On Nonparametric Image Registration

Image registration aims to map one image to another of a same scene. It is a fundamental task in many imaging applications. Most existing image registration methods assume that the mapping transformation has a parametric form or satisfies certain regularity conditions (e.g., it is a smooth function with continuous first or higher order derivatives). They often estimate the mapping transformation globally by solving a global minimization/maximization problem. Such global smoothing methods usually cannot preserve singularities (e.g., discontinuities) and other features of the mapping transformation well. Further, the ill-posed nature of the image registration problem, namely, the mapping transformation is not well defined at certain places, including the place where the true image intensity surface is straight, is not handled properly by such methods. In this paper, we suggest solving the image registration problem locally, by first studying the local properties of a mapping transformation. To this end, some concepts for describing such local properties are suggested, and a local smoothing method for estimating the mapping transformation is proposed. Because of the flexibility of local smoothing, our method does not require any parametric form or other global regularity conditions on the mapping transformation. Both theoretical and numerical studies show that it is effective in various applications. Supplementary materials are available online.