We define distances between geometric curves by the square root of the minimal energy required to transform one curve into the other. The energy is formally defined from a left invariant Riemannian… (More)
This paper reviews literature, current concepts and approaches in computational anatomy (CA). The model of CA is a Grenander deformable template, an orbit generated from a template under groups of… (More)
Studying large deformations with a Riemannian approach has been an efficient point of view to generate metrics between deformable objects, and to provide accurate, non ambiguous and smooth matchings… (More)
This paper constructs metrics on the space of images I defined as orbits under group actions G. The groups studied include the finite dimensional matrix groups and their products, as well as the… (More)
A three-dimensional (3D) diffusion-weighted imaging (DWI) method for measuring cardiac fiber structure at high spatial resolution is presented. The method was applied to the ex vivo reconstruction of… (More)
In this paper, we discuss a geometrical model of a space of deformable images or shapes, in which infinitesimal variations are combinations of elastic deformations (warping) and of photometric… (More)
We propose a simple and eecient method to interpolate landmark matching by a non-ambiguous mapping (a diieomorphism). This method is based on spline interpolation, and on recent techniques developed… (More)
In this paper, we present a linear setting for statistical analysis of shape and an optimization approach based on a recent derivation of a conservation of momentum law for the geodesics of… (More)
We formally analyze a computational problem which has important applications in image understanding and shape analysis. The problem can be summarized as follows. Starting from a group action on a… (More)