Optimal mechanisms are determined for the hierarchical decomposition of wire-frame surfaces. A family of box-splines with compact support, suitable for the approximation of wire-frames is first defined, generated by a...
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ISBN:
(纸本)0819425915
Optimal mechanisms are determined for the hierarchical decomposition of wire-frame surfaces. A family of box-splines with compact support, suitable for the approximation of wire-frames is first defined, generated by arbitrary sampling matrices with integer eigenvalues. For each such box-spline, the optimal positioning of the wire-frame nodes is determined for each level of the hierarchical wire-frame decomposition. Criterion of optimality is the minimization of the variance of the error difference between the original surface and its representation at each resolution levels. This is needed so as to ensure that the wire mesh produces at each resolution as close a replica of the original surface as possible. The application of the proposed scheme to the hierarchical coding of 3D wire meshes is experimentally evaluated.
The application of the wavelet transform in imageprocessing is most frequently based on a separable construction. Lines and columns in an image are treated independently and the basis functions are simply products of...
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ISBN:
(纸本)0819450804
The application of the wavelet transform in imageprocessing is most frequently based on a separable construction. Lines and columns in an image are treated independently and the basis functions are simply products of the corresponding one dimensional functions. Such method keeps simplicity in design and computation, but is not capable of capturing properly all the properties of an image. In this paper, a new truly separable discrete multi-directional transform is proposed with a subsampling method based on lattice theory. Alternatively, the subsampling can be omitted and this leads to a multi-directional frame. This transform can be applied in many areas like denoising, non-linear approximation and compression. The results on non-linear approximation and denoising show interesting gains compared to the standard two-dimensional analysis.
We show how periodized wavelet packet transforms and periodized wavelet transforms can be implemented on a quantum computer. Surprisingly, we find that the implementation of wavelet packet transforms is less costly th...
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ISBN:
(纸本)0819432997
We show how periodized wavelet packet transforms and periodized wavelet transforms can be implemented on a quantum computer. Surprisingly, we find that the implementation of wavelet packet transforms is less costly than the implementation of wavelet transforms on a quantum computer.
作者：
Torres, MEGamero, LFlandrin, PAbry, PFacultad de Ingeniería
Universidad Nacional de Entre Ríos 3100 Paraná (E.R.) C.C. 57 Sue. 3 Argentina CNRS
URA 1325 Laboratoire de Physique-Ecole Normale Supérieure de Lyon 69364 Lyon cedex 07 46 Allée d'Ltalie France
In this paper, we consider the problem of detecting changes ill dynamical systems from the analysis of the signals they produce. A notion of continuous multiresolution entropy is introduced, which combine advantages s...
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ISBN:
(纸本)0819425915
In this paper, we consider the problem of detecting changes ill dynamical systems from the analysis of the signals they produce. A notion of continuous multiresolution entropy is introduced, which combine advantages stemming from both classical entropy and wavelet analysis. The relevance of the approach, together with its robustness in tile presence of moderate noise, is supported by numerical investigations.
The developments in wavelet theory have given rise to the wavelet thresholding method, for extracting a signal from noisy data [1,2]. Multiwavelets, wavelets with several scaling functions, have recently been introduc...
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ISBN:
(纸本)0780376226
The developments in wavelet theory have given rise to the wavelet thresholding method, for extracting a signal from noisy data [1,2]. Multiwavelets, wavelets with several scaling functions, have recently been introduced and they offer simultaneous orthogonality, symmetry and short support;which is not possible with ordinary wavelets, also called scalar wavelets [3]. This property makes multiwavelets more suitable for various signalprocessingapplications, especially compression and denoising. Like scalar wavelets, multiwavelets can be realized as filterbanks, however the filterbanks are now matrix-valued;requiring two or more input streams, which can be accomplished by prefiltering. In this paper, several thresholding methods to be used with different multiwavelets for image denoising are presented. The performances of multiwavelets are compared with those of scalar wavelets. Simulations reveal that multiwavelet based image denoising schemes outperform wavelet based methods both subjectively and objectively.
This paper deals with two types of sampling systems;namely, the interpolation and approximation sampling systems. Closed-form expressions are derived for the frequency responses of the filters used in these systems th...
