Region matching with missing parts

We present a variational approach to the problem of registering planar shapes despite missing parts. Registration is achieved through the evolution of a partial differential equation that simultaneously estimates the shape of the missing region, the underlying ‘complete shape’ and the collection of group elements (Euclidean, affine) corresponding to the registration. Our technique can be used both for shapes, for instance represented as characteristic functions (binary images) and for grayscale images where it can be interpreted as region ‘inpainting.’ The novelty of the approach lies on the fact that, rather than estimating the missing region in each image independently, we pose the problem as a joint registration with respect to an underlying ‘complete shape’ from which the complete version of the original data is obtained via a group action. We simultaneously estimate the complete shape and the group action in an alternating minimization scheme.