Laurent Younes

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This paper examine the Euler-Lagrange equations for the solution of the large deformation diffeomorphic metric mapping problem studied in Dupuis et al. (1998) and Trouvé (1995) in which two images I 0, I 1 are given and connected via the diffeomorphic change of coordinates I 0○ϕ−1=I 1 where ϕ=Φ1 is the end point at t= 1 of curve Φ t , t∈[0, 1] satisfying .Φ(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 diffeomorphisms. The metric space of all anatomical images is constructed from the geodesic connecting one anatomical structure to another in the orbit. The(More)
During the past few years, the use of the theory of partial differential equations has provided a solid formal approach to image processing and analysis research, and has yielded provably well-posed algorithms within a set of clearly defined hypotheses. These algorithms are the state-of-the-art in a large number of application fields such as image(More)
We deene distances between geometric curves by the square root of the minimal energy required to transform one curve into the other. The energy is formally deened from a left invariant Riemannian distance on an innnite dimensional group acting on the curves, which can be explicitely computed. The obtained distance boils down to a variational problem for(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 for the estimation of ows of diieomorphisms. Experimental results show interpolations of remarkable quality. Moreover, the method provides a Riemannian distance(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 diffeomorphic flow. Once a template is fixed, the space of initial momentum becomes an appropriate space for studying shape via geodesic flow since the flow at any point(More)
This paper proposes a method to match diffusion tensor magnetic resonance images (DT-MRIs) through the large deformation diffeomorphic metric mapping of vector fields, focusing on the fiber orientations, considered as unit vector fields on the image volume. We study a suitable action of diffeomorphisms on such vector fields, and provide an extension of the(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 infinite dimensional diffeomorphisms examined in Trouvé (1999, Quaterly of Applied Math.) and Dupuis et al. (1998). Quaterly of Applied Math. Left-invariant metrics(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 the fiber architecture of seven canine hearts. A novel hypothesis-testing method was developed and used to show that distinct populations of secondary and(More)
In the paper, we study the problem of optimal matching of two generalized functions (distributions) via a diffeomorphic transformation of the ambient space. In the particular case of discrete distributions (weighted sums of Dirac measures), we provide a new algorithm to compare two arbitrary unlabelled sets of points, and show that it behaves properly in(More)