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547
Contentbased image indexing and searching using Daubechies' wavelets
, 1998
"... This paper describes WBIIS (WaveletBased Image Indexing and Searching), a new image indexing and retrieval algorithm with partial sketch image searching capability for large image databases. The algorithm characterizes the color variations over the spatial extent of the image in a manner that provi ..."
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Cited by 91 (21 self)
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This paper describes WBIIS (WaveletBased Image Indexing and Searching), a new image indexing and retrieval algorithm with partial sketch image searching capability for large image databases. The algorithm characterizes the color variations over the spatial extent of the image in a manner that provides semantically meaningful image comparisons. The indexing algorithm applies a Daubechies' wavelet transform for each of the three opponent color components. The wavelet coefficients in the lowest few frequency bands, and their variances, are stored as feature vectors. To speed up retrieval, a twostep procedure is used that first does a crude selection based on the variances, and then renes the search by performing a feature vector match between the selected images and the query. For better accuracy in searching, twolevel multiresolution matching may also be used. Masks are used for partialsketch queries. This technique performs much better in capturing coherence of image, object granular...
Wavelets for Computer Graphics: A Primer  Part 2
 IEEE Computer Graphics and Applications
, 1995
"... this paper. Thanks also go to Ronen Barzel, Steven Gortler, Michael Shantzis, and the anonymous reviewers for their many helpful comments. This work was supported by NSF Presidential and National Young Investigator awards (CCR8957323 and CCR9357790), by NSF grant CDA9123308, by an NSF Graduate Res ..."
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Cited by 87 (1 self)
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this paper. Thanks also go to Ronen Barzel, Steven Gortler, Michael Shantzis, and the anonymous reviewers for their many helpful comments. This work was supported by NSF Presidential and National Young Investigator awards (CCR8957323 and CCR9357790), by NSF grant CDA9123308, by an NSF Graduate Research Fellowship, by the University of Washington Royalty Research Fund (659731), and by industrial gifts from Adobe, Aldus, Microsoft, and Xerox. References
Stability of Multiscale Transformations
 J. Fourier Anal. Appl
, 1996
"... After briefly reviewing the interrelation between Rieszbases, biorthogonality and a certain stability notion for multiscale basis transformations we establish a basic stability criterion for a general Hilbert space setting. An important tool in this context is a strengthened Cauchy inequality. It i ..."
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Cited by 86 (22 self)
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After briefly reviewing the interrelation between Rieszbases, biorthogonality and a certain stability notion for multiscale basis transformations we establish a basic stability criterion for a general Hilbert space setting. An important tool in this context is a strengthened Cauchy inequality. It is based on direct and inverse estimates for a certain scale of spaces induced by the underlying multiresolution sequence. Furthermore, we highlight some properties of these spaces pertaining to duality, interpolation, and applications to norm equivalences for Sobolev spaces. AMS Subject Classification: 41A17, 41A65, 46A35, 46B70, 46E35 Key Words: Riesz bases, biorthogonality, stability, projectors, interpolation theory, Kmethod, duality, Jackson, Bernstein inequalities 1 Background and Motivation A standard framework for approximately recapturing a function v in some infinite dimensional separable Hilbert space V , say, either from explicitly given data or as a solution of an operator equ...
The Discrete Wavelet Transform in S
 Journal of Computational and Graphical Statistics
, 1996
"... The theory of wavelets has recently undergone a period of rapid development. We introduce a software package called wavethresh that works within the statistical language S to perform one and twodimensional discrete wavelet transforms. The transforms and their inverses can be computed using any par ..."
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Cited by 81 (24 self)
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The theory of wavelets has recently undergone a period of rapid development. We introduce a software package called wavethresh that works within the statistical language S to perform one and twodimensional discrete wavelet transforms. The transforms and their inverses can be computed using any particular wavelet selected from a range of different families of wavelets. Pictures can be drawn of any of the one or twodimensional wavelets available in the package. The wavelet coefficients can be presented in a variety of ways to aid in the interpretation of data. The package's wavelet transform "engine" is written in C for speed and the objectorientated functionality of S makes wavethresh easy to use. We provide a tutorial introduction to wavelets and the wavethresh software. We also discuss how the software may be used to carry out nonlinear regression and image compression. In particular, thresholding of wavelet coefficients is a method for attempting to extract signal from noise and ...
Theory Of Regular MBand Wavelet Bases
 IEEE TRANS. ON SIGNAL PROCESSING
, 1993
"... This paper constructs Kregular Mband orthonormal wavelet bases. Kregularity of the wavelet basis is known to be useful in numerical analysis applications and in image coding using wavelet techniques. Several characterizations of Kregularity and their importance are described. An explicit formula ..."
