Learn More
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)
Acknowlegments This thesis was funded by the Mexican National Council for Science and Technology (CONACYT) through the scholarship offered in conjunction with the French Society for the Exportation of Educational Resources (SFERE). I am grateful to Luis Alvarez, Joachim Weickert and Laurent Younes for accepting to be reviewers of the thesis dis-sertation.(More)
We analyse the convergence of stochastic algorithms with Markovian noise when the ergodicity of the Markov chain governing the noise rapidly decreases as the control parameter tends to innnity. In such a case, there may be a positive probabilityof divergence of the algorithm in the classic Robbins-Monro form. We provide modiications of the algorithm which(More)
Diffusion tensor imaging (DTI) can reveal detailed white matter anatomy and has the potential to detect abnormalities in specific white matter structures. Such detection and quantification are, however, not straightforward. The voxel-based analysis after image normalization is one of the most widely used methods for quantitative image analyses. To apply(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)
Hippocampal surface structure was assessed at twice 2 years apart in 26 nondemented subjects (CDR 0), in 18 subjects with early dementia of Alzheimer type (DAT, CDR 0.5), and in 9 subjects who converted from the nondemented (CDR 0) to the demented (CDR 0.5) state using magnetic resonance (MR) imaging. We used parallel transport in diffeomorphisms under the(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)
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)