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130
Independent Component Filters Of Natural Images Compared With Simple Cells In Primary Visual Cortex
, 1998
"... this article we investigate to what extent the statistical properties of natural images can be used to understand the variation of receptive field properties of simple cells in the mammalian primary visual cortex. The receptive fields of simple cells have been studied extensively (e.g., Hubel & Wies ..."
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Cited by 273 (0 self)
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this article we investigate to what extent the statistical properties of natural images can be used to understand the variation of receptive field properties of simple cells in the mammalian primary visual cortex. The receptive fields of simple cells have been studied extensively (e.g., Hubel & Wiesel 1968, DeValois et al. 1982a, DeAngelis et al. 1993): they are localised in space and time, have bandpass characteristics in the spatial and temporal frequency domains, are oriented, and are often sensitive to the direction of motion of a stimulus. Here we will concentrate on the spatial properties of simple cells. Several hypotheses as to the function of these cells have been proposed. As the cells preferentially respond to oriented edges or lines, they can be viewed as edge or line detectors. Their joint localisation in both the spatial domain and the spatial frequency domain has led to the suggestion that they mimic Gabor filters, minimising uncertainty in both domains (Daugman 1980, Marcelja 1980). More recently, the match between the operations performed by simple cells and the wavelet transform has attracted attention (e.g., Field 1993). The approaches based on Gabor filters and wavelets basically consider processing by the visual cortex as a general image processing strategy, relatively independent of detailed assumptions about image statistics. On the other hand, the edge and line detector hypothesis is based on the intuitive notion that edges and lines are both abundant and important in images. This theme of relating simple cell properties with the statistics of natural images was explored extensively by Field (1987, 1994). He proposed that the cells are optimized specifically for coding natural images. He argued that one possibility for such a code, sparse coding...
Local Feature Analysis: A general statistical theory for object representation
, 1996
"... . Lowdimensional representations of sensory signals are key to solving many of the computational problems encountered in highlevel vision. Principal Component Analysis has been used in the past to derive practically useful compact representations for different classes of objects. One major object ..."
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Cited by 229 (9 self)
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. Lowdimensional representations of sensory signals are key to solving many of the computational problems encountered in highlevel vision. Principal Component Analysis has been used in the past to derive practically useful compact representations for different classes of objects. One major objection to the applicability of PCA is that it invariably leads to global, nontopographic representations that are not amenable to further processing and are not biologically plausible. In this paper we present a new mathematical constructionLocal Feature Analysis (LFA)for deriving local topographic representations for any class of objects. The LFA representations are sparsedistributed and, hence, are effectively lowdimensional and retain all the advantages of the compact representations of the PCA. But unlike the global eigenmodes, they give a description of objects in terms of statistically derived local features and their positions. We illustrate the theory by using it to extract loca...
Image compression via joint statistical characterization in the wavelet domain
, 1997
"... We develop a statistical characterization of natural images in the wavelet transform domain. This characterization describes the joint statistics between pairs of subband coefficients at adjacent spatial locations, orientations, and scales. We observe that the raw coefficients are nearly decorrelate ..."
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Cited by 194 (29 self)
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We develop a statistical characterization of natural images in the wavelet transform domain. This characterization describes the joint statistics between pairs of subband coefficients at adjacent spatial locations, orientations, and scales. We observe that the raw coefficients are nearly decorrelated, but their magnitudes are highly correlated. A linear magnitude predictor coupled with both multiplicative and additive uncertainties accounts for the joint coefficient statistics of a wide variety of images including photographic images, graphical images, and medical images. In order to directly demonstrate the power of this model, we construct an image coder called EPWIC (Embedded Predictive Wavelet Image Coder), in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes probabilities calculated from the model. Bitplanes are ordered using a greedy algorithm that considers the MSE reduction per encoded bit. The decoder uses the statistical model to predict coefficient values based on the bits it has received. The ratedistortion performance of the coder compares favorably with the current best image coders in the literature. 1
Non Linear Neurons in the Low Noise Limit: A Factorial Code Maximizes Information Transfer
, 1994
"... We investigate the consequences of maximizing information transfer in a simple neural network (one input layer, one output layer), focussing on the case of non linear transfer functions. We assume that both receptive fields (synaptic efficacies) and transfer functions can be adapted to the environm ..."
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Cited by 141 (18 self)
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We investigate the consequences of maximizing information transfer in a simple neural network (one input layer, one output layer), focussing on the case of non linear transfer functions. We assume that both receptive fields (synaptic efficacies) and transfer functions can be adapted to the environment. The main result is that, for bounded and invertible transfer functions, in the case of a vanishing additive output noise, and no input noise, maximization of information (Linsker'sinfomax principle) leads to a factorial code  hence to the same solution as required by the redundancy reduction principle of Barlow. We show also that this result is valid for linear, more generally unbounded, transfer functions, provided optimization is performed under an additive constraint, that is which can be written as a sum of terms, each one being specific to one output neuron. Finally we study the effect of a non zero input noise. We find that, at first order in the input noise, assumed to be small ...
