A Semidiscrete Version of the Citti-Petitot-Sarti Model as a Plausible Model for Anthropomorphic Image Reconstruction and Pattern Recognition

Dario Prandi, Jean-Paul Gauthier (Autoren)

Buch | Softcover

XIV, 113 Seiten

2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-78481-6 (ISBN)

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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.

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.

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.

"The book is written in a very accessible fashion and the proposed methods are described in depth. It is suitable for graduate students and for researchers and professionals interested in image reconstruction and pattern recognition." (Krzystof Gdawiec, zbMATH 1415.68007, 2019)

“The book is written in a very accessible fashion and the proposed methods are described in depth. It is suitable for graduate students and for researchers and professionals interested in image reconstruction and pattern recognition.” (Krzystof Gdawiec, zbMATH 1415.68007, 2019)

Erscheinungsdatum	22.06.2018
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	XIV, 113 p. 14 illus., 6 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	206 g
Themenwelt	Informatik ► Grafik / Design ► Digitale Bildverarbeitung
	Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Abstract harmonic analysis • Almost-periodic functions • Fourier descriptors • Hypoelliptic diffusion • Neurogeometry
ISBN-10	3-319-78481-1 / 3319784811
ISBN-13	978-3-319-78481-6 / 9783319784816
Zustand	Neuware