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36
A theory for multiresolution signal decomposition : the wavelet representation
 IEEE Transaction on Pattern Analysis and Machine Intelligence
, 1989
"... AbstractMultiresolution representations are very effective for analyzing the information content of images. We study the properties of the operator which approximates a signal at a given resolution. We show that the difference of information between the approximation of a signal at the resolutions ..."
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Cited by 2354 (12 self)
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AbstractMultiresolution representations are very effective for analyzing the information content of images. We study the properties of the operator which approximates a signal at a given resolution. We show that the difference of information between the approximation of a signal at the resolutions 2 ’ + ’ and 2jcan be extracted by decomposing this signal on a wavelet orthonormal basis of L*(R”). In LL(R), a wavelet orthonormal basis is a family of functions ( @ w (2’ ~n)),,,“jEZt, which is built by dilating and translating a unique function t+r (xl. This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror lilters. For images, the wavelet representation differentiates several spatial orientations. We study the application of this representation to data compression in image coding, texture discrimination and fractal analysis. Index TermsCoding, fractals, multiresolution pyramids, quadrature mirror filters, texture discrimination, wavelet transform. I I.
Prior Learning and Gibbs ReactionDiffusion
, 1997
"... This article addresses two important themes in early visual computation: rst it presents a novel theory for learning the universal statistics of natural images { a prior model for typical cluttered scenes of the world { from a set of natural images, second it proposes a general framework of designi ..."
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Cited by 148 (18 self)
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This article addresses two important themes in early visual computation: rst it presents a novel theory for learning the universal statistics of natural images { a prior model for typical cluttered scenes of the world { from a set of natural images, second it proposes a general framework of designing reactiondiusion equations for image processing. We start by studying the statistics of natural images including the scale invariant properties, then generic prior models were learned to duplicate the observed statistics, based on the minimax entropy theory studied in two previous papers. The resulting Gibbs distributions have potentials of the form U(I; ; S) = P K I)(x; y)) with S = fF g being a set of lters and = f the potential functions. The learned Gibbs distributions con rm and improve the form of existing prior models such as lineprocess, but in contrast to all previous models, inverted potentials (i.e. (x) decreasing as a function of jxj) were found to be necessary. We nd that the partial dierential equations given by gradient descent on U(I; ; S) are essentially reactiondiusion equations, where the usual energy terms produce anisotropic diusion while the inverted energy terms produce reaction associated with pattern formation, enhancing preferred image features. We illustrate how these models can be used for texture pattern rendering, denoising, image enhancement and clutter removal by careful choice of both prior and data models of this type, incorporating the appropriate features. Song Chun Zhu is now with the Computer Science Department, Stanford University, Stanford, CA 94305, and David Mumford is with the Division of Applied Mathematics, Brown University, Providence, RI 02912. This work started when the authors were at ...
A Model of Visual Masking for Computer Graphics
, 1997
"... In this paper we develop a computational model of visual masking based on psychophysical data. The model predicts how the presence of one visual pattern affects the detectability of another. The model allows us to choose texture patterns for computer graphics images that hide the effects of faceting ..."
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Cited by 97 (6 self)
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In this paper we develop a computational model of visual masking based on psychophysical data. The model predicts how the presence of one visual pattern affects the detectability of another. The model allows us to choose texture patterns for computer graphics images that hide the effects of faceting, banding, aliasing, noise and other visual artifacts produced by sources of error in graphics algorithms. We demonstrate the utility of the model by choosing a texture pattern to mask faceting artifacts caused by polygonal tesselation of a flatshaded curved surface. The model predicts how changes in the contrast, spatial frequency, and orientation of the texture pattern, or changes in the tesselation of the surface will alter the masking effect. The model is general and has uses in geometric modeling, realistic image synthesis, scientific visualization, image compression, and imagebased rendering.
Perceptual Image Quality Based On A Multiple Channel HVS Model
 Proceedings of ICASSP
, 1995
"... We propose a new measure of perceptual image quality based on a multiple channel human visual system (HVS) model for use in digital image compression. The model incorporates the HVS light sensitivity, spatial frequency and orientation sensitivity, and masking effects. The model is based on the conce ..."