Statistical Models for Images: Compression, Restoration and Synthesis
 In 31st Asilomar Conf on Signals, Systems and Computers
, 1997
"... this paper, we examine the problem of decomposing digitized images, through linear and/or nonlinear transformations, into statistically independent components. The classical approach to such a problem is Principal Components Analysis (PCA), also known as the KarhunenLoeve (KL) or Hotelling transfor ..."
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Cited by 138 (33 self)
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this paper, we examine the problem of decomposing digitized images, through linear and/or nonlinear transformations, into statistically independent components. The classical approach to such a problem is Principal Components Analysis (PCA), also known as the KarhunenLoeve (KL) or Hotelling transform. This is a linear transform that removes secondorder dependencies between input pixels. The most wellknown description of image statistics is that their power spectra take the form of a power law [e.g., 20, 11, 24]. Coupled with a constraint of translationinvariance, this suggests that the Fourier transform is an appropriate PCA representation. Fourier and related representations are widely used in image processing applications.
Natural Signal Statistics and Sensory Gain Control
 Nature Neuroscience
, 2001
"... The statistical properties of natural images suggest an optimal form of nonlinear decomposition, in which the image is decomposed using a set of linear filters at a variety of positions, scales and orientations, and these linear responses are then rectified and divided by a weighted sum of rectified ..."
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Cited by 130 (24 self)
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The statistical properties of natural images suggest an optimal form of nonlinear decomposition, in which the image is decomposed using a set of linear filters at a variety of positions, scales and orientations, and these linear responses are then rectified and divided by a weighted sum of rectified responses of nearby filters. Such divisive normalization models have become widely used in modeling steadystate responses of neurons in primary visual cortex. In addition to providing a surprisingly good characterization of "typical" neurons, the statistically optimal version of the model is consistent with unusual changes in tuning properties of these neurons at different contrast levels. These results suggest that the nonlinear response properties of cortical neurons are not an accident of biophysical implementation, but serve an important functional role.
Scale Mixtures of Gaussians and the Statistics of Natural Images
 in Adv. Neural Information Processing Systems
, 2000
"... The statistics of photographic images, when represented using multiscale (wavelet) bases, exhibit two striking types of nonGaussian behavior. First, the marginal densities of the coefficients have extended heavy tails. Second, the joint densities exhibit variance dependencies not captured by secon ..."
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Cited by 118 (19 self)
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The statistics of photographic images, when represented using multiscale (wavelet) bases, exhibit two striking types of nonGaussian behavior. First, the marginal densities of the coefficients have extended heavy tails. Second, the joint densities exhibit variance dependencies not captured by secondorder models. We examine properties of the class of Gaussian scale mixtures, and show that these densities can accurately characterize both the marginal and joint distributions of natural image wavelet coefficients. This class of model suggests a Markov structure, in which wavelet coefficients are linked by hidden scaling variables corresponding to local image structure. We derive an estimator for these hidden variables, and show that a nonlinear ``normalization'' procedure can be used to Gaussianize the coefficients.
Modeling the Joint Statistics of Images in the Wavelet Domain
 IN PROC SPIE, 44TH ANNUAL MEETING
, 1999
"... I describe a statistical model for natural photographic images, when decomposed in a multiscale wavelet basis. In particular, I examine both the marginal and pairwise joint histograms of wavelet coefficients at adjacent spatial locations, orientations, and spatial scales. Although the histograms ar ..."
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Cited by 98 (3 self)
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I describe a statistical model for natural photographic images, when decomposed in a multiscale wavelet basis. In particular, I examine both the marginal and pairwise joint histograms of wavelet coefficients at adjacent spatial locations, orientations, and spatial scales. Although the histograms are highly nonGaussian, they are nevertheless well described using fairly simple parameterized density models.
Statistics of Cone Responses to Natural Images: Implications for Visual Coding
 Journal of the Optical Society of America A
, 1998
"... ted in the first stage of retinal processing, the photoreceptor layer. In this work we measure the spectral distributions of light present in natural images by using a hyperspectral camera, 1215 which provides a complete spectrum at each pixel. We derive human cone responses at each spatial loc ..."
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Cited by 97 (2 self)
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ted in the first stage of retinal processing, the photoreceptor layer. In this work we measure the spectral distributions of light present in natural images by using a hyperspectral camera, 1215 which provides a complete spectrum at each pixel. We derive human cone responses at each spatial location from the spectra, and from these we gather cone response statistics for analysis. This approach is related to that of Webster and Mollon, with the key difference that whereas they contrast the differences between various images, we study the ensemble statistics as averaged over images. Our results are qualitatively similar to those of Buchsbaum and Gottschalk, who sought to understand theoretically, by using model stimuli, how the visual system might decorrelate natural cone signals through an orthogonal linear transformation. They found that under certain conditions this can be achieved through a transformation to a luminancelike channel and a pair of blue yellow and redgre
Bayesian Denoising of Visual Images in the Wavelet Domain
 LECTURE NOTES IN STATISTICS
, 1999
"... ..."