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Emergence of Phase and ShiftInvariant Features by Decomposition of Natural Images into Independent Feature Subspaces
, 2000
"... this article, we show that the same principle of independence maximization can explain the emergence of phase and shiftinvariant features, similar to those found in complex cells. This new kind of emergence is obtained by maximizing the independence between norms of projections on linear subspaces ..."
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Cited by 201 (31 self)
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this article, we show that the same principle of independence maximization can explain the emergence of phase and shiftinvariant features, similar to those found in complex cells. This new kind of emergence is obtained by maximizing the independence between norms of projections on linear subspaces (instead of the independence of simple linear filter outputs). Thenorms of the projections on such "independent feature subspaces" then indicate the values of invariant features
HighDimensional Data Analysis: The Curses and Blessings of Dimensionality
, 2000
"... The coming century is surely the century of data. A combination of blind faith and serious purpose makes our society invest massively in the collection and processing of data of all kinds, on scales unimaginable until recently. Hyperspectral Imagery, Internet Portals, Financial tickbytick data, an ..."
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Cited by 169 (0 self)
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The coming century is surely the century of data. A combination of blind faith and serious purpose makes our society invest massively in the collection and processing of data of all kinds, on scales unimaginable until recently. Hyperspectral Imagery, Internet Portals, Financial tickbytick data, and DNA Microarrays are just a few of the betterknown sources, feeding data in torrential streams into scientific and business databases worldwide. In traditional statistical data analysis, we think of observations of instances of particular phenomena (e.g. instance ↔ human being), these observations being a vector of values we measured on several variables (e.g. blood pressure, weight, height,...). In traditional statistical methodology, we assumed many observations and a few, wellchosen variables. The trend today is towards more observations but even more so, to radically larger numbers of variables – voracious, automatic, systematic collection of hyperinformative detail about each observed instance. We are seeing examples where the observations gathered on individual instances are curves, or spectra, or images, or
Probabilistic framework for the adaptation and comparison of image codes
 J. OPT. SOC. AM. A
, 1999
"... We apply a Bayesian method for inferring an optimal basis to the problem of finding efficient image codes for natural scenes. The basis functions learned by the algorithm are oriented and localized in both space and frequency, bearing a resemblance to twodimensional Gabor functions, and increasing ..."
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Cited by 140 (10 self)
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We apply a Bayesian method for inferring an optimal basis to the problem of finding efficient image codes for natural scenes. The basis functions learned by the algorithm are oriented and localized in both space and frequency, bearing a resemblance to twodimensional Gabor functions, and increasing the number of basis functions results in a greater sampling density in position, orientation, and scale. These properties also resemble the spatial receptive fields of neurons in the primary visual cortex of mammals, suggesting that the receptivefield structure of these neurons can be accounted for by a general efficient coding principle. The probabilistic framework provides a method for comparing the coding efficiency of different bases objectively by calculating their probability given the observed data or by measuring the entropy of the basis function coefficients. The learned bases are shown to have better coding efficiency than traditional Fourier and wavelet bases. This framework also provides a Bayesian solution to the problems of image denoising and filling in of missing pixels. We demonstrate that the results obtained by applying the learned bases to these problems are improved over those obtained with traditional techniques.
Efficient coding of natural sounds
 Nature Neuroscience
, 2002
"... The auditory system encodes sound by decomposing the amplitude signal arriving at the ear into multiple frequency bands whose center frequencies and bandwidths are approximately logarithmic functions of the distance from the stapes. This particular organization is thought to result from the adaptati ..."
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Cited by 136 (3 self)
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The auditory system encodes sound by decomposing the amplitude signal arriving at the ear into multiple frequency bands whose center frequencies and bandwidths are approximately logarithmic functions of the distance from the stapes. This particular organization is thought to result from the adaptation of cochlear mechanisms to the statistics of an animal’s auditory environment. Here we report that several basic auditory nerve fiber tuning properties can be accounted for by adapting a population of filter shapes to optimally encode natural sounds. The form of the code is dependent on the class of sounds, resembling a Fourier transformation when optimized for animal vocalizations and a wavelet transformation when optimized for nonbiological environmental sounds. Only for a combined set of vocalizations and environmental sounds does the optimal code follow scaling characteristics that are consistent with physiological data. These results suggest that the population of auditory nerve fibers encode a broad set of natural sounds in a manner that is consistent with information theoretic principles. Correspondence:
A TwoLayer Sparse Coding Model Learns Simple and Complex Cell Receptive Fields and Topography From Natural Images
 VISION RESEARCH
, 2001
"... The classical receptive fields of simple cells in the visual cortex have been shown to emerge from the statistical properties of natural images by forcing the cell responses to be maximally sparse, i.e. significantly activated only rarely. Here, we show that this single principle of sparseness can ..."
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Cited by 110 (16 self)
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The classical receptive fields of simple cells in the visual cortex have been shown to emerge from the statistical properties of natural images by forcing the cell responses to be maximally sparse, i.e. significantly activated only rarely. Here, we show that this single principle of sparseness can also lead to emergence of topography (columnar organization) and complex cell properties as well. These are obtained by maximizing the sparsenesses of locally pooled energies, which correspond to complex cell outputs. Thus we obtain a highly parsimonious model of how these properties of the visual cortex are adapted to the characteristics of the natural input.
On the Spatial Statistics of Optical Flow
 In ICCV
, 2005
"... We develop a method for learning the spatial statistics of optical flow fields from a novel training database. Training flow fields are constructed using range images of natural scenes and 3D camera motions recovered from handheld and carmounted video sequences. A detailed analysis of optical flow ..."
