Showing papers on "Multiresolution analysis published in 1995"
15 Sep 1995
TL;DR: A method for overcoming the subdivision connectivity restriction, meaning that completely arbitrary meshes can now be converted to multiresolution form, is presented, based on the approximation of an arbitrary initial mesh M by a mesh MJ that has subdivision connectivity and is guaranteed to be within a specified tolerance.
Abstract: In computer graphics and geometric modeling, shapes are often represented by triangular meshes. With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace. Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit. Multiresolution analysis offers a simple, unified, and theoretically sound approach to dealing with these problems. Lounsbery et al. have recently developed a technique for creating multiresolution representations for a restricted class of meshes with subdivision connectivity. Unfortunately, meshes encountered in practice typically do not meet this requirement. In this paper we present a method for overcoming the subdivision connectivity restriction, meaning that completely arbitrary meshes can now be converted to multiresolution form. The method is based on the approximation of an arbitrary initial mesh M by a mesh MJ that has subdivision connectivity and is guaranteed to be within a specified tolerance. The key ingredient of our algorithm is the construction of a parametrization of M over a simple domain. We expect this parametrization to be of use in other contexts, such as texture mapping or the approximation of complex meshes by NURBS patches. CR
1,411 citations
TL;DR: Wavelets are a mathematical tool for hierarchically decomposing functions as mentioned in this paper, which can be described in terms of a coarse overall shape, plus details that range from broad to narrow.
Abstract: Wavelets are a mathematical tool for hierarchically decomposing functions. Using wavelets, a function can be described in terms of a coarse overall shape, plus details that range from broad to narrow. Regardless of whether the function of interest is an image, a curve, or a surface, wavelets provide an elegant technique for representing the levels of detail present. This primer is intended to provide those working in computer graphics with some intuition for what wavelets are, as well as to present the mathematical foundations necessary for studying and using them. In Part I, we discussed the simple case of Haar wavelets in one and two dimensions, and showed how they can be used for image compression. Part II presents the mathematical theory of multiresolution analysis, develops bounded-interval spline wavelets, and describes their use in multiresolution curve and surface editing.
294 citations
TL;DR: In this article, the authors proposed the use of compactly supported semi-orthogonal (SO) wavelets specially constructed for the bounded interval in solving first-kind integral equations, and applied this technique to analyze a problem involving 2D EM scattering from metallic cylinders.
Abstract: The conventional method of moments (MoM), when applied directly to integral equations, leads to a dense matrix which often becomes computationally intractable. To overcome the difficulties, wavelet-bases have been used previously which lead to a sparse matrix. The authors refer to "MoM with wavelet bases" as "wavelet MoM". There have been three different ways of applying the wavelet techniques to boundary integral equations: 1) wavelets on the entire real line which requires the boundary conditions to be enforced explicitly, 2) wavelet bases for the bounded interval obtained by periodizing the wavelets on the real line, and 3) "wavelet-like" basis functions. Furthermore, only orthonormal (ON) bases have been considered. The present authors propose the use of compactly supported semi-orthogonal (SO) spline wavelets specially constructed for the bounded interval in solving first-kind integral equations. They apply this technique to analyze a problem involving 2D EM scattering from metallic cylinders. It is shown that the number of unknowns in the case of wavelet MoM increases by m-1 as compared to conventional MoM, where m is the order of the spline function. Results for linear (m=2) and cubic (m=4) splines are presented along with their comparisons to conventional MoM results. It is observed that the use of cubic spline wavelets almost "diagonalizes" the matrix while maintaining less than 1.5% of relative normed error. The authors also present the explicit closed-form polynomial representation of the scaling functions and wavelets. >
243 citations
TL;DR: An optimal P-band perfect reconstruction filter bank (PRFB) is derived in this paper, which minimizes the approximation error (in the mean-square sense) between the original signal and its low-resolution version.
