Landmark Matching via Large Deformation Diffeomorphisms on the Sphere

Authors:
Joan Glaunès;Marc Vaillant;Michael I. Miller
Affiliations:
Laboratoire d'Analyse, Géométrie et Applications et Laboratoire de Traitement et Transport de l'Information, Université Paris 13, Villetaneuse. glaunes@math.univ-paris13.fr< ...;Center for Imaging Science, Department of Biomedical Engineering, Johns Hopkins University. marc@jhu.edu;Center for Imaging Science, Whiting School of Engineering, Johns Hopkins University. mim@cis.jhu.edu
Venue:
Journal of Mathematical Imaging and Vision
Year:
2004

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Abstract

This paper presents a methodology and algorithm for generating diffeomorphisms of the sphere onto itself, given the displacements of a finite set of template landmarks. Deformation maps are constructed by integration of velocity fields that minimize a quadratic smoothness energy under the specified landmark constraints. We present additional formulations of this problem which incorporate a given error variance in the positions of the landmarks. Finally, some experimental results are presented. This work has application in brain mapping, where surface data is typically mapped to the sphere as a common coordinate system.