Directional Wavelets Revisited: Cauchy Wavelets and Symmetry Detection in Patterns
Applied and Computational Harmonic AnalysisPublished 1 May 1999Open access
Jean-Pierre Antoine, Romain Murenzi, Pierre Vandergheynst
Citations113
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TL;DR
The class of Cauchy wavelets, which are strictly supported in a (narrow) convex cone in spatial frequency space, are studied, which have excellent angular selectivity, and they have minimal uncertainty.
Abstract
The analysis of oriented features in images requires two-dimensional directional wavelets. Among these, we study in detail the class of Cauchy wavelets, which are strictly supported in a (narrow) convex cone in spatial frequency space. They have excellent angular selectivity, as shown by a standard calibration test, and they have minimal uncertainty. In addition, we present a new application of directional wavelets, namely a technique for determining the symmetries of a given pattern with respect to rotations and dilation. (C) 1999 Academic Press.
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