Abstract: An important issue in multiresolution analysis is that of optimal basis selection. An optimal P-band perfect reconstruction filter bank (PRFB) is derived in this paper, which minimizes the approximation error (in the mean-square sense) between the original signal and its low-resolution version. The resulting PRFB decomposes the input signal into uncorrelated, low-resolution principal components with decreasing variance. Optimality issues are further analyzed in the special case of stationary and cyclostationary processes. By exploiting the connection between discrete-time filter banks and continuous wavelets, an optimal multiresolution decomposition of L/sub 2/(R) is obtained. Analogous results are also derived for deterministic signals. Some illustrative examples and simulations are presented. >
194 citations
TL;DR: A novel set of shape descriptors that represents a digitized pattern in a concise way and that is particularly well-suited for the recognition of handprinted characters that are derived from the wavelet transform of a pattern's contour.
167 citations
TL;DR: In this article, a general solution of the orthogonality conditions up to J = 5 is presented, and a classification of the solutions according to the degree of symmetry of the associated scaling function is proposed.
159 citations
TL;DR: This paper extends earlier results on adaptive control and estimation of nonlinear systems using gaussian radial basis functions to the on-line generation of irregularly sampled networks, using tools from multiresolution analysis and wavelet theory to yield much more compact and efficient system representations.
130 citations
TL;DR: This tutorial presents an intuitive introduction to wavelets and the wavelet transform, concentrating on the multiresolution approach to wavelet analysis of ERP data.
123 citations
TL;DR: By reconstructing only a small localized region at high resolution, the authors show how radiation exposure and computation can be significantly reduced, compared to a standard reconstruction.
Abstract: Shows how the separable two-dimensional wavelet representation leads naturally to an efficient multiresolution tomographic reconstruction algorithm. This algorithm is similar to the conventional filtered backprojection algorithm, except that the filters are now angle dependent, and the backprojection gives the wavelet coefficients of the reconstruction, which are then used to synthesize the reconstruction at various resolution levels. By reconstructing only a small localized region at high resolution, the authors show how radiation exposure and computation can be significantly reduced, compared to a standard reconstruction. >
114 citations
TL;DR: By analyzing the signal-to-noise ratios and visual aesthetics of the fused images, contrast-sensitivity-based fusion is shown to provide excellent fusion results and to outperform previous fusion methods.
Abstract: A perceptual-based multiresolution image fusion technique is demonstrated using the Airborne Visible and Infrared Imaging Spectrometer (AVIRIS) hyperspectral sensor data. The AVIRIS sensor, which simultaneously collects information in 224 spectral bands that range from 0.4 to 2.5 μm in approximately 10-nm increments, produces 224 images, each representing a single spectral band. The fusion algorithm consists of three stages. First, a Daubechies orthogonal wavelet basis set is used to perform a multiresolution decomposition of each spectral image. Next, the coefficients from each image are combined using a perceptual-based weighting. The weighting of each coefficient, from a given spectral band image, is determined by the spatial-frequency response (contrast sensitivity) of the human visual system. The spectral image with the higher saliency value, where saliency is based on a perceptual energy, will receive the larger weight. Finally, the fused coefficients are used for reconstruction to obtain the fused image. The image fusion algorithm is analyzed using test images with known image characteristics and image data from the AVIRIS hyperspectral sensor. By analyzing the signal-to-noise ratios and visual aesthetics of the fused images, contrast-sensitivity-based fusion is shown to provide excellent fusion results and to outperform previous fusion methods.
108 citations
TL;DR: In this paper, a multiresolution strategy for homogenization of linear ODEs with variable coefficients and forcing terms has been proposed, where wave propagation in a stratified medium is considered.
12 Jun 1995
TL;DR: A class of processing operators which are diagonal in the wavelet basis and which can be used for smoothing and enhancement are described.
Abstract: Wavelets are a powerful tool for planar image processing. The resulting algorithms are straightforward, fast, and efficient. With the recently developed spherical wavelets this framework can be transposed to spherical textures. We describe a class of processing operators which are diagonal in the wavelet basis and which can be used for smoothing and enhancement. Since the wavelets (filters) are local in space and frequency, complex localized constraints and spatially varying characteristics can be incorporated easily. Examples from environment mapping and the manipulation of topography/bathymetry data are given.
