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Efficient image reconstruction for point-based and line-based rendering

COMPUTERS & GRAPHICS-UK 2008年第2期32卷 189-203页

作者： Marroquim, Ricardo Kraus, Martin Cavalcanti, Paulo Roma Tech Univ Munich Comp Graph & Visualizat Grp D-85748 Garching Germany Univ Fed Rio de Janeiro COPPE Sistemas BR-21945970 Rio De Janeiro RJ Brazil

We address the problem of an efficient image-space reconstruction of adaptively sampled scenes in the context of point-based and line-based graphics. The image-space reconstruction offers an advantageous time complexity compared to surface splatting techniques and, in fact, our improved GPU implementation performs significantly better than splatting implementations for large point-based models. We discuss the integration of elliptical Gaussian weights for enhanced image quality and generalize the image-space reconstruction to line segments. Furthermore, we present solutions for the efficient combination of points, lines, and polygons in a single image. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： point-based graphics point-based rendering line-based rendering pyramid algorithm

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Quasi-convolution pyramidal blurring

Quasi-convolution pyramidal blurring

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3rd International Conference on Computer Graphics Theory and Applications

作者： Kraus, Martin Tech Univ Munich Comp Graph & Visualizat Grp D-8046 Garching Germany

ISBN: (纸本)9789898111203

Efficient image blurring techniques based on the pyramid algorithm can be implemented on modem graphics hardware;thus, image blurring with arbitrary blur width is possible in real time even for large images. However, pyramidal blurring methods do not achieve the image quality provided by convolution filters;in particular, the shape of the corresponding filter kernel varies locally, which potentially results in objectionable rendering artifacts. In this work, a new analysis filter is designed that significantly reduces this variation for a particular pyramidal blurring technique. Moreover, an efficient implementation for programmable graphics hardware is presented. The proposed method is named "quasi-convolution pyramidal blurring" since the resulting effect is very close to image blurring based on a convolution filter for many applications.

关键词： rendering image processing blurring pyramid algorithm GPU real-time

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pyramid filters based on bilinear interpolation

Pyramid filters based on bilinear interpolation

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2nd International Conference on Computer Graphics Theory and Applications/2nd International Conference on Computer Vision Theory and Applications

作者： Kraus, Martin Strengert, Magnus Tech Univ Munich Comp Graph & Visualizat Grp D-8000 Munich Germany Univ Stuttgart Visualizat & Interact Syst Grp Stuttgart Germany

ISBN: (纸本)9789728865719

The implementation of several pyramid methods on programmable graphics processing units (GPUs) in recent years led to additional research interest in pyramid algorithms for real-time computer graphics. Of particular interest are efficient analysis and synthesis filters based on hardware-supported bilinear texture interpolation because they can be used as building blocks for many GPU-based pyramid methods. In this work, several new and extremely efficient GPU-implementations of pyramid filters are presented for the first time. The discussion employs a new notation, which was developed for the consistent and precise specification of these filters and also allowed us to systematically explore appropriate filter designs. The presented filters cover analysis and synthesis filters, (quasi-)interpolation and approximation, as well as discontinuous, continuous, and smooth filters. Thus, a toolbox of filters and their efficient implementations for a great variety of GPU-based pyramid methods is presented.

关键词： signal processing image processing multi resolution pyramid algorithm graphics hardware

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Efficient wavelet prefilters with optimal time-shifts

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2005年第7期53卷 2451-2461页

作者： Ericsson, S Grip, N Lulea Univ Technol Dept Math SE-97187 Lulea Sweden

A wavelet prefilter maps sample values of an analyzed signal to the scaling function coefficient input of standard discrete wavelet transform (DWT) algorithms. The prefilter is the inverse of a certain posyfilter convolution matrix consisting of integer sample values of a noninteger-shifted wavelet scaling function. For the prefilter and the DWT algorithms to have similar computational complexity, it is often necessary to use a "short enough" approximation of the prefilter. In addition to well-known quadrature formula and identity matrix prefilter approximations, we propose a Neumann series approximation, which is a band matrix truncation of the optimal prefilter, and derive simple formulas for the operator norm approximation error. This error shows a dramatic dependence on how the postfilter noninteger shift is chosen. We explain the meaning of this shift in practical applications, describe how to choose it, and plot optimally shifted prefilter approximation errors for 95 different Daubechies, Symlet, and B-spline wavelets. Whereas the truncated inverse is overall superior, the Neumann filters are by far the easiest ones to compute, and for some short support wavelets, they also give the smallest approximation error. For example, for Daubechies 1-5 wavelets, the simplest Neumann prefilter provide an approximation error reduction corresponding to 100-10 000 times oversampling in a nonprefiltered system.

