Geometry, Imaging and Computing

Volume 1 (2014)

Number 1

Gaussian diffeons for surface and image matching within a Lagrangian framework

Pages: 141 – 171

DOI: http://dx.doi.org/10.4310/GIC.2014.v1.n1.a3

Author

Laurent Younes (Center for Imaging Science, Johns Hopkins University, Baltimore, Maryland, U.S.A.)

Abstract

Lagrangian particle formulations of the large deformation diffeomorphic metric mapping algorithm (LDDMM) can be numerically challenging when the number of particles is large. In this paper, we introduce and discuss numerical schemes that can be used for surface and image matching and are based on representing the Eulerian velocity over a finite-dimensional basis that deforms over time. The method is described under the optimal control formalism, and optimality conditions and derived, together with the equations that are needed to implement gradient-based methods. Experimental results are shown, both with surfaces and images.

Keywords

shape analysis, optimal control, groups of diffeomorphisms, Subriemannian geometry

2010 Mathematics Subject Classification

49N90, 49Q10, 58D05, 68-xx

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