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312
Components of bottomup gaze allocation in natural images
, 2005
"... ... showed that a model of bottomup visual attention can account in part for the spatial locations fixated by humans while freeviewing complex natural and artificial scenes. That study used a definition of salience based on local detectors with coarse global surround inhibition. Here, we use a sim ..."
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Cited by 64 (13 self)
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... showed that a model of bottomup visual attention can account in part for the spatial locations fixated by humans while freeviewing complex natural and artificial scenes. That study used a definition of salience based on local detectors with coarse global surround inhibition. Here, we use a similar framework to investigate the roles of several types of nonlinear interactions known to exist in visual cortex, and of eccentricitydependent processing. For each of these, we added a component to the salience model, including richer interactions among orientationtuned units, both at spatial short range (for clutter reduction) and long range (for contour facilitation), and a detailed model of eccentricitydependent changes in visual processing. Subjects freeviewed naturalistic and artificial images while their eye movements were recorded, and the resulting fixation locations were compared with the modelsÕ predicted salience maps. We found that the proposed interactions indeed play a significant role in the spatiotemporal deployment of attention in natural scenes; about half of the observed intersubject variance can be explained by these different models. This suggests that attentional guidance does not depend solely on local visual features, but must also include the effects of interactions among features. As models of these interactions become more accurate in predicting behaviorallyrelevant salient locations, they become useful to a range of applications in computer vision and humanmachine interface design.
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 63 (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.
Image hallucination with primal sketch priors
 Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR
, 2003
"... In this paper, we propose a Bayesian approach to image hallucination. Given a generic low resolution image, we hallucinate a high resolution image using a set of training images. Our work is inspired by recent progress on natural image statistics that the priors of image primitives can be well repre ..."
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Cited by 60 (6 self)
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In this paper, we propose a Bayesian approach to image hallucination. Given a generic low resolution image, we hallucinate a high resolution image using a set of training images. Our work is inspired by recent progress on natural image statistics that the priors of image primitives can be well represented by examples. Specifically, primal sketch priors (e.g., edges, ridges and corners) are constructed and used to enhance the quality of the hallucinated high resolution image. Moreover, a contour smoothness constraint enforces consistency of primitives in the hallucinated image by a Markovchain based inference algorithm. A reconstruction constraint is also applied to further improve the quality of the hallucinated image. Experiments demonstrate that our approach can hallucinate high quality superresolution images. 1.
Beamlets and Multiscale Image Analysis
 in Multiscale and Multiresolution Methods
, 2001
"... We describe a framework for multiscale image analysis in which line segments play a role analogous to the role played by points in wavelet analysis. ..."
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Cited by 56 (16 self)
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We describe a framework for multiscale image analysis in which line segments play a role analogous to the role played by points in wavelet analysis.
Energybased models for sparse overcomplete representations
 Journal of Machine Learning Research
, 2003
"... We present a new way of extending independent components analysis (ICA) to overcomplete representations. In contrast to the causal generative extensions of ICA which maintain marginal independence of sources, we define features as deterministic (linear) functions of the inputs. This assumption resul ..."
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Cited by 55 (14 self)
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We present a new way of extending independent components analysis (ICA) to overcomplete representations. In contrast to the causal generative extensions of ICA which maintain marginal independence of sources, we define features as deterministic (linear) functions of the inputs. This assumption results in marginal dependencies among the features, but conditional independence of the features given the inputs. By assigning energies to the features a probability distribution over the input states is defined through the Boltzmann distribution. Free parameters of this model are trained using the contrastive divergence objective (Hinton, 2002). When the number of features is equal to the number of input dimensions this energybased model reduces to noiseless ICA and we show experimentally that the proposed learning algorithm is able to perform blind source separation on speech data. In additional experiments we train overcomplete energybased models to extract features from various standard datasets containing speech, natural images, handwritten digits and faces.
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 54 (5 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
On the local behavior of spaces of natural images
 Internat. J. Comput. Vision
, 2006
"... In this study we concentrate on qualitative topological analysis of the local behavior of the space of natural images. To this end, we use a space of 3 by 3 highcontrast patches M studied by Mumford et al. We develop a theoretical model for the highdensity 2dimensional submanifold of M showing th ..."
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Cited by 50 (12 self)
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In this study we concentrate on qualitative topological analysis of the local behavior of the space of natural images. To this end, we use a space of 3 by 3 highcontrast patches M studied by Mumford et al. We develop a theoretical model for the highdensity 2dimensional submanifold of M showing that it has the topology of the Klein bottle. Using our topological software package PLEX we experimentally verify our theoretical conclusions. We use polynomial representation to give coordinatization to various subspaces of M. We find the bestfitting embedding of the Klein bottle into the ambient space of M. Our results are currently being used in developing a compression algorithm based on a Klein bottle dictionary.
Topographic product models applied to natural scene statistics
 Neural Computation
, 2005
"... We present an energybased model that uses a product of generalised Studentt distributions to capture the statistical structure in datasets. This model is inspired by and particularly applicable to “natural ” datasets such as images. We begin by providing the mathematical framework, where we discus ..."
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Cited by 49 (7 self)
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We present an energybased model that uses a product of generalised Studentt distributions to capture the statistical structure in datasets. This model is inspired by and particularly applicable to “natural ” datasets such as images. We begin by providing the mathematical framework, where we discuss complete and overcomplete models, and provide algorithms for training these models from data. Using patches of natural scenes we demonstrate that our approach represents a viable alternative to “independent components analysis ” as an interpretive model of biological visual systems. Although the two approaches are similar in flavor there are also important differences, particularly when the representations are overcomplete. By constraining the interactions within our model we are also able to study the topographic organization of Gaborlike receptive fields that are learned by our model. Finally, we discuss the relation of our new approach to previous work — in particular Gaussian Scale Mixture models, and variants of independent components analysis. 1
Barcodes: The persistent topology of data
, 2007
"... Abstract. This article surveys recent work of Carlsson and collaborators on applications of computational algebraic topology to problems of feature detection and shape recognition in highdimensional data. The primary mathematical tool considered is a homology theory for pointcloud data sets—persis ..."
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Cited by 48 (2 self)
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Abstract. This article surveys recent work of Carlsson and collaborators on applications of computational algebraic topology to problems of feature detection and shape recognition in highdimensional data. The primary mathematical tool considered is a homology theory for pointcloud data sets—persistent homology—and a novel representation of this algebraic characterization— barcodes. We sketch an application of these techniques to the classification of natural images. 1. The shape of data When a topologist is asked, “How do you visualize a fourdimensional object?” the appropriate response is a Socratic rejoinder: “How do you visualize a threedimensional object? ” We do not see in three spatial dimensions directly, but rather via sequences of planar projections integrated in a manner that is sensed if not comprehended. We spend a significant portion of our first year of life learning how to infer threedimensional spatial data from paired planar projections. Years of practice have tuned a remarkable ability to extract global structure from representations