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Building Your Own Wavelets at Home
"... Wavelets have been making an appearance in many pure and applied areas of science and engineering. Computer graphics with its many and varied computational problems has been no exception to this rule. In these notes we will attempt to motivate and explain the basic ideas behind wavelets and what mak ..."
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Cited by 127 (13 self)
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Wavelets have been making an appearance in many pure and applied areas of science and engineering. Computer graphics with its many and varied computational problems has been no exception to this rule. In these notes we will attempt to motivate and explain the basic ideas behind wavelets and what makes them so successful in application areas. The main
Spherical Wavelets: Texture Processing
, 1995
"... 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 ..."
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Cited by 30 (4 self)
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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.
Compactly Supported Wavelets Which Are Biorthogonal with Respect to a Weighted Inner Product
 In Proceedings of the 14th IMACS World Congress
"... this paper we show how to construct wavelets adapted to a weighted inner product. We call such wavelets weighted wavelets . ..."
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Cited by 4 (0 self)
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this paper we show how to construct wavelets adapted to a weighted inner product. We call such wavelets weighted wavelets .
Multiresolution Techniques In Image Processing
, 1995
"... Multiresolution, an effective paradigm for signal processing, offers a natural, hierarchical view of information. As a computational tool, multiresolution can be applied to a variety of problems in signal and image processing. For instance, feature detection and extraction can be performed quickly a ..."
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Cited by 2 (0 self)
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Multiresolution, an effective paradigm for signal processing, offers a natural, hierarchical view of information. As a computational tool, multiresolution can be applied to a variety of problems in signal and image processing. For instance, feature detection and extraction can be performed quickly and efficiently using a multiresolutional method to analyze images. This dissertation addresses the problems of segmentation and edge detection in images with particular emphasis on satellite images which display features of a fine nature, such as the Atlantic Gulf Stream. The dissertation also describes a portable toolkit, for conventional and multiresolutional image processing, that was developed to test the various algorithms described in this research. The dissertation is motivated by the importance of the problems of segmentation and edge detection in the area of image processing, and the everpresent need for effective, efficient algorithms.
Locally SelfSimilar Processes and Their Wavelet Analysis
"... Introduction A stochastic process Y (t) is defined as selfsimilar with selfsimilarity parameter H if for any positive stretching factor c, the distribution of the rescaled and reindexed process c Y (c t) is equivalent to that of the original process Y (t). This means for any sequence of time p ..."
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Introduction A stochastic process Y (t) is defined as selfsimilar with selfsimilarity parameter H if for any positive stretching factor c, the distribution of the rescaled and reindexed process c Y (c t) is equivalent to that of the original process Y (t). This means for any sequence of time points t 1 ; : : : ; t n and any positive constant c, the collections fc Y (c t 1 ); : : : ; c Y (ct n )g and fY (t 1 ); : : : ; Y (t n )g are governed by the same probability law. As a consequence, the qualitative features of a sample path of a selfsimilar process are invariant to magnification or shrinkage, so that the path will retain the same general appearance regardless of the distance from which it is observed. Although selfsimilar processes were first introduced in a theoretical context by Kolmogorov (1941), statisticians were made aware of the practical applicability of such processes through the work of B.B. Mandelbrot (Mandelbrot and van Ness, 1968; Mandelbrot and Wallis,