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Hierarchical Bayesian Inference in the Visual Cortex
, 2002
"... this paper, we propose a Bayesian theory of hierarchical cortical computation based both on (a) the mathematical and computational ideas of computer vision and pattern the ory and on (b) recent neurophysiological experimental evidence. We ,2 have proposed that Grenander's pattern theory 3 could pot ..."
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Cited by 173 (0 self)
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this paper, we propose a Bayesian theory of hierarchical cortical computation based both on (a) the mathematical and computational ideas of computer vision and pattern the ory and on (b) recent neurophysiological experimental evidence. We ,2 have proposed that Grenander's pattern theory 3 could potentially model the brain as a generafive model in such a way that feedback serves to disambiguate and 'explain away' the earlier representa tion. The Helmholtz machine 4, 5 was an excellent step towards approximating this proposal, with feedback implementing priors. Its development, however, was rather limited, dealing only with binary images. Moreover, its feedback mechanisms were engaged only during the learning of the feedforward connections but not during perceptual inference, though the Gibbs sampling process for inference can potentially be interpreted as topdown feedback disambiguating low level representations? Rao and Ballard's predictive coding/Kalman filter model 6 did integrate generafive feedback in the perceptual inference process, but it was primarily a linear model and thus severely limited in practical utility. The datadriven Markov Chain Monte Carlo approach of Zhu and colleagues 7, 8 might be the most successful recent application of this proposal in solving real and difficult computer vision problems using generafive models, though its connection to the visual cortex has not been explored. Here, we bring in a powerful and widely applicable paradigm from artificial intelligence and computer vision to propose some new ideas about the algorithms of visual cortical process ing and the nature of representations in the visual cortex. We will review some of our and others' neurophysiological experimental data to lend support to these ideas
A Bayesian approach to the evolution of perceptual and cognitive systems
 COGNITIVE SCIENCE
, 2003
"... We describe a formal framework for analyzing how statistical properties of natural environments and the process of natural selection interact to determine the design of perceptual and cognitive systems. The framework consists of two parts: a Bayesian ideal observer with a utility function appropriat ..."
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Cited by 17 (1 self)
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We describe a formal framework for analyzing how statistical properties of natural environments and the process of natural selection interact to determine the design of perceptual and cognitive systems. The framework consists of two parts: a Bayesian ideal observer with a utility function appropriate for natural selection, and a Bayesian formulation of Darwin’s theory of natural selection. Simulations of Bayesian natural selection were found to yield new insights, for example, into the coevolution of camouflage, color vision, and decision criteria. The Bayesian framework captures and generalizes, in a formal way, many of the important ideas of other approaches to perception and cognition.
Contrast statistics for foveated visual systems: fixation selection by minimizing contrast entropy
 Journal of the Optical Society of America A
, 2005
"... The human visual system combines a wide field of view with a highresolution fovea and uses eye, head, and body movements to direct the fovea to potentially relevant locations in the visual scene. This strategy is sensible for a visual system with limited neural resources. However, for this strategy ..."
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Cited by 17 (3 self)
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The human visual system combines a wide field of view with a highresolution fovea and uses eye, head, and body movements to direct the fovea to potentially relevant locations in the visual scene. This strategy is sensible for a visual system with limited neural resources. However, for this strategy to be effective, the visual system needs sophisticated central mechanisms that efficiently exploit the varying spatial resolution of the retina. To gain insight into some of the design requirements of these central mechanisms, we have analyzed the effects of variable spatial resolution on local contrast in 300 calibrated natural images. Specifically, for each retinal eccentricity (which produces a certain effective level of blur), and for each value of local contrast observed at that eccentricity, we measured the probability distribution of the local contrast in the unblurred image. These conditional probability distributions can be regarded as posterior probability distributions for the “true ” unblurred contrast, given an observed contrast at a given eccentricity. We find that these conditional probability distributions are adequately described by a few simple formulas. To explore how these statistics might be exploited by central perceptual mechanisms, we consider the task of selecting successive fixation points, where the goal on each fixation is to maximize total contrast information gained about the image (i.e., minimize total contrast uncertainty). We derive an entropy minimization algorithm and find that it performs optimally at reducing total contrast uncertainty and that it also works well at reducing the mean squared error
Encoding multielement scenes: Statistical learning of visual feature hierarchies
 Journal of Experimental Psychology: General
, 2005
"... The authors investigated how human adults encode and remember parts of multielement scenes composed of recursively embedded visual shape combinations. The authors found that shape combinations that are parts of larger configurations are less well remembered than shape combinations of the same kind t ..."