关键词： biorthogonal wavelet B-spline wavelet Daubechies wavelet FWT algorithm initialization Lagrange interpolant Neumann series prefilter pyramid algorithm quadrature formula quadrature mirror filter sampling Sard optimal Symlet

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Measures in wavelet decompositions

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ADVANCES IN APPLIED MATHEMATICS 2005年第3期34卷 561-590页

作者： Jorgensen, PET Univ Iowa Dept Math Iowa City IA 52242 USA

In applications, choices of orthonormal bases in Hilbert space H may come about from the simultaneous diagonalization of some specific abelian algebra of operators. This is the approach of quantum theory as suggested by John von Neumann;but as it turns out, much more recent constructions of bases in wavelet theory, and in dynamical systems, also fit into this scheme. However, in these modem applications, the basis typically comes first, and the abelian algebra might not even be made explicit. It was noticed recently that there is a certain finite set of non-commuting operators F-i, first introduced by engineers in signal processing, which helps to clarify this connection, and at the same time throws light on decomposition possibilities for wavelet packets used in pyramid algorithms. There are three interrelated components to this: an orthonormal basis, an abelian algebra, and a projection-valued measure. While the operators F-i were originally intended for quadrature mirror filters of signals, recent papers have shown that they are ubiquitous in a variety of modem wavelet constructions, and in particular in the selection of wavelet packets from libraries of bases. These are constructions which make a selection of a basis with the best frequency concentration in signal or data-compression problems. While the algebra A generated by the F-i-system is non-abelian, and goes under the name "Cuntz algebra" in C*-algebra theory, each of its representations contains a canonical maximal abelian subalgebra, i.e., the subalgebra is some C(X) for a Gelfand space X. A given representation of A, restricted to C(X), naturally induces a projection-valued measure on X, and each vector in H induces a scalar-valued measure on X. We develop this construction in the general context with a view to wavelet applications, and we show that the measures that had been studied earlier for a very restrictive class of F-i-systems (i.e., the Lemarie-Meyer quadrature mirror filters) in the theory of

关键词： Hilbert space Cuntz algebra completely positive map creation operators wavelet packets pyramid algorithm product measures orthogonality relations equivalence of measures iterated function systems (IFS) scaling function multiresolution subdivision scheme singular measures absolutely continuous measures

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Multitemporal and multiresolution fusion of wide field of view and high spatial resolution images through morphological pyramid

Multitemporal and multiresolution fusion of wide field of vi...

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Conference on Image and Signal Processing for Remote Sensing X

作者： Laporterie-Dejean, F Flouzat, G Lopez-Ornelas, E CNES F-31401 Toulouse 9 France

ISBN: (纸本)0819455202

To study vegetation from space, both high spatial resolution and high temporal frequency images are needed. However, a satellite sensor, for technological reasons, cannot provides such images. But merge several kinds of images coming from several sensors enables to overgo this problem. In this article, we propose a fusion method based on pyramid algorithms and on morphological filtering to create synthesis images having both high spatial resolution and high temporal frequency. This process is validated by high resolution reference images. The study uses the ADAM (C) database provided with courtesy of Centre National d'Etude Spatiale (CNES - French Space Agency).

关键词： fusion multiresolution spatial resolution pyramid algorithm mathematical morphology SPOT4

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Wavelet-Galerkin method for the Kolmogorov equation

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MATHEMATICAL AND COMPUTER MODELLING 2004年第9-10期40卷 1093-1121页

