Computable elastic distances between shapes
SIAM Journal on Applied Mathematics
Diffeomorphisms Groups and Pattern Matching in Image Analysis
International Journal of Computer Vision
Variational problems on flows of diffeomorphisms for image matching
Quarterly of Applied Mathematics
Computational anatomy: an emerging discipline
Quarterly of Applied Mathematics - Special issue on current and future challenges in the applications of mathematics
Group Actions, Homeomorphisms, and Matching: A General Framework
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: Part II
Geodesic Interpolating Splines
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
A new image registration technique with free boundary constraints: application to mammography
Computer Vision and Image Understanding - Special issue on nonrigid image registration
Landmark Matching via Large Deformation Diffeomorphisms on the Sphere
Journal of Mathematical Imaging and Vision
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
Optimal Control Theory for Applications
Optimal Control Theory for Applications
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Landmark matching via large deformation diffeomorphisms
IEEE Transactions on Image Processing
Large Deformation Diffeomorphic Metric Curve Mapping
International Journal of Computer Vision
Statistical Computing on Manifolds: From Riemannian Geometry to Computational Anatomy
Emerging Trends in Visual Computing
Optimal data-driven sparse parameterization of diffeomorphisms for population analysis
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation
International Journal of Computer Vision
Sparse Adaptive Parameterization of Variability in Image Ensembles
International Journal of Computer Vision
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We propose a new approach in the context of diffeomorphic image matching with free boundaries. A region of interest is triangulated over a template, which is considered as a grey level textured mesh. A diffeomorphic transformation is then approximated by the piecewise affine deformation driven by the displacements of the vertices of the triangles. This provides a finite dimensional, landmark-type, reduction for this dense image comparison problem. Based on an optimal control model, we analyze and compare two optimization methods formulated in terms of the initial momentum: direct optimization by gradient descent, or root-finding for the transversality equation, enhanced by a preconditioning of the Jacobian. We finally provide a series of numerical experiments on digit and face matching.