Several algorithms are reviewed for computing various types of wavelet transforms: the Mallat algorithm (1989), the 'a trous' algorithm, and their generalizations by Shensa. The goal of this work is to develop guidelines for implementing discrete and continuous wavelet transforms efficiently, and to compare the various algorithms obtained and give an idea of possible gains by providing operation counts. Most wavelet transform algorithms compute sampled coefficients of the continuous wavelet transform using the filter bank structure of the discrete wavelet transform. Although this general method is already efficient, it is shown that noticeable computational savings can be obtained by applying known fast convolution techniques, such as the FFT (fast Fourier transform), in a suitable manner. The modified algorithms are termed 'fast' because of their ability to reduce the computational complexity per computed coefficient from L to log L (within a small constant factor) for large filter lengths L. For short filters, smaller gains are obtained: 'fast running FIR (finite impulse response) filtering' techniques allow one to achieve typically 30% savings in computations. >

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Fast algorithms for discrete and continuous wavelet transforms

The paper presents an application of the wavelet transform for damage detection based on optical measurements. A number of important issues, that needs to be considered when image sequences are used for vibration analysis, are discussed. These include: correspondence of image features from image to image, image calibration and spatial resolution. The principles of image edge detection are discussed and a comparison between the wavelet approach and the classical method is presented. A novel damage detection method based on optically measured modeshape data is proposed. The method is illustrated using a simple cantilever beam experiment. The major advantage of the method is the significantly increased number of discrete points used to describe modeshapes. This is in contrast to classical techniques where in practice a small number of measurement points are obtained from a limited number of sensors.

Damage Detection Using Optical Measurements and Wavelets

The image for the face candidate region is obtained, extraction conditions are determined for extracting the eye and the mouth pixels from the candidate region based on the size of the face candidate region. The eye pixels and the mouth pixels are then extracted from the face candidate region based on the determined extraction conditions, and then the area ratio of the eyes and the area ratio of mouth are calculated for the face candidate region based on the eye pixels and the mouth pixels. Next the area ratio for the eyes and mouth is input into the neural network and a determinations is made as to whether the face candidate region is the face of a person using the neural network.

Image processing method, image processing apparatus and image processing program

In this paper, we originally propose a multiscale feature extraction method of finger-vein patterns based on curvelets and local interconnection structure neural networks. The curvelets is used to perform the multiscale self-adaptive enhancement transform on the finger-vein image and a neural network with local interconnection structure is designed to extract the features of the finger-vein pattern. This method has the following features: Firstly, the feature of finger-vein is line feature, or anisotropy, which is more suitable to be processed by curvelets than wavelets, especially when dealing with the obscure anisotropic features. Secondly, when the multiscale self-adaptive enhancement transform is applied to the finger-vein image, the finger-vein pattern is emphasized and noises are refrained greatly. Thirdly, a local interconnection neural network with linear receptive field is designed to deal with finger-vein patterns of different thickness and capture the patterns. Fourthly, the method is very fast by using the integral image method. The experimental results show the proposed method is superior to other methods in finger-vein feature extraction and solve the problem of how to extract features from obscure images efficiently. The EER of the proposed method is 0.128%.

Multiscale Feature Extraction of Finger-Vein Patterns Based on Curvelets and Local Interconnection Structure Neural Network

Time-frequency analysis of the first and the second heartbeat sounds

An algorithm that reconstructs one-dimensional signals and images from their sharper variation points at dyadic scales is described. This algorithm exactly reconstructs images from their multiscale edges. It is proved that the evolution across scales of the wavelet maxima characterizes the local shape of the sharp variations of the signal. One can thus not only detect edges but also classify them. The wavelet maxima representation is a new reorganization of the image information that makes it possible to develop algorithms uniquely based on edges for solving image processing problems. >

S. Zhong

Papers

Signal characterization from multiscale edges