Laurent Younes

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Michael I. Miller281
Sarang C. Joshi99
Ulf Grenander86
Alain Trouvé70
John G. Csernansky64
187Michael I. Miller
75John Tilak Ratnanather
75Sarang C. Joshi
68Peter W. Michor
56Alain Trouvé

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1992
2017

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Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
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)
On the metrics and euler-lagrange equations of computational anatomy.
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)
Variational Methods for Multimodal Image Matching
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)
On the Convergence of Markovian Stochastic Algorithms with Rapidly Decreasing Ergodicity Rates
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)
Group Actions, Homeomorphisms, and Matching: A General Framework
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)
Parallel transport in diffeomorphisms distinguishes the time-dependent pattern of hippocampal surface deformation due to healthy aging and the dementia of the Alzheimer's type
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)
Computable Elastic Distances Between Shapes
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)
Geodesic Shooting for Computational Anatomy
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)
Large Deformation Diffeomorphism and Momentum Based Hippocampal Shape Discrimination in Dementia of the Alzheimer type
In large-deformation diffeomorphic metric mapping (LDDMM), the diffeomorphic matching of images are modeled as evolution in time, or a flow, of an associated smooth velocity vector field v controlling the evolution. The initial momentum parameterizes the whole geodesic and encodes the shape and form of the target image. Thus, methods such as principal… (More)