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

Description

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. Front Matter ....Pages i-xiv Introduction (Dario Prandi, Jean-Paul Gauthier)....Pages 1-12 Preliminaries (Dario Prandi, Jean-Paul Gauthier)....Pages 13-34 Lifts (Dario Prandi, Jean-Paul Gauthier)....Pages 35-42 Almost-Periodic Interpolation and Approximation (Dario Prandi, Jean-Paul Gauthier)....Pages 43-52 Pattern Recognition (Dario Prandi, Jean-Paul Gauthier)....Pages 53-76 Image Reconstruction (Dario Prandi, Jean-Paul Gauthier)....Pages 77-87 Applications (Dario Prandi, Jean-Paul Gauthier)....Pages 89-101 Back Matter ....Pages 103-113