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Cited by 79 (6 self)
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This paper constructs Kregular Mband orthonormal wavelet bases. Kregularity of the wavelet basis is known to be useful in numerical analysis applications and in image coding using wavelet techniques. Several characterizations of Kregularity and their importance are described. An explicit formula is obtained for all minimal length Mband scaling filters. A new statespace approach to constructing the wavelet filters from the scaling filters is also described. When Mband wavelets are constructed from unitary filter banks they give rise to wavelet tight frames in general (not orthonormal bases). Conditions on the scaling filter so that the wavelet bases obtained from it is orthonormal is also described.
Frames and Stable Bases for ShiftInvariant Subspaces of . . .
, 1994
"... Let X be a countable fundamental set in a Hilbert space H, and let T be the operator T : ` 2 (X) ! H : c 7! X x2X c(x)x: Whenever T is welldefined and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding T is inje ..."
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Cited by 75 (22 self)
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Let X be a countable fundamental set in a Hilbert space H, and let T be the operator T : ` 2 (X) ! H : c 7! X x2X c(x)x: Whenever T is welldefined and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding T is injective is a stable basis (also known as a Riesz basis). This paper considers the above three properties for subspaces H of L 2 (IR d ), and for sets X of the form X = fOE(\Delta \Gamma ff) : OE 2 \Phi; ff 2 ZZ d g; with \Phi either a singleton, a finite set, or, more generally, a countable set. The analysis is performed on the Fourier domain, where the two operators TT and T T are decomposed into a collection of simpler "fiber" operators. The main theme of the entire analysis is the characterization of each of the above three properties in terms of the analogous property of these simpler operators. AMS (MOS) Subject Classifications: 42C15 Key Words: Riesz bases, stable bases, shif...
Wavelet transforms versus Fourier transforms
 Department of Mathematics, MIT, Cambridge MA
, 213
"... Abstract. This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The "wavelet transform " maps each f(x) to its coefficients with respect to this basis. The mathematics is simple and the transfo ..."
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Cited by 71 (2 self)
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Abstract. This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The "wavelet transform " maps each f(x) to its coefficients with respect to this basis. The mathematics is simple and the transform is fast (faster than the Fast Fourier Transform, which we briefly explain), but approximation by piecewise constants is poor. To improve this first wavelet, we are led to dilation equations and their unusual solutions. Higherorder wavelets are constructed, and it is surprisingly quick to compute with them — always indirectly and recursively. We comment informally on the contest between these transforms in signal processing, especially for video and image compression (including highdefinition television). So far the Fourier Transform — or its 8 by 8 windowed version, the Discrete Cosine Transform — is often chosen. But wavelets are already competitive, and they are ahead for fingerprints. We present a sample of this developing theory. 1. The Haar wavelet To explain wavelets we start with an example. It has every property we hope for, except one. If that one defect is accepted, the construction is simple and the computations are fast. By trying to remove the defect, we are led to dilation equations and recursively defined functions and a small world of fascinating new problems — many still unsolved. A sensible person would stop after the first wavelet, but fortunately mathematics goes on. The basic example is easier to draw than to describe: W(x)
Fast Multiresolution Surface Meshing
, 1995
"... We are presenting a new method for adaptive surface meshing and triangulation which controls the local levelofdetail of the surface approximation by local spectral estimates. These estimates are figured out by a wavelet representation of the surface data. The basic idea is to decompose the initial ..."
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Cited by 70 (3 self)
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We are presenting a new method for adaptive surface meshing and triangulation which controls the local levelofdetail of the surface approximation by local spectral estimates. These estimates are figured out by a wavelet representation of the surface data. The basic idea is to decompose the initial data set by means of an orthogonal or semiorthogonal tensor product wavelet transform (WT) and to analyze the resulting coefficients. In surface regions, where the partial energy of the resulting coefficients is low, the polygonial approximation of the surface can be performed with larger triangles without loosing too much fine grain details. However, since the localization of the WT is bound by the Heisenberg principle the meshing method has to be controlled by the detail signals rather than directly by the coefficients. The dyadic scaling of the WT stimulated us to build an hierachical meshing algorithm which transforms the initially regular data grid into a quadtree representation by...
Islands of Music  Analysis, Organization, and Visualization of Music Archives
, 2001
"... This report summarizes the master's thesis Islands of Music: Analysis, Organization, and Visualization of Music Archives, which I submitted to the Vienna University of Technology on December 11th, 2001. I wrote it at the Department of Software Technology and Interactive Systems, supervised by Dr. An ..."
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Cited by 68 (15 self)
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This report summarizes the master's thesis Islands of Music: Analysis, Organization, and Visualization of Music Archives, which I submitted to the Vienna University of Technology on December 11th, 2001. I wrote it at the Department of Software Technology and Interactive Systems, supervised by Dr. Andreas Rauber, and assessed by Prof. Dr. Dieter Merkl