Minimum distance between pattern transformation manifolds: Algorithm and Applications
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Manifold models provide low-dimensional representations that are useful for analyzing and classifying data in a transformation-invariant way. In this paper we study the problem of jointly building multiple pattern transformation manifolds from a collection ...
The set of solutions of a parameter-dependent linear partial differential equation with smooth coefficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for ...
Machine learning is most often cast as an optimization problem. Ideally, one expects a convex objective function to rely on efficient convex optimizers with nice guarantees such as no local optima. Yet, non-convexity is very frequent in practice and it may ...
Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as ...
This paper addresses the problem of image alignment based on random measurements. Image alignment consists of estimating the relative transformation between a query image and a reference image. We consider the specific problem where the query image is prov ...
We address the problem of building a manifold in order to represent a set of geometrically transformed images by selecting a good common sparse approximation of them with parametric atoms. We propose a greedy method to construct a representative pattern su ...
The first example of a closed orientable hyperbolic 3-manifold was constructed by F. Lobell in 1931 from eight copies of the right-angled 14-hedron. We consider the family of hyperbolic polyhedra which generalize the Lambert cube and the Lobell polyhedron. ...
We focus on image restoration that consists in regularizing a quadratic data-fidelity term with the standard l1 sparse-enforcing norm. We propose a novel algorithmic approach to solve this optimization problem. Our idea amounts to approximating the result ...
Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several transformation manif ...
Institute of Electrical and Electronics Engineers2011
In this work, we exploit the fact that wavelets can represent magnetic resonance images well, with relatively few coefficients. We use this property to improve magnetic resonance imaging (MRI) reconstructions from undersampled data with arbitrary k-space t ...
Institute of Electrical and Electronics Engineers2011