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- Mirza Faisal Beg, Michael I. Miller, Alain Trouvé, Laurent Younes
- International Journal of Computer Vision
- 2005

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)

- Michael I Miller, Alain Trouve, Laurent Younes
- Annual review of biomedical engineering
- 2002

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)

- Gerardo Hermosillo Valadez, Nicholas Ayache, +4 authors Luc Robert
- 2002

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)

- 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)

- Michael I. Miller, Laurent Younes
- International Journal of Computer Vision
- 2001

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)

- 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)

- Anqi Qiu, Laurent Younes, Michael I. Miller, John G. Csernansky
- NeuroImage
- 2008

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)

- Laurent Younes
- SIAM Journal of Applied Mathematics
- 1998

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)

- Michael I. Miller, Alain Trouvé, Laurent Younes
- Journal of Mathematical Imaging and Vision
- 2006

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)

- Lei Wang, Mirza Faisal Beg, +5 authors Michael I. Miller
- IEEE Trans. Med. Imaging
- 2007

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)