A Semidiscrete Version of the Citti-Petitot-Sarti Model as a Plausible Model for Anthropomorphic Image Reconstruction and Pattern Recognition [electronic resource] /
Prandi, Dario.author.
Gauthier, Jean-Paul.author.
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.
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.
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.
Harmonic analysis.
Computer science-Mathematics.
Computer mathematics.
Optical data processing.
Abstract Harmonic Analysis.
Mathematical Applications in Computer Science.
Computer Imaging, Vision, Pattern Recognition and Graphics.