A Semidiscrete Version of the Citti-Petitot-Sarti Model as a Plausible Model for Anthropomorphic Image Reconstruction and Pattern Recognition
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.
| Autor: | Gauthier, Jean-Paul Prandi, Dario |
|---|---|
| ISBN: | 9783319784816 |
| Sprache: | Englisch |
| Seitenzahl: | 113 |
| Produktart: | Kartoniert / Broschiert |
| Verlag: | Springer International Publishing |
| Veröffentlicht: | 20.06.2018 |
| Schlagworte: | Abstract harmonic analysis Almost-periodic functions Fourier descriptors Hypoelliptic diffusion Neurogeometry |
Dario Prandi was born in 1986. He received is PhD 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, CentraleSupélec, Gif-sur-Yvette. His research interests include sub-Riemannian geometry, image processing and, neuroscience. Jean-Paul Gauthier was born in 1952. He received his PhDs 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.