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Cited by 16 (5 self)
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The authors investigated how human adults encode and remember parts of multielement scenes composed of recursively embedded visual shape combinations. The authors found that shape combinations that are parts of larger configurations are less well remembered than shape combinations of the same kind that are not embedded. Combined with basic mechanisms of statistical learning, this embeddedness constraint enables the development of complex new features for acquiring internal representations efficiently without being computationally intractable. The resulting representations also encode parts and wholes by chunking the visual input into components according to the statistical coherence of their constituents. These results suggest that a bootstrapping approach of constrained statistical learning offers a unified framework for investigating the formation of different internal representations in pattern and scene perception.
Local luminance and contrast in natural images
 Vision Research
, 2006
"... Within natural images there is substantial spatial variation in both local contrast and local luminance. Understanding the statistics of these variations is important for understanding the dynamics of receptive field stimulation that occur under natural viewing conditions and for understanding the r ..."
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Cited by 8 (0 self)
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Within natural images there is substantial spatial variation in both local contrast and local luminance. Understanding the statistics of these variations is important for understanding the dynamics of receptive field stimulation that occur under natural viewing conditions and for understanding the requirements for effective luminance and contrast gain control. Local luminance and contrast were measured in a large set of calibrated 12bit grayscale natural images, for a number of analysis patch sizes. For each image and patch size we measured the range of contrast, the range of luminance, the correlation in contrast and luminance as a function of the distance between patches, and the correlation between contrast and luminance within patches. The same analyses were also performed on hand segmented regions containing only ‘‘sky’’, ‘‘ground’’, ‘‘foliage’’, or ‘‘backlit foliage’’. Within the typical image, the 95 % range (2.5–97.5 percentile) for both local luminance and local contrast is somewhat greater than a factor of 10. The correlation in contrast and the correlation in luminance diminish rapidly with distance, and the typical correlation between luminance and contrast within patches is small (e.g., 0.2 compared to 0.8 for 1/f noise). We show that eye movements are frequently large enough that there will be little correlation in the contrast or luminance on a receptive field from one fixation to the next, and thus rapid contrast and luminance gain control are essential. The low correlation between local luminance and contrast implies that efficient contrast gain control mechanisms can operate largely independently of luminance gain control mechanisms. Ó 2005 Elsevier Ltd. All rights reserved. 1.
Simplicity Versus Likelihood Principles in Perception
"... Discussions of the foundations of perceptual inference have often centered on 2 governing principles, the likelihood principle and the simplicity principle. Historically, these principles have usually been seen as opposed, but contemporary statistical (e.g., Bayesian) theory tends to see them as con ..."
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Discussions of the foundations of perceptual inference have often centered on 2 governing principles, the likelihood principle and the simplicity principle. Historically, these principles have usually been seen as opposed, but contemporary statistical (e.g., Bayesian) theory tends to see them as consistent, because for a variety of reasons simpler models (i.e., those with fewer dimensions or free parameters) make better predictors than more complex ones. In perception, many interpretation spaces are naturally hierarchical, meaning that they consist of a set of mutually embedded model classes of various levels of complexity, including simpler (lower dimensional) classes that are special cases of more complex ones. This article shows how such spaces can be regarded as algebraic structures, for example, as partial orders or lattices, with interpretations ordered in terms of dimensionality. The natural inference rule in such a space is a kind of simplicity rule: Among all interpretations qualitatively consistent with the image, draw the one that is lowest in the partial order, called the maximumdepth interpretation. This interpretation also maximizes the Bayesian posterior under certain simplifying assumptions, consistent with a unification of simplicity and likelihood principles. Moreover, the algebraic approach brings out the compositional structure inherent in such spaces, showing how perceptual interpretations are composed from a lexicon of primitive perceptual descriptors.
Contents lists available at ScienceDirect Cognition
"... journal homepage: www.elsevier.com/locate/COGNIT ..."
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, 2011
"... doi: 10.3389/fnhum.2011.00039 A Bayesian foundation for individual learning under uncertainty ..."
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doi: 10.3389/fnhum.2011.00039 A Bayesian foundation for individual learning under uncertainty
SYSTEMS NEUROSCIENCE ORIGINAL RESEARCH ARTICLE
, 2011
"... doi: 10.3389/fnsys.2011.00084 Map formation in the olfactory bulb by axon guidance of olfactory neurons ..."
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doi: 10.3389/fnsys.2011.00084 Map formation in the olfactory bulb by axon guidance of olfactory neurons
Coupling the world with the observer: from analysis of information to active vision
 SPATIAL VISION
, 2009
"... In this paper we define the content of information in an image and show how it can be computed by taking into account different levels of resolution, in the framework of information theory and the thermodynamics of irreversible transformations. The results thus obtained will eventually be exploited ..."
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In this paper we define the content of information in an image and show how it can be computed by taking into account different levels of resolution, in the framework of information theory and the thermodynamics of irreversible transformations. The results thus obtained will eventually be exploited to derive a mechanism for active exploration of visual space suitable to perform a dynamic coupling between the agent and its environment