A Statistical Approach to Large Deformation Diffeomorphisms

This paper is concerned with the theory of non-rigid registration and image warping. Our approach combines the Brownian warps model proposed by Nielsen et al. with the differential operator approach proposed by Joshi & Miller. Using standard statistical assumptions we derive a stochastic differential equation generating flows of diffeomorphisms of d-dimensional space. The coefficients in the stochastic differential equation encode the statistical properties of the flow and the driving Brownian motions encode the actual appearance of the flow. We discuss the choice of the coefficients and introduce a renormalization for the Brownian motions. The renormalization allows for maximum a posteriori estimation of the unobserved Brownian motions. Finally we investigate the landmark matching problem.