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

• Main Authors: Prandi, Dario (Author, http://id.loc.gov/vocabulary/relators/aut), Gauthier, Jean-Paul (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: SpringerBriefs in Mathematics,
• Subjects: 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.
• Physical Description: XIV, 113 p. 14 illus., 6 illus. in color. online resource.
• ISBN: 9783319784823
• ISSN: 2191-8198
• DOI: 10.1007/978-3-319-78482-3

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.