On Nonparametric Image Registration

Abstract

Image registration (IR) aims to map one image to another of a same scene. It is a fundamental task in many imaging applications. Most existing IR 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 IR 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 article, we suggest solving the IR 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.

KEY WORDS:

• Degenerate pixels
• Discontinuity
• Image mapping
• Image transformation
• Local approximation
• Local smoothing
• Nonparametric transformation
• Statistical properties

ACKNOWLEDGMENTS

The authors thank the editor, the associate editor, and two referees for many constructive comments and suggestions that greatly improved the quality of the article. This research is supported in part by an NSF grant.