TL;DR: In this article, a tensor product approach was used to construct a multiresolution analysis and a wavelet basis on two specific compact manifolds using special charts, the problem was reduced to finding appropriate nested spaces on rectangular domains.
Abstract: In this paper, we construct a multiresolution analysis and a wavelet basis on two specific compact manifolds. Using special charts, the problem is reduced to finding appropriate nested spaces on rectangular domains. The claim of C 1-continuity gives rise to certain boundary conditions on the rectangles. To satisfy these conditions, we use a tensor product approach in which one factor is an exponential spline.
TL;DR: In this paper, the irregular sampling problem in wavelet subspaces has been discussed and a regular sampling theorem has been established for the Paley-Wiener space with both regular and irregular sampling.
Abstract: As a particular wavelet subspace, the Paley-Wiener space \(B_{\pi}\) has both regular and irregular sampling theorems A regular sampling theorem in general wavelet subspaces has been established for several years In this paper, we discuss the irregular sampling problem in wavelet subspaces
TL;DR: A wavelet-based approach to linear inverse problems in image processing where both the images and the linear operator to be inverted are represented by wavelet expansions, leading to a multiresolution sparse matrix representation of the inverse problem.
Abstract: We describe a wavelet-based approach to linear inverse problems in image processing. In this approach, both the images and the linear operator to be inverted are represented by wavelet expansions, leading to a multiresolution sparse matrix representation of the inverse problem. The constraints for a regularized solution are enforced through wavelet expansion coefficients. A unique feature of the wavelet approach is a general and consistent scheme for representing an operator in different resolutions, an important problem in multigrid/multiresolution processing. This and the sparseness of the representation induce a multigrid algorithm. The proposed approach was tested on image restoration problems and produced good results. >
TL;DR: In this article, it was shown that for every expanding integer matrix A ∈ Mn(ℤ) there is a Haar type orthonormal wavelet basis having dilation factor A and translation lattice ℤn.
Abstract: K.-H. Grochenig and A. Haas asked whether for every expanding integer matrix A ∈ Mn(ℤ) there is a Haar type orthonormal wavelet basis having dilation factor A and translation lattice ℤn. They proved that this is the case when the dimension n = 1. This article shows that this is also the case when the dimension n = 2.
TL;DR: This paper presents a texture segmentation algorithm based on a hierarchical wavelet decomposition using Daubechies four-tap filter that propagates through the pyramid to a higher resolution with continuously improving the segmentation.
TL;DR: The results demonstrate the capabilities of the wavelet transform, as an alternative to the Fourier transform, for the representation and analysis of non-stationary EEG signals.
TL;DR: In this article, a wavelet approach is presented for treating the two-dimensional electromagnetic scattering problems over curved computation domains, in which the wavelet expansion method is combined with the boundary element method (BEM) to solve the integral equation for the unknown surface current.
Abstract: A new wavelet approach is presented for treating the two-dimensional electromagnetic scattering problems over curved computation domains. The wavelet expansion method, in combination with the boundary element method (BEM), is applied to solve the integral equation for the unknown surface current. The unknown surface current is expanded in terms of a basis derived from a periodic, orthogonal wavelet in interval [0, 1]. The geometrical representation of the BEM is employed to establish the map between the curved computation domain and the interval [0, 1]. This technique exhibits the advantages of both the wavelet expansion method and the boundary element method: sparse matrix system and accurately modeling of curved surfaces. Comparisons of the results from the new technique with the moment method solutions, the analytical solutions or the data in previous publications are provided. Good agreements are observed. >
TL;DR: It is shown that wide-sense stationarity may be achieved by adequately selecting the analysis wavelet and that the latter possesses additional properties which are useful in the presence of other types of nonstationarities.