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This paper deals with two types of sampling systems;namely, the interpolation and approximation sampling systems. Closed-form expressions are derived for the frequency responses of the filters used in these systems that are matched to the input process in the mean squared sense, Closed-form expressions are also derived for the mean squared error between the input and the reconstructed processes for these matched sampling systems. Using these expressions, it is shown that the Meyer scaling function and wavelet or functions derived from these arise naturally in the con text of subsampled bandlimited processes. To implement these systems, the perfect reconstruction circular convolution (PRCC) filter bank is proposed as a framework for the frequency-sampled implementation of these systems. Examples of matched interpolation and approximation sampling systems are provided, and their performance is compared with some standard interpolators to demonstrate their efficacy.
This paper presents an approach for early diagnostic of Breast Cancer using the dual-tree complex wavelet transform (DT-CWT), which detect micro-calcifications in digital mammograms. The approach follows four basic st...
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ISBN:
(纸本)9789896740078
This paper presents an approach for early diagnostic of Breast Cancer using the dual-tree complex wavelet transform (DT-CWT), which detect micro-calcifications in digital mammograms. The approach follows four basic strategies, namely, image denoising, band suppression, morphological transformation and inverse complex wavelet transform. The procedure of image denoising is carried out with a thresholding algorithm that computes recursively the optimal threshold at each level of wavelet decomposition. In order to maximize the detection a morphological conversion is proposed and applied to the high-frequencies subbands of the wavelet transformation. This procedure is applied to a set of digital mammograms from the Mammography image Analysis Society (MIAS) database. Experimental results show that the proposed denoising algorithm and morphological transformation in combination with the DT-CWT procedure performs better than previous reported approaches.
A wavelet-based image gradient transform is proposed. The proposed transform, called multi-scale gradient transform (MSGT), obtains the first order derivative of an image in terms of the wavelet detail coefficients. W...
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ISBN:
(纸本)9781467345729
A wavelet-based image gradient transform is proposed. The proposed transform, called multi-scale gradient transform (MSGT), obtains the first order derivative of an image in terms of the wavelet detail coefficients. While traditional methods estimate the image gradients at each wavelet scale in terms of the horizontal and vertical wavelet coefficients only, the proposed transform obtains the gradients in terms of the diagonal, as well as the horizontal and vertical wavelet coefficients. The proposed MSGT is designed to be invertible, non-redundant and computationally efficient. We demonstrate the potential applications of the proposed transform in texture feature extraction, multi-scale edge detection, image quality assessment and image watermarking.
Integration of the nonlinear approaches for system identification is proposed for spectral differentiation and object recognition in this research. Multi-scale nonlinear principal component analysis (NCA) has been imp...
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ISBN:
(纸本)9781424446018
Integration of the nonlinear approaches for system identification is proposed for spectral differentiation and object recognition in this research. Multi-scale nonlinear principal component analysis (NCA) has been implemented to analyze the individual components of approximations and details based on wavelet transform. Neural network training has been applied to NCA while both ID and 2D wavelet transform have been conducted across different scales. At each scale, the principal components are selected in order to reconstruct the intrinsic signal and image. This statistical identification approach is essential to enhance multivariate data processing. Case studies on signal and imageprocessing are both conducted. In addition, quantitative measures are presented to analyze the nonlinear multi-scale approach from the objective perspectives.
We develop a novel measure of joint time-frequency localization applicable to equivalence classes of finite-length discrete signals, which are of increasing importance in modern signal and imageprocessing application...
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ISBN:
(纸本)0769515371
We develop a novel measure of joint time-frequency localization applicable to equivalence classes of finite-length discrete signals, which are of increasing importance in modern signal and imageprocessingapplications. Like the well-known Heisenberg-Weyl uncertainty principle that quantifies joint localization for continuous signals, this new measure is translation invariant and admits an intuitively satisfying interpretation in terms of the statistical variance of signal energy in time or space and in frequency. The new measure is used to design a now low-pass wavelet analysis filter with optimal joint localization. This new filter is then used to construct a localized separable 2-D discrete wavelet transform which is demonstrated on several images of general interest in practical applications.
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