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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.

Mathematics. --- Computer graphics. --- Harmonic analysis. --- Computer science --- Computer mathematics. --- Abstract Harmonic Analysis. --- Mathematical Applications in Computer Science. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Image reconstruction --- Pattern perception --- Mathematical models. --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Image restoration --- Reconstruction, Image --- Restoration, Image --- Image processing --- Computer vision. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Computer science—Mathematics. --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Computer mathematics --- Optical equipment