This book proposes a semi-discrete version of the theory of Petitot and Citti-Sarti, leading to a left-invariant structure over the group
SE(2, N), restricted to a finite number of rotations. This apparently very simple group is in fact quite atypical: it is maximally almost periodic, which leads to much simpler harmonic analysis compared to
SE(2). Based upon this semi-discrete model, the authors improve on previous image-reconstruction algorithms and develop a pattern-recognition theory that also leads to very efficient algorithms in practice.
विषयसूची
1 Introduction.- 2 Preliminaries.- 3 Lifts.- 4 Almost-periodic interpolation and approximation.- 5 Pattern recognition.- 6 Image reconstruction.- 7 Applications.- 8 Appendix: A Circulant matrices.- 9 Appendix B: Bispectrally admissible sets.
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Dario Prandi was born in 1986. He received is Ph D in applied mathematics from École Polyechnique, Palaiseau, France, and SISSA, Trieste, Italy, in 2014, and is currently a CNRS researcher at Laboratoire des Signaux et des Systèmes, Centrale Supélec, Gif-sur-Yvette. His research interests include sub-Riemannian geometry, image processing and, neuroscience.
Jean-Paul Gauthier was born in 1952. He received his Ph Ds in computer science and physics in 1978 and 1982 respectively. He started his career as a CNRS research worker, and from 1988 onward was a professor at various French universities. In 2007 he became a professor at Toulon University, and has been professor emeritus since 2017. His fields of interest include control theory and its applications, image processing, and sub-Riemannian geometry. He was featured in a review by the American Mathematical Society in 2001, and he has been a member of Institut Universitaire de France (IUF) since 1992.
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