Efficient Neighbourhood Computing for Discrete Rigid Transformation Graph Search

Kenmochi, Yukiko; Ngo, Phuc; Talbot, Hugues; Passat, Nicolas

doi:10.1007/978-3-319-09955-2_9

Cited by 1 publication

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“…The remainder of this article -that is an extended and improved version of the conference papers [5,6] -is organized as follows. Section 2 introduces and formalizes the optimization problem of image registration, and our specific purpose, namely discrete 40 image registration.…”

Section: Introductionmentioning

confidence: 99%

Discrete rigid registration: A local graph-search approach

Ngo

Kenmochi²,

Sugimoto

et al. 2017

Discrete Applied Mathematics

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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

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Section: Introductionmentioning

confidence: 99%