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664
The Contourlet Transform: An Efficient Directional Multiresolution Image Representation
 IEEE TRANSACTIONS ON IMAGE PROCESSING
"... The limitations of commonly used separable extensions of onedimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a “true” twodimensional transform that can capture the intrinsic geometrical structure t ..."
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Cited by 513 (20 self)
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link between the developed filter bank and the associated continuousdomain contourlet expansion via a directional multiresolution analysis framework. We show that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth
Optimal paths for a car that goes both forwards and backwards
 PACIFIC JOURNAL OF MATHEMATICS
, 1990
"... The path taken by a car with a given minimum turning radius has a lower bound on its radius of curvature at each point, but the path has cusps if the car shifts into or out of reverse gear. What is the shortest such path a car can travel between two points if its starting and ending directions are s ..."
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Cited by 279 (0 self)
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are specified? One need consider only paths with at most 2 cusps or reversals. We give a set of paths which is sufficient in the sense that it always contains a shortest path and small in the sense that there are at most 68, but usually many fewer paths in the set for any pair of endpoints and directions. We
On Twochannel Filter Banks with Directional Vanishing Moments
, 2005
"... The contourlet transform was proposed to address the limited directional resolution of the separable wavelet transform. In order to guarantee good nonlinear approximation behavior, the directional filters in the contourlet filter bank require sharp frequency response which incurs a large support siz ..."
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Cited by 10 (5 self)
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size. We seek to isolate the key filter property that ensures good approximation. In this direction, we propose filters with directional vanishing moments (DVM). These filters, we show, annihilate information along a given direction. We study twochannel filter banks with DVM filters. We provide
Biorthogonal filter banks with directional vanishing moments
 in Proceedings of the IEEE ICASSP
, 2005
"... In this paper we study 2D nonseparable filter banks that annihilate information along a certain discrete direction. This is done by having filters with directional vanishing moments (DVM). We study the approximation property of such filters and the design problem providing conditions for its solvab ..."
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Cited by 5 (3 self)
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In this paper we study 2D nonseparable filter banks that annihilate information along a certain discrete direction. This is done by having filters with directional vanishing moments (DVM). We study the approximation property of such filters and the design problem providing conditions for its
Directional Filter Banks with Directional Vanishing Moments: A Brief Review
"... Contourlet transform is an efficient directional multiscale decomposition of images that combines the Laplacian pyramid (LP) with directional filter banks (DFBs). The LP decomposes the input image into multiple scales, whereas the DFBs applied on bandpass images of the pyramid yields directional loc ..."
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localization. Similar to wavelets in 1D, the key feature of contourlets is that they can quickly “feel ” the edges of images. This is attributed to their ability to annihilate directional smoothness. One way to achieve this annihilating property is to impose the socalled directional vanishing moments (DVMs
Contourlets and Sparse Image Expansions
"... Recently, the contourlet transform 1 has been developed as a true twodimensional representation that can capture the geometrical structure in pictorial information. Unlike other transforms that were initially constructed in the continuousdomain and then discretized for sampled data, the contourlet ..."
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Cited by 4 (0 self)
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natural images. Inspired by the vanishing moment property which is the key for the good approximation behavior of wavelets, we introduce the directional vanishing moment condition for contourlets. We show that with anisotropic scaling and sufficient directional vanishing moments, contourlets essentially
Twodimensional orthogonal filter banks with directional vanishing moments
 IEEE Trans. Signal Proc
"... We present twodimensional filter banks with directional vanishing moments. The directionalvanishingmoment condition is crucial for the regularity of directional filter banks. However, it is a challenging task to design orthogonal filter banks with directional vanishing moments. Due to the lack of ..."
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Cited by 1 (1 self)
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We present twodimensional filter banks with directional vanishing moments. The directionalvanishingmoment condition is crucial for the regularity of directional filter banks. However, it is a challenging task to design orthogonal filter banks with directional vanishing moments. Due to the lack
The effect of solar radiation variations on the climate of the Earth
 Tellus
, 1969
"... It follows from the analysis of observation data that the secular variation of the mean temperature of the Earth can be explained by the variation of shortwave radiation, arriving at the surface of the Earth. In connection with this, the influence of longterm changes of radiation, caused by variat ..."
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Cited by 171 (0 self)
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by variations of atmospheric transparency on the thermal regime is being studied. Taking into account the influence of changes of planetary albedo of the Earth under the development of glaciations on the thermal regime, it is found that comparatively small variations of atmospheric transparency could be sufficient
Threefolds with vanishing Hodge cohomology
 Trans. Amer. Math. Soc. 357, Number
"... Abstract) = 0 for all j ≥ 0 and i> 0. Let X be a smooth completion of Y with D = X − Y, an effective divisor on X with normal crossings. If the Ddimension of X is not zero, then Y is a fibre space over a smooth affine curve C (i.e., we have a surjective morphism from Y to C such that general fi ..."
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Cited by 7 (6 self)
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fibre is smooth and irreducible) such that every fibre satisfies the same vanishing condition. If an irreducible smooth fibre is not affine, then the Kodaira dimension of X is − ∞ and the Ddimension of X is 1. We also discuss sufficient conditions from the behavior of fibres or higher direct images
Results 1  10
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664