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A Semidiscrete Version of the Citti-Petitot-Sarti Model as a Plausible Model for Anthropomorphic Image Reconstruction and Pattern Recognition
ISBN-13:
9783319784823
Veröffentl:
2018
Einband:
eBook
Seiten:
113
Autor:
Dario Prandi
Serie:
SpringerBriefs in Mathematics
eBook Typ:
PDF
eBook Format:
Reflowable eBook
Kopierschutz:
Digital Watermark [Social-DRM]
Sprache:
Englisch
Beschreibung:
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.
This book proposes a semi-discrete version of the theory of Petitot and Citti-Sarti, leading to a left-invariant structure over the groupSE(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 toSE(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.