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Cited by 102 (8 self)
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We develop a method for learning the spatial statistics of optical flow fields from a novel training database. Training flow fields are constructed using range images of natural scenes and 3D camera motions recovered from handheld and carmounted video sequences. A detailed analysis of optical flow statistics in natural scenes is presented and machine learning methods are developed to learn a Markov random field model of optical flow. The prior probability of a flow field is formulated as a FieldofExperts model that captures the higher order spatial statistics in overlapping patches and is trained using contrastive divergence. This new optical flow prior is compared with previous robust priors and is incorporated into a recent, accurate algorithm for dense optical flow computation. Experiments with natural and synthetic sequences illustrate how the learned optical flow prior quantitatively improves flow accuracy and how it captures the rich spatial structure found in natural scene motion.
Independent component analysis applied to feature extraction from colour and stereo images
 Network Computation in Neural Systems
, 2000
"... Previous work has shown that independent component analysis (ICA) applied to feature extraction from natural image data yields features resembling Gabor functions and simplecell receptive fields. This article considers the effects of including chromatic and stereo information. The inclusion of colo ..."
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Cited by 77 (5 self)
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Previous work has shown that independent component analysis (ICA) applied to feature extraction from natural image data yields features resembling Gabor functions and simplecell receptive fields. This article considers the effects of including chromatic and stereo information. The inclusion of colour leads to features divided into separate red/green, blue/yellow, and bright/dark channels. Stereo image data, on the other hand, leads to binocular receptive fields which are tuned to various disparities. The similarities between these results and observed properties of simple cells in primary visual cortex are further evidence for the hypothesis that visual cortical neurons perform some type of redundancy reduction, which was one of the original motivations for ICA in the first place. In addition, ICA provides a principled method for feature extraction from colour and stereo images; such features could be used in image processing operations such as denoising and compression, as well as in pattern recognition.
Imaging brain dynamics using independent component analysis
 Proceedings of the IEEE
"... The analysis of electroencephalographic (EEG) and magnetoencephalographic (MEG) recordings is important both for basic brain research and for medical diagnosis and treatment. Independent component analysis (ICA) is an effective method for removing artifacts and separating sources of the brain signal ..."
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Cited by 77 (25 self)
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The analysis of electroencephalographic (EEG) and magnetoencephalographic (MEG) recordings is important both for basic brain research and for medical diagnosis and treatment. Independent component analysis (ICA) is an effective method for removing artifacts and separating sources of the brain signals from these recordings. A similar approach is proving useful for analyzing functional magnetic resonance brain imaging (fMRI) data. In this paper, we outline the assumptions underlying ICA and demonstrate its application to a variety of electrical and hemodynamic recordings from the human brain. Keywords—Blind source separation, EEG, fMRI, independent component analysis.
Learning to Represent Spatial Transformations with Factored HigherOrder Boltzmann Machines
, 2010
"... To allow the hidden units of a restricted Boltzmann machine to model the transformation between two successive images, Memisevic and Hinton (2007) introduced threeway multiplicative interactions that use the intensity of a pixel in the first image as a multiplicative gain on a learned, symmetric we ..."
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Cited by 75 (18 self)
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To allow the hidden units of a restricted Boltzmann machine to model the transformation between two successive images, Memisevic and Hinton (2007) introduced threeway multiplicative interactions that use the intensity of a pixel in the first image as a multiplicative gain on a learned, symmetric weight between a pixel in the second image and a hidden unit. This creates cubically many parameters, which form a threedimensional interaction tensor. We describe a lowrank approximation to this interaction tensor that uses a sum of factors, each of which is a threeway outer product. This approximation allows efficient learning of transformations between larger image patches. Since each factor can be viewed as an image filter, the model as a whole learns optimal filter pairs for efficiently representing transformations. We demonstrate the learning of optimal filter pairs from various synthetic and real image sequences. We also show how learning about image transformations allows the model to perform a simple visual analogy task, and we show how a completely unsupervised network trained on transformations perceives multiple motions of transparent dot patterns in the same way as humans.
Sparse components of images and optimal atomic decomposition
 Constr. Approx
"... Recently, Field, Lewicki, Olshausen, and Sejnowski have reported efforts to identify the “Sparse Components ” of image data. Their empirical findings indicate that such components have elongated shapes and assume a wide range of positions, orientations, and scales. To date, Sparse Components Analysi ..."
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Cited by 73 (4 self)
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Recently, Field, Lewicki, Olshausen, and Sejnowski have reported efforts to identify the “Sparse Components ” of image data. Their empirical findings indicate that such components have elongated shapes and assume a wide range of positions, orientations, and scales. To date, Sparse Components Analysis (SCA) has only been conducted on databases of small (e.g. 16by16) image patches and there seems limited prospect of dramatically increased resolving power. In this article, we apply mathematical analysis to a specific formalization of SCA using synthetic image models, hoping to gain insight into what might emerge from a higherresolution SCA based on n by n image patches for large n but constant field of view. In our formalization, we study a class of objects F in a functional space; they are to be represented by linear combinations of atoms from an overcomplete dictionary, and sparsity is measured by the ℓ p norm of the coefficients in the linear combination. We focus on the class F = Star α of blackandwhite images with the black region consisting of a starshaped set with αsmooth boundary. We aim to find an optimal dictionary, one achieving the optimal