Publication

Directional Wavelets Revisited: Cauchy Wavelets and Symmetry Detection in Patterns

Pierre Vandergheynst
1999
Journal Articles

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.

Official source

https://infoscience.epfl.ch/entities/publication/cea2ba74-5494-4c39-af2a-137408c9e291

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Pierre Vandergheynst
1999
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/cea2ba74-5494-4c39-af2a-137408c9e291

About this result

Related concepts (21)

Discrete wavelet transform

In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time). Haar wavelet The first DWT was invented by Hungarian mathematician Alfréd Haar. For an input represented by a list of numbers, the Haar wavelet transform may be considered to pair up input values, storing the difference and passing the sum.

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Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor.

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Edge detection includes a variety of mathematical methods that aim at identifying edges, curves in a at which the image brightness changes sharply or, more formally, has discontinuities. The same problem of finding discontinuities in one-dimensional signals is known as step detection and the problem of finding signal discontinuities over time is known as change detection. Edge detection is a fundamental tool in , machine vision and computer vision, particularly in the areas of feature detection and feature extraction.

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