Similarity with wavelet-transforms

As stated previously, with most applications in analytical chemistry and chemometrics, the data we wish to transform are not continuous and infinite in size but discrete and finite. We cannot simply discretise the continuous wavelet transform equations to provide us with the lattice decomposition and reconstruction equations. Furthermore it is not possible to define a MRA for discrete data. One approach taken is similar to that of the continuous Fourier transform and its associated discrete Fourier series and discrete Fourier transform. That is, we can define a discrete wavelet series by using the fact that discrete data can be viewed as a sequence of weights of a set of continuous scaling functions. This can then be extended to defining a discrete wavelet transform (over a finite interval) by equating it to one period of the data length and generating a discrete wavelet series by its infinite periodic extension. This can be conveniently done in a matrix framework. 

Abstract— This paper describes an approach for texture characterization based on nonseparable quincunx wavelet decomposition transforms and its application for the discrimination of visually similar ultrasound renal stone images. The proposed feature extraction method applies quincunx wavelet transform and calculation of second order (GLCM) and FFT parameter form LL and HH part of decomposed image. This Characterization is experimented on a set of one hundred and twelve (112) different stones, which also validated with FTIR analysis in standard laboratory. It shows that GLCM, FFT transform evaluation in combination with quincunx wavelet decomposition could be a reliable method for a texture characterization. 

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