We present here a new approach to wavelet transforms based on techniques of SHA. It is a version of HA which operates in spline spaces. SHA enjoys various applications but here we outline a recent application of SHA t...
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ISBN:
(纸本)0819416274;9780819416278
We present here a new approach to wavelet transforms based on techniques of SHA. It is a version of HA which operates in spline spaces. SHA enjoys various applications but here we outline a recent application of SHA techniques, namely, accomplishing on the base of periodic splines the wavelet transforms of periodic signals as well as the remarkable informative digital representation of the signals. SHA approach to wavelets yields a tool just as for the constructing a diversity of spline wavelet bases, so for a fast implementation of a decomposition of a function into a fitting wavelet representation and its reconstruction. This approach allows to construct WP bases for refined frequency resolution of signals.
We present in the following work, a multiscale edge detection algorithm whose aim is to detect edges of any slope. Our work is based on a generalization of the Canny-Deriche filter, modelized by a more realistic edge ...
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ISBN:
(纸本)0819416274;9780819416278
We present in the following work, a multiscale edge detection algorithm whose aim is to detect edges of any slope. Our work is based on a generalization of the Canny-Deriche filter, modelized by a more realistic edge than the traditional step shape edge. The filter impulse response is used to generate a frame of wavelets. For the merging of the wavelet coefficients, we use a geometrical classifier developed in our laboratory. The segmentation system thus set up and after the training phase does not require any adjustment nor parameter. The main original property of this algorithm is that it leads to a binary edge image without any threshold setting.
Unlike the classical wavelet decomposition scheme it is possible to have different scaling and wavelet functions at every scale by using non-stationary multiresolution analyses. For the bidimensional case inhomogeneou...
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ISBN:
(纸本)0819416274;9780819416278
Unlike the classical wavelet decomposition scheme it is possible to have different scaling and wavelet functions at every scale by using non-stationary multiresolution analyses. For the bidimensional case inhomogeneous multiresolution analyses using different scaling and wavelet functions for the two variables are introduced. Beyond it, these two methods are combined. All this freedom is used for compact image coding. The idea is to build out of the functions in a library that special non-stationary and/or inhomogeneous multiresolution analysis, that is best suited for a given image in the context of compact coding (in the sense of optimizing certain cost-functions).
We study the general problem of oblique projections in discrete shift-invariant spaces of l2 and we give error bounds on the approximation. We define the concept of discrete multiresolutions and wavelet spaces and sho...
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ISBN:
(纸本)0819416274;9780819416278
We study the general problem of oblique projections in discrete shift-invariant spaces of l2 and we give error bounds on the approximation. We define the concept of discrete multiresolutions and wavelet spaces and show that the oblique projections on certain subclasses of discrete multiresolutions and their associated wavelet spaces can be obtained using perfect reconstruction filter banks. Therefore we obtain a discrete analog of the Cohen-Daubechies-Feauveau results on biorthogonal wavelets.
Finite elements with support on two intervals span the space of piecewise polynomomials with degree 2 n - 1 and n - 1 continuous derivatives. Function values and n - 1 derivatives at each meshpoint determine these `He...
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ISBN:
(纸本)0819416274
Finite elements with support on two intervals span the space of piecewise polynomomials with degree 2 n - 1 and n - 1 continuous derivatives. Function values and n - 1 derivatives at each meshpoint determine these `Hermite finite elements'. The n basis functions satisfy a dilation equation with n by n matrix coefficients. Orthogonal to this scaling subspace is a wavelet subspace. It is spanned by the translates of n wavelets Wi(t), each supported on three intervals. The wavelets are orthogonal to all rescalings Wi(2jt-k), but not to translates at the same level (j equals 0). These new multiwavelets achieve 2 n vanishing moments and high regularity with symmetry and short support.
The paper contains a brief description of fractal image compression methods with sample compression results. We also present comparative results between two fractal schemes, discrete cosine transform, and a wavelet me...
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In this paper, we establish a mathematical connection between dyadic-wavelet-based contrast enhancement and traditional unsharp masking. Our derivation is completely based in the discrete domain. These findings may pr...
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ISBN:
(纸本)0819416274;9780819416278
In this paper, we establish a mathematical connection between dyadic-wavelet-based contrast enhancement and traditional unsharp masking. Our derivation is completely based in the discrete domain. These findings may provide a better theoretical understanding of these algorithms, and facilitate the acceptance of multiscale enhancement techniques applied to medical imaging.
This paper attempts to synthesize the wavelet theories to simple design procedures so that applied researchers can readily select or design wavelets with chosen characteristics for particular applications. The paper h...
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This paper attempts to synthesize the wavelet theories to simple design procedures so that applied researchers can readily select or design wavelets with chosen characteristics for particular applications. The paper highlights the importance of the four most desirable characteristics of wavelets for use in digital signalprocessing, namely- orthonormality, symmetry, compactness and smoothness. Some of these characteristics are mutually exclusive and require design compromise. Examples of some most popular wavelets and the effects their characteristics have on the quality of the reconstructed image in wavelet-based image coding, are given for comparison.
In this work, we use the 1D Haar transform fractal estimation algorithm to calculate the local fractal dimension estimates of 2D texture data. The new algorithm provides directed fractal dimension estimates which are ...
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ISBN:
(纸本)0819416282
In this work, we use the 1D Haar transform fractal estimation algorithm to calculate the local fractal dimension estimates of 2D texture data. The new algorithm provides directed fractal dimension estimates which are used as features for texture segmentation. The method is fast due to the pyramid structure of the Haar transform and nearly optimal in the maximum likelihood sense for fBm data. We compare the low complexity of this new algorithm with the complexity of existing fractal feature extraction techniques, and test our new method on fBm data and real Brodatz textures.
The topics included are mathematics and equation solvers;communications;signal and imageprocessing;computer vision;data compression and recognition;radar processing;earth sciences and remote sensing;industrial applic...
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ISBN:
(纸本)0819415464
The topics included are mathematics and equation solvers;communications;signal and imageprocessing;computer vision;data compression and recognition;radar processing;earth sciences and remote sensing;industrial applications of wavelets;imageprocessing, recognition, and implementation;wavelets and neural networks;biomedical applications;and acoustic signal detection and recognition.
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