The Visual System's Internal Model of the World

The Bayesian paradigm has provided a useful conceptual theory for understanding perceptual computation in the brain. While the detailed neural mechanisms of Bayesian inference are not fully understood, recent computational and neurophysiological works have illuminated the underlying computational principles and representational architecture. The fundamental insights are that the visual system is organized as a modular hierarchy to encode an internal model of the world, and that perception is realized by statistical inference based on such internal model. In this paper, we will discuss and analyze the varieties of representational schemes of these internal models and how they might be used to perform learning and inference. We will argue for a unified theoretical framework for relating