Discrete rigid registration: A local graph-search approach

Abstract

International audienceImage registration has become a crucial step in a wide range of imaging domains, from computer vision to computer graphics. The core of image registration consists of determining the transformation that induces the best mapping between two images. This problem is ill-posed; it is also difficult to handle, due to the high size of the images and the high dimension of the transformation parameter spaces. Computing an actually optimal solution is practically impossible when transformations are assumed continuous (i.e., defined on R n). In this article, we initiate the exploration of a new way of considering image registration. Since digital images are basically defined in a discrete framework (i.e., in Z n), the transformation spaces – despite a potentially high complexity – actually remain finite, allowing for the development of explicit exploration of the parameter space via discrete optimization schemes. We propose an analysis of the very basis of registration, by considering rigid registration between 2D images. We show, in particular, how this problem can be handled in a fully discrete fashion, by computing locally the combinatorial structure of the parameter space of discrete rigid transformations, and by navigating on-the-flight within this space via gradient descent paradigms. This registration framework is applied in real imaging cases, emphasising the relevance of our approach, and the potential usefulness of its further extension to higher dimension images and richer transformations. ✩ The research leading to these results has received funding from the French Agence Nationale de la Recherche (Grant Agreement ANR-2010-BLAN-0205) and the Programme d'Investissements d'Avenir (LabEx Bézout

A Review on Registration of Medical Images Using Graph Theoretic Approaches

“…The optimization process uses a multi-scale approach to speed it up. The parameters used for validation are the run time complexity, distance based on signed function and the average degree of DRT graphs [48]. Zakharov Et al.…”