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Cited by 40 (8 self)
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We propose a new measure of perceptual image quality based on a multiple channel human visual system (HVS) model for use in digital image compression. The model incorporates the HVS light sensitivity, spatial frequency and orientation sensitivity, and masking effects. The model is based on the concept of local bandlimited contrast (LBC) in oriented spatial frequency bands. This concept leads to a simple masking function. The model has the flexibility to account for the changes in frequency sensitivity as a function of local luminance and is consistent with masking experiments using gratings and edges. Numerical scaling experiments with a test panel and a set a test images that were coded using different coding algorithms showed that the proposed measure correlates better with perceptual image quality than the conventional SNR measure. 1. INTRODUCTION In optimization and evaluation of digital image compression algorithms, the signal to noise ratio (SNR) is generally used as a measure...
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 35 (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
Geodesic Active Contours for Supervised Texture Segmentation
, 1999
"... This paper presents a variational method for supervised texture segmentation, which is based on ideas coming from the curve propagation theory. We assume that a preferable texture pattern is known (e.g. the pattern that we want to distinguish from the rest of the image). The textured feature space i ..."
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Cited by 29 (3 self)
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This paper presents a variational method for supervised texture segmentation, which is based on ideas coming from the curve propagation theory. We assume that a preferable texture pattern is known (e.g. the pattern that we want to distinguish from the rest of the image). The textured feature space is generated by filtering the input and the preferable pattern image using Gabor filters, and analyzing their responses as multicomponent conditional probability density functions. The texture segmentation is obtained by minimizing a Geodesic Active Contour Model objective function where the boundarybased information is expressed via discontinuities on the statistical space associated with the multimodal textured feature space. This function is minimized using a gradient descent method where the obtained PDE is implemented using a level set approach, that handles naturally the topological changes. Finally, a fast method is used for the level set implementation. The performance of our method is demonstrated on a variety of synthetic and real textured images. 1
A Parametric Texture Model Based on Joint . . .
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2000
"... We present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform. The model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. We de ..."
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Cited by 26 (0 self)
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We present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform. The model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. We develop an efficient algorithm for synthesizing random images subject to these constraints, by iteratively projecting onto the set of images satisfying each constraint, and we use this to test the perceptual validity of the model. In particular, we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set. We also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures.
Texture Modeling and Synthesis using Joint Statistics of Complex Wavelet Coefficients
 IN IEEE WORKSHOP ON STATISTICAL AND COMPUTATIONAL THEORIES OF VISION, FORT COLLINS
, 1999
"... We present a statistical characterization of texture images in the context of an overcomplete complex wavelet transform. The characterization is based on empirical observations of statistical regularities in such images, and parameterized by (1) the local autocorrelation of the coefficients in each ..."
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Cited by 22 (2 self)
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We present a statistical characterization of texture images in the context of an overcomplete complex wavelet transform. The characterization is based on empirical observations of statistical regularities in such images, and parameterized by (1) the local autocorrelation of the coefficients in each subband; (2) both the local autocorrelation and crosscorrelation of coefficient magnitudes at other orientations and spatial scales; and (3) the first few moments of the image pixel histogram. We develop an efficient algorithm for synthesizing random images subject to these constraints using alternated projections, and demonstrate its effectiveness on a wide range of synthetic and natural textures. In particular, we show that many important structural elements in textures (e.g., edges, repeated patterns or alternated patches of simpler texture), can be captured through joint second order statistics of the coefficient magnitudes. We also show the flexibility of the representation, by applying to a variety...
Adaptive Perceptual Pattern Recognition by SelfOrganizing Neural Networks: Context, Uncertainty, Multiplicity, and Scale
 NEURAL NETWORKS
, 1995
"... A new contextsensitive neural network, called an "EXIN" (excitatory+inhibitory) network, is described. EXIN networks selforganize in complex perceptual environments, in the presence of multiple superimposed patterns, multiple scales, and uncertainty. The networks use a new inhibitory learning rule ..."
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Cited by 19 (9 self)
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A new contextsensitive neural network, called an "EXIN" (excitatory+inhibitory) network, is described. EXIN networks selforganize in complex perceptual environments, in the presence of multiple superimposed patterns, multiple scales, and uncertainty. The networks use a new inhibitory learning rule, in addition to an excitatory learning rule, to allow superposition of multiple simultaneous neural activations (multiple winners), under strictly regulated circumstances, instead of forcing winnertakeall pattern classifications. The multiple activations represent uncertainty or multiplicity in perception and pattern recognition. Perceptual scission (breaking of linkages) between independent category groupings thus arises and allows effective global contextsensitive segmentation constraint satisfaction, and exclusive credit attribution. A Weber Law neurongrowth rule lets the network learn and classify input patterns despite variations in their spatial scale. Applications of the new techn...