Structural Image Restoration through Deformable Templates

Prior knowledge on the space of possible images is given in the form of a function or template in some domain. The set of all possible true images is assumed to be formed by a composition of that function with continuous mappings of the domain into itself. A prior Gaussian distribution is given on the set of continuous mappings. The observed image is assumed to be a degradation of the true image with additive noise. Given the observed image, a posterior distribution is then obtained and has the form of a nonlinear perturbation of the Gaussian measure on the space of mappings. We present simulations of the posterior distribution that lead to structural reconstructions of the true image in the sense that it enables us to determine landmarks and other characteristic features of the image, as well as to spot pathologies in it. Moreover, we show that the reconstruction algorithm is relatively robust when the images are degraded by noise that is not necessarily additive.