作者： Liang, ZG Yau, SST Univ Illinois Dept MSCS Chicago IL 60607 USA

It is well known that the Kolmogorov equation plays an important role in applied science. For example, the nonlinear filtering problem, which plays a key role in modern technologies, was solved by Yau and Yau [1] by reducing it to the off-line computation of the Kolmogorov equation. In this paper, we develop a theorical foundation of using the wavelet-Galerkin method to solve linear parabolic P.D.E. We apply our theory to the Kolmogorov equation. We give a rigorous proof that the solution of the Kolmogorov equation can be approximated very well in any finite domain by our wavelet-Galerkin method. An example is provided by using Daubechies D-4 scaling functions. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： nonlinear filtering Kolmogorov equation Wavelet-Galerkin method Daubechies scaling function pyramid algorithm

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Iterated function systems, representations, and Hilbert space

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INTERNATIONAL JOURNAL OF MATHEMATICS 2004年第8期15卷 813-832页

作者： Jorgensen, PET Univ Iowa Dept Math Iowa City IA 52242 USA

In this paper, we axe concerned with spectral-theoretic features of general iterated function systems (IFS). Such systems arise from the study of iteration limits of a finite family of maps tau(i) = 1,...,N, in some Hausdorff space Y. There is a standard construction which generally allows us to reduce to the case of a compact invariant subset X subset of Y. Typically, some kind of contractivity property for the maps tau(i) is assumed, but our present considerations relax this restriction. This means that there is then not a natural equilibrium measure p available which allows us to pass the point-maps tau(i) to operators on the Hilbert space L-2(mu). Instead, we show that it is possible to realize the maps tau(i) quite generally in Hilbert spaces H(X) of square-densities on X. The elements in H(X) axe equivalence classes of pairs (phi, mu), where phi is a Borel function on X, mu is a positive Borel measure on X, and integral(X) \phi\(2) dmu < infinity. We say that (phi, mu) similar to (phi, nu) if there is a positive Borel measure lambda such that mu much less than lambda, nu much less than lambda, and phirootdmu/dlambda = psirootdnu/dlambda, lambda a.e. on X. We prove that, under general conditions on the system (X, tau(i)), there are isometries S-i: (phi, mu) --> (phi (.) sigma, mu (.) tau(i)(-1)) in H(X) satisfying Sigma(i=1)(N) SiSi* = I = the identity operator in H(X). For the construction we assume that some mapping sigma: X --> X satisfies the conditions sigma (.) tau(i) = id(X), i = 1,...N. We further prove that this representation in the Hilbert space H(X) has several universal properties.

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Optimal wavelet expansion via sampled-data control theory

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IEEE SIGNAL PROCESSING LETTERS 2004年第2期11卷 79-82页

作者： Kashima, K Yamamoto, Y Nagahara, M Kyoto Univ Grad Sch Informat Dept Appl Anal & Complex Dynam Syst Kyoto 6068501 Japan

Discrete wavelet transform is usually executed by the so-called pyramid algorithm. It, however, requires a proper initialization, i.e., expansion coefficients with respect to the basis of one of the desired approximation subspaces. An interesting question here is how we can obtain such coefficients when only sampled values of signals are available. This letter provides a design method for a digital filter that (sub-)optimally gives such coefficients assuming certain a Priori knowledge on the frequency characteristic of target functions. We then extend the result to the case of nonorthogonal wavelets. Examples show the effectiveness of the proposed method.

关键词： discrete wavelet transform (DWT) pyramid algorithm sampled-data control

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Wavelet-based steganography

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Cryptologia 2004年第2期28卷 157-174页

作者： Driskell, Lisa Columbiaville MI 48421 811 Columbiaville Road United States

Wavelets, which are used to separate data into different components, have many applications. Steganography, one such application, is a form of secret communication where the existence of a message is concealed. Methods for applying univariate and bivariate wavelets to steganography include embedding messages into the insignificant wavelet coefficients of decomposed signals and images. Recomposing then creates stego-objects that appear unaltered from the original cover-objects. First demonstrated is at echnique for hiding messages in strings of data with linear trends using the univariate Daubechies D₄ wavelets. Then, after developing the bivariate Haar wavelets and filters, a unique process of decomposing and recomposing an image in greyscale in order to implement steganography will be illustrated. © 2004, United States Military Academy., All rights reserved.

关键词： Bivariate haar wavelets Cover-object F5 Filter coefficients Hard thresholding JSteg Pre-processed image pyramid algorithm Refinement coefficients Regularity Robustness Scaling function Steganography Stego-object Univariate daubechies wavelets Wavelet coefficients Wavelet-based steganography Wavelets

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