Publication

A geometric framework for registration of sparse images

Pascal Frossard
2013
Conference Papers

Abstract

We examine the problem of image registration when images have a sparse representation in a dictionary of geometric features. We propose a novel algorithm for aligning images by pairing their sparse components. We show numerically that this algorithm works well in practice and analyze key properties on the dictionary that drive the registration performance. We compare these properties to existing characterizations of redundant dictionaries (i.e., coherence, restricted isometry property) and show that the newly introduced properties finely capture the behaviour of our registration algorithm.

Official source

https://infoscience.epfl.ch/entities/publication/3ab56d3e-74e9-418a-91b6-04f8234eaa6c

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Pascal Frossard
2013
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/3ab56d3e-74e9-418a-91b6-04f8234eaa6c

About this result

Related concepts (28)

Sparse dictionary learning

Sparse dictionary learning (also known as sparse coding or SDL) is a representation learning method which aims at finding a sparse representation of the input data in the form of a linear combination of basic elements as well as those basic elements themselves. These elements are called atoms and they compose a dictionary. Atoms in the dictionary are not required to be orthogonal, and they may be an over-complete spanning set. This problem setup also allows the dimensionality of the signals being represented to be higher than the one of the signals being observed.

Image registration

Image registration is the process of transforming different sets of data into one coordinate system. Data may be multiple photographs, data from different sensors, times, depths, or viewpoints. It is used in computer vision, medical imaging, military automatic target recognition, and compiling and analyzing images and data from satellites. Registration is necessary in order to be able to compare or integrate the data obtained from these different measurements.

Sparse approximation

Sparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding these solutions and exploiting them in applications have found wide use in , signal processing, machine learning, medical imaging, and more. Consider a linear system of equations , where is an underdetermined matrix and . The matrix (typically assumed to be full-rank) is referred to as the dictionary, and is a signal of interest.

Related publications (1)

A geometric framework for registration of sparse images

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MATHICSE Technical Report : Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem