Penrose tilings, quasi-crystals, and wavelets

Jean-Pierre Antoine; Laurent Jacques; Pierre Vandergheynst

doi:10.1117/12.366795

26 October 1999 Penrose tilings, quasi-crystals, and wavelets

Jean-Pierre Antoine, Laurent Jacques, Pierre Vandergheynst

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366795
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

The analysis of oriented features in images requires 2D directional wavelets, for instance in standard tasks such as edge detection or directional filtering. In addition we present here a new application, namely a technique for determining all the (statistical) symmetries of a given pattern with respect to rotations and dilations. Examples are Penrose tilings, mathematical quasicrystals or various quasiperiodic planar point sets or patterns.

Citation Download Citation

Jean-Pierre Antoine, Laurent Jacques, and Pierre Vandergheynst "Penrose tilings, quasi-crystals, and wavelets", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366795

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