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44
Shiftable Multiscale Transforms
, 1992
"... Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavel ..."
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Cited by 531 (41 self)
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Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavelet transforms are also unstable with respect to dilations of the input signal, and in two dimensions, rotations of the input signal. We formalize these problems by defining a type of translation invariance that we call "shiftability". In the spatial domain, shiftability corresponds to a lack of aliasing; thus, the conditions under which the property holds are specified by the sampling theorem. Shiftability may also be considered in the context of other domains, particularly orientation and scale. We explore "jointly shiftable" transforms that are simultaneously shiftable in more than one domain. Two examples of jointly shiftable transforms are designed and implemented: a onedimensional tran...
The steerable pyramid: A flexible architecture for multiscale derivative computation
 in IEEE International Conference on Image Processing
, 1995
"... ..."
Perceptual image distortion
 In Proceedings of SPIE
, 1994
"... In this paper, we present a perceptual distortion measure that predicts image integrity far better than meansquared error. This perceptual distortion measure is based on a model of human visual processing that ts empirical measurements of the psychophysics of spatial pattern detection. The model of ..."
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Cited by 167 (0 self)
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In this paper, we present a perceptual distortion measure that predicts image integrity far better than meansquared error. This perceptual distortion measure is based on a model of human visual processing that ts empirical measurements of the psychophysics of spatial pattern detection. The model of human visual processing proposed involves two major components: a steerable pyramid transform and contrast normalization. We also illustrate the usefulness of the model in predicting perceptual distortion in real images. 1.
Mammographic Feature Enhancement by Multiscale Analysis
 IEEE Transactions on Medical Imaging
, 1994
"... This paper introduces a novel approach for accomplishing mammographic feature analysis by overcomplete multiresolution representations. We show that efficient representations may be identified within a continuum of scalespace and used to enhance features of importance to mammography. Methods of con ..."
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Cited by 82 (16 self)
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This paper introduces a novel approach for accomplishing mammographic feature analysis by overcomplete multiresolution representations. We show that efficient representations may be identified within a continuum of scalespace and used to enhance features of importance to mammography. Methods of contrast enhancement are described based on three overcomplete multiscale representations: (1) The dyadic wavelet transform (separable), (2) The ' transform (nonseparable, nonorthogonal), and (3) The hexagonal wavelet transform (nonseparable). Multiscale edges identified within distinct levels of transform space provide local support for image enhancement. Mammograms are reconstructed from wavelet coefficients modified at one or more levels by local and global nonlinear operators. In each case, edges and gain parameters are identified adaptively by a measure of energy within each level of scalespace. We show quantitatively that transform coefficients, modified by adaptive nonlinear oper...
Brushlets: A Tool for Directional Image Analysis and Image Compression
, 1997
"... This paper is organized as follows. In the next section we review the construction of orthonormal windowed Fourier bases. This is followed in section III by a description of biorthogonal windowed Fourier bases. The new brushlet basis is given in section IV. A biorthogonal brushlet basis is presented ..."
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Cited by 81 (11 self)
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This paper is organized as follows. In the next section we review the construction of orthonormal windowed Fourier bases. This is followed in section III by a description of biorthogonal windowed Fourier bases. The new brushlet basis is given in section IV. A biorthogonal brushlet basis is presented in section V. In section VI we describe the image compression algorithm based on a brushlet expansion of the image. Results of experiments are presented in Section VII
Subband Transforms
, 1990
"... this paper, the boxes H i #!# indicate circular convolution of a #nite input image of size N with a #lter with impulse response h i #n# and Fourier transform ..."
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Cited by 34 (8 self)
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this paper, the boxes H i #!# indicate circular convolution of a #nite input image of size N with a #lter with impulse response h i #n# and Fourier transform
Can recent innovations in harmonic analysis `explain' key findings in natural image statistics
 Network: Computation in Neural Systems
"... Recently, applied mathematicians have been pursuing the goal of sparse coding of certain mathematical models of images with edges. They have found by mathematical analysis that, instead of wavelets and Fourier methods, sparse coding leads towards new systems: ridgelets and curvelets. These new syste ..."
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Cited by 30 (1 self)
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Recently, applied mathematicians have been pursuing the goal of sparse coding of certain mathematical models of images with edges. They have found by mathematical analysis that, instead of wavelets and Fourier methods, sparse coding leads towards new systems: ridgelets and curvelets. These new systems have elements distributed across a range of scales and locations, but also orientations. In fact they have highly directionspecific elements and exhibit increasing numbers of distinct directions as we go to successively finer scales. Meanwhile, researchers in Natural Scene Statistics (NSS) have been attempting to find sparse codes for natural images. The new systems they have found by computational optimization have elements distributed across a range of scales and locations, but also orientations. The new systems are certainly unlike wavelet and gabor systems, on the one hand because of the multiorientation and on the other hand because of the multiscale nature. There is a certain degree of visual resemblance between the findings in the two fields, which suggests the hypothesis that certain important findings in the NSS literature
Construction of Bivariate Compactly Supported Biorthogonal Box Spline Wavelets with Arbitrarily High Regularities
 APPL. COMPUT. HARMON. ANAL
"... We give a simple formula for the duals of the filters associated with bivariate box spline functions. We show how to construct bivariate nonseparable compactly supported biorthogonal wavelets associated with box spline functions which have arbitrarily high regularities. ..."
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Cited by 22 (7 self)
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We give a simple formula for the duals of the filters associated with bivariate box spline functions. We show how to construct bivariate nonseparable compactly supported biorthogonal wavelets associated with box spline functions which have arbitrarily high regularities.
The RedBlack Wavelet Transform
, 1997
"... We present a new kind of second generation wavelets on a rectangular grid. These wavelets are constructed using a 2D lifting scheme which is based on a redblack blocking scheme. Compared to classical tensor product wavelets on the same grid, these new wavelets show less anisotropy. The performance ..."
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Cited by 14 (3 self)
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We present a new kind of second generation wavelets on a rectangular grid. These wavelets are constructed using a 2D lifting scheme which is based on a redblack blocking scheme. Compared to classical tensor product wavelets on the same grid, these new wavelets show less anisotropy. The performance of the new wavelets is compared to tensor product wavelets in an image denoising application.