Journal ArticleDOI
Zero-crossings of a wavelet transform
TLDR
An alternative projection algorithm is described that reconstructs a signal from azero-crossing representation, which is stabilized by keeping the value of the wavelet transform integral between each pair of consecutive zero-crossings.Abstract:
The completeness, stability, and application to pattern recognition of a multiscale representation based on zero-crossings is discussed. An alternative projection algorithm is described that reconstructs a signal from a zero-crossing representation, which is stabilized by keeping the value of the wavelet transform integral between each pair of consecutive zero-crossings. The reconstruction algorithm has a fast convergence and each iteration requires O(N log/sup 2/ (N)) computation for a signal of N samples. The zero-crossings of a wavelet transform define a representation which is particularly well adapted for solving pattern recognition problems. As an example, the implementation and results of a coarse-to-fine stereo-matching algorithm are described. >read more
Citations
More filters
Book
Characterization of Signals From Multiscale Edges
Stéphane Mallat,S. Zhong +1 more
TL;DR: The authors describe an algorithm that reconstructs a close approximation of 1-D and 2-D signals from their multiscale edges and shows that the evolution of wavelet local maxima across scales characterize the local shape of irregular structures.
Book
Wavelets and Subband Coding
Martin Vetterli,Jelena Kovacevic +1 more
TL;DR: Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding and developed the theory in both continuous and discrete time.
Book
Introduction to Wavelets and Wavelet Transforms: A Primer
TL;DR: This work describes the development of the Basic Multiresolution Wavelet System and some of its components, as well as some of the techniques used to design and implement these systems.
Book
Remote sensing, models, and methods for image processing
TL;DR: The Nature of Remote Sensing: Introduction, Sensor Characteristics and Spectral Stastistics, and Spatial Transforms: Introduction.
Journal ArticleDOI
Detection of ECG characteristic points using wavelet transforms
TL;DR: An algorithm based on wavelet transforms (WT's) has been developed for detecting ECG characteristic points and the relation between the characteristic points of ECG signal and those of modulus maximum pairs of its WT's is illustrated.
References
More filters
Journal ArticleDOI
A theory for multiresolution signal decomposition: the wavelet representation
TL;DR: In this paper, it is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2 /sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions.
Journal ArticleDOI
Theory of Edge Detection
David Marr,Ellen C. Hildreth +1 more
TL;DR: The theory of edge detection explains several basic psychophysical findings, and the operation of forming oriented zero-crossing segments from the output of centre-surround ∇2G filters acting on the image forms the basis for a physiological model of simple cells.
Journal ArticleDOI
The wavelet transform, time-frequency localization and signal analysis
TL;DR: Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied and the notion of time-frequency localization is made precise, within this framework, by two localization theorems.
Journal ArticleDOI
Decomposition of Hardy functions into square integrable wavelets of constant shape
A. Grossmann,J. Morlet +1 more
TL;DR: In this article, the authors studied square integrable coefficients of an irreducible representation of the non-unimodular $ax + b$-group and obtained explicit expressions in the case of a particular analyzing family that plays a role analogous to coherent states (Gabor wavelets) in the usual $L_2 $ -theory.
Book ChapterDOI
Scale-space filtering
TL;DR: Scale-space filtering is a method that describes signals qualitatively, managing the ambiguity of scale in an organized and natural way.