Analysis of Singularities From Modulus Maxima of Complex Wavelets

Tu, Chun-Liang; Hwang, Wen-Liang; Ho, Jinn

doi:10.1109/tit.2004.842706

Cited by 101 publications

(61 citation statements)

References 16 publications

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“…Tu and Hwang (2005) show that complex-valued wavelets can be used to analyze signal singularities. Their paper constitutes an extension of Mallat's work on the subject discussed in this paper.…”

Section: Resultsmentioning

confidence: 99%

Application of Cubic Box Spline Wavelets in the Analysis of Signal Singularities

Rakowski

2015

International Journal of Applied Mathematics and Computer Science

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In the subject literature, wavelets such as the Mexican hat (the second derivative of a Gaussian) or the quadratic box spline are commonly used for the task of singularity detection. The disadvantage of the Mexican hat, however, is its unlimited support; the disadvantage of the quadratic box spline is a phase shift introduced by the wavelet, making it difficult to locate singular points. The paper deals with the construction and properties of wavelets in the form of cubic box splines which have compact and short support and which do not introduce a phase shift. The digital filters associated with cubic box wavelets that are applied in implementing the discrete dyadic wavelet transform are defined. The filters and the algorithmè a trous of the discrete dyadic wavelet transform are used in detecting signal singularities and in calculating the measures of signal singularities in the form of a Lipschitz exponent. The article presents examples illustrating the use of cubic box spline wavelets in the analysis of signal singularities.

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Section: Resultsmentioning

confidence: 99%

Application of Cubic Box Spline Wavelets in the Analysis of Signal Singularities

Rakowski

2015

International Journal of Applied Mathematics and Computer Science

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“…Before applying our prototype-generation algorithm, we had to preprocess the binary images to extract the corners of their contours. To detect corners, we used a chain-code algorithm to extract a contour and a singularity-detection algorithm from the modulus maxima of wavelet coefficients of the contour [2], [13], [18]. There are many other corner-detection methods [9], [12], [21] that could be used.…”

Section: Resultsmentioning

confidence: 99%

Planar-shape prototype generation using a tree-based random greedy algorithm

Chen

Hwang

Lin

2006

IEEE Trans. Syst., Man, Cybern. B

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Abstract-A prototype is representative of a set of similar objects. This paper proposes an approach that formulates the problem of prototype generation as finding the mean from a given set of objects, where the prototype solution must satisfy certain constraints. These constraints describe the important perceptual features of the sample shapes that the proposed prototype must retain. The contour prototype generated from a set of planar objects was used as an example of the approach, and the corners were used as the perceptual features to be preserved in the proposed prototype shape. However, finding a prototype solution for more than two contours is computationally intractable. A tree-based approach is therefore proposed in which an efficient greedy random algorithm is used to obtain a good approximation of the proposed prototype and analyze the expected complexity of the algorithm. The proposed prototype-generation process for hand-drawn patterns is described and discussed in this paper.

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“…Hence, analyzing the derivatives of this function would reveal the instant of occurrence. It has been shown that if the chosen mother wavelet has sufficient number of vanishing moment, the wavelet transform is akin to evaluating the derivative of a function [14][15][16]. Hence, the wavelet coefficients, akin to the signal's derivatives, would change significantly at the instants when the disturbance begins and ends.…”

Section: Duration Determinationmentioning

confidence: 99%

A Wavelet Transform Method for Characterization of Voltage Variations

Zhu

Chen

2006

2006 International Conference on Power System Technology

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Short duration voltage variation is one of the most commonly encountered power quality disturbances. The severity is generally determined by the remaining voltage RMS magnitude and the duration of the disturbance. These are generally determined through the RMS measurement method, which at times faces difficulties especially with variations of very short duration. This paper proposes an alternative technique to effectively characterize voltage variations of all durations. It uses wavelet analysis to zoom into a high frequency band for the time information, and the fundamental frequency band for the magnitude change. It is shown to be effective even for very short interruption, which is difficult to determine using the RMS method. Compared to other wavelet methods, its low computational requirement makes it suitable for real-time application. Dynamic simulations were used to demonstrate the capability of this method.

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Analysis of Singularities From Modulus Maxima of Complex Wavelets

Cited by 101 publications

References 16 publications

Application of Cubic Box Spline Wavelets in the Analysis of Signal Singularities

Application of Cubic Box Spline Wavelets in the Analysis of Signal Singularities

Planar-shape prototype generation using a tree-based random greedy algorithm

A Wavelet Transform Method for Characterization of Voltage Variations

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