Abstract: Processing nonstationary signals is an important and challenging problem. We focus on the class of nonstationary processes with stationary increments of an arbitrary order, and place them in a multiscale framework. Unlike other related studies, we concentrate on the discrete-time analysis and derive a number of new results in addition to placing the related existing ones in the same framework. We extend the study to various parametric models for which we derive the resulting multiresolution description. We show that wide-sense stationarity may be achieved by adequately selecting the analysis wavelet. After generalizing the study to wavelet packet analysis, we show that the latter possesses additional properties which are useful in the presence of other types of nonstationarities. >
TL;DR: The application of the proposed pixelwise resolution determination algorithm to the conventional Canny and LoG edge detectors, for example, gives the proposed multiresolution edge detection techniques.
12 Mar 1995
TL;DR: A multirate wavelet based modulation format is presented which can utilize existing channels designed for conventional QAM and has advantages including dimensionality in both time and frequency for flexible channel exploitation and an efficient all digital filter bank implementation.
Abstract: Building on recently introduced multidimensional signalling techniques, a multirate wavelet based modulation format is presented which can utilize existing channels designed for conventional QAM. Customizable wavelet packet basis functions are employed as novel pulse shapes upon which independent QAM data at lower rates are placed. The advantages include dimensionality in both time and frequency for flexible channel exploitation and an efficient all digital filter bank implementation. >
Dissertation•
01 Jan 1995
TL;DR: The classical discrete wavelet transform is generalized, and wavelet transforms that are shift-invariant, time-varying, undecimated, and signal dependent are constructed that are suitable for a wide variety of signal processing tasks, e.g., data compression, signal analysis, noise reduction, statistical estimation, and detection.
Abstract: In this thesis, we generalize the classical discrete wavelet transform, and construct wavelet transforms that are shift-invariant, time-varying, undecimated, and signal dependent. The result is a set of powerful and eecient algorithms suitable for a wide variety of signal processing tasks, e.g., data compression, signal analysis, noise reduction, statistical estimation, and detection. These algorithms are comparable and often superior to traditional methods. In this sense, we put wavelets in action. Acknowledgments I want to thank my thesis advisor, Dr. Sidney Burrus, for introducing me into the theory of wavelets, and for his encouragement and guidance. His perspective and insight had a profound innuence on this thesis. I also would like to thank the members of my thesis committee, Dr. Richard Baraniuk and Dr. Ronny Wells. They all provided substantial input throughout the period during which this research was being done. I am also indebted to Ramesh Gopinath for his help and encouragement. Thanks to the members of the DSP group and the Computational Mathematic Laboratory of Rice University for many fruitful discussions and collaborations. Special thanks to Odegard of the DSP group for reading earlier drafts of this thesis. The generous nancial support of ARPA and Texas ATP grant that made this research possible is also gratefully acknowledged. Also, I would like to thank all those authors who made their technical reports and publications readily available on the Internet and the World Wide Web. On the personal side, I would like to thank my parents for making this all possible through their constant support and understanding over the years. I really appreciate the love and support of my companion, Lin Yue, who has been exploring life with me and shares my interest in academic endeavor.
TL;DR: A detailed analysis of the differential approach for motion estimation in video image sequences and some key elements for an effective implementation of a complete motion estimation scheme are drawn.
Abstract: This paper presents a detailed analysis of the differential approach for motion estimation in video image sequences. The models considered are defined either by a parametric approach, or by a physical approach (in terms of parameters of the pick-up equipment, movement and object structures). The relationships between the 2D and the 3D approaches are examined. The ambiguities inherent in a physical interpretation of a set of descriptors identified from image sequences are underlined. The critical points when using differential estimators are discussed, in particular, we study several classical image processing tools which improve the convergence rate of these estimators (hierarchical analysis, multiresolution, spatial interpolation of the luminance…). Definition and tuning of gains, initialization stage, cross-dependence between image segmentation and identification of the parameters associated to each region (as well as the duality between top-down and bottom-up approaches), which partly condition the behavior of the algorithms, are studied too. Results in terms of motion and segmentation maps, images predicted from one or several previous images by motion compensation, convergence curves of some of the proposed iterative algorithms illustrate this paper. Finally, we draw from these theoretical developments and the associated simulations some key elements for an effective implementation of a complete motion estimation scheme. We conclude by some perspectives for future work.
TL;DR: A joint wavelet-transform correlator in which the wavelet function is combined with the input image as the input joint image to realize the wavelets transform of the objective image.
Abstract: We describe a joint wavelet-transform correlator in which the wavelet function is combined with the input image as the input joint image to realize the wavelet transform of the objective image. The Haar wavelet and the Roberts filter are chosen as the wavelet functions to extract the features of the objective image. The relationship of the Haar wavelet and the Roberts filter is analyzed mathematically based on admissible condition of the wavelet. Computer simulations are provided to verify the theory and to illustrate the performance of this correlator.
23 Oct 1995
TL;DR: An automatic registration procedure based on a multiresolution analysis of images that can effectively cope with a considerable range of transformations, and is outperforming the best algorithms available at present and used in industrial applications.
Abstract: The paper describes an automatic registration procedure based on a multiresolution analysis of images. The approach is quite general and can be applied to a large variety of images. Furthermore the algorithm is very robust and can effectively cope with a considerable range of transformations, since the registration is obtained iteratively at different multiresolution scales. The procedure is completely automatic, and relies on the grey level information content of the images. We have applied the algorithm to test images of banknotes, aerial stereo pairs, multispectral and SAR images. In all the cases we have obtained excellent results, outperforming the best algorithms available at present and used in industrial applications.
TL;DR: The wavelets method simplifies significantly both the theoretical and the practical computations for estimating multivariate densities using wavelets.
Abstract: This paper describes a practical method for estimating multivariate densities using wavelets. As in kernel methods, wavelet methods depend on two types of parameters. On the one hand we have a functional parameter: the wavelet O (comparable to the kernel K) and on the other hand we have a smoothing parameter: the resolution index (comparable to the bandwidth h). Classically, we determine the resolution index with a cross-validation method. The advantage of wavelet methods compared to kernel methods is that we have a technique for choosing the wavelet O among a fixed family. Moreover, the wavelets method simplifies significantly both the theoretical and the practical computations.
TL;DR: In this article, a spline wavelets element method that combines the versatility of the finite element method with the accuracy of spline functions approximation and the multiresolution strategy of wavelets is proposed for frame structures vibration analysis.
Abstract: A spline wavelets element method that combines the versatility of the finite element method with the accuracy of spline functions approximation and the multiresolution strategy of wavelets is proposed for frame structures vibration analysis. Instead of exploring orthogonal wavelets for specific differential operators, the spline wavelets are applied directly in finite element implementation for general differential operators. Although lacking orthogonality, the “two-scale relations” of spline functions and its corresponding wavelets from multiresolution analysis are employed to facilitate the elemental matrices manipulation by constructing two transform matrices under the constraint of finite domain of elements. In the actual formulation, the segmental approach for spline functions is provided to simplify the computation, much as conventional finite element procedure does. The assembled system matrices at any resolution level are reusable for the furthur finer resolution improvement. The local approximation and hiararchy merits make the approach competitive especially for higher mode vibration analysis. Some examples are studied as verification and demonstration of the approach.
TL;DR: In this article, moments with scaling functions are applied directly to Maxwell's equations and a new three-dimensional time domain scheme with highly linear dispersion characteristics is obtained, which allows one to incorporate the advantages of multiresolution analysis.
Abstract: The method of moments with scaling functions is applied directly to Maxwell's equations. As a result, we obtain a new three-dimensional time domain scheme with highly linear dispersion characteristics that allows one to incorporate the advantages of multiresolution analysis. First examples suggest significant reductions with respect to computer resources. >
TL;DR: A new switch between ENO and central interpolation is proposed, which provides a truly “tolerably oscillatory” interpolation and is proved to ensure that wherever the central stencil is used, it will still result is an essentially nonoscillatory interpolation.