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This paper examine the Euler-Lagrange equations for the solution of the large deformation diffeomor-phic 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 = φ 1 is the end point at t = 1 of curve φ t , t ∈ [0, 1](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)
This paper constructs metrics on the space of images I deened as orbits under group actions G. The groups studied include the nite dimensional matrix groups and their products, as well as the innnite dimensional diieomorphisms examined in 21, 12]. Left-invariant metrics are deened on the product G I thus allowing the generation of transformations of the(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 between images. In this paper, we study the geodesics of such large deformation diffeomorphisms, and more precisely, introduce a fundamental property that they(More)
—We define a distance between textures for texture classification from texture features based on windowed Fourier filters. The definition of the distance relies on an interpretation of our texture attributes in terms of spectral density when the texture can be considered as a Gaussian random field. The distance between textures is then defined as a(More)
In the paper, we study the problem of optimal matching of two generalized functions (distributions) via a diffeomor-phic 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)
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)
We present a matching criterion for curves and integrate it into the large deformation diffeomorphic metric mapping (LDDMM) scheme for computing an optimal transformation between two curves embedded in Euclidean space ℝ d. Curves are first represented as vector-valued measures, which incorporate both location and the first order geometric structure of the(More)
Templates play a fundamental role in Computational Anatomy. In this paper, we present a Bayesian model for template estimation. It is assumed that observed images I(1), I(2),...,I(N) are generated by shooting the template J through Gaussian distributed random initial momenta theta(1), theta(2),...,theta(N). The template is J modeled as a deformation from a(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)