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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)

- Laurent Younes
- 1998

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)

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)

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)

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)

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)

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)

- Can Ceritoglu, Kenichi Oishi, Xin Li, Ming-Chung Chou, Laurent Younes, Marilyn S. Albert +4 others
- NeuroImage
- 2009

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)

- Laurent Younes
- 2006

This paper presents a series of applications of the Jacobi evolution equations along geodesics in groups of diffeomorphisms. We describe, in particular, how they can be used to perform implementable gradient descent algorithms for image matching, in several situations, and illustrate this with 2D and 3D experiments. We also discuss parallel translation in… (More)