flow. The second part of the paper combines the prior model with a likelihood model for image sequences. The combined model is employed to study the warp field for an image sequence of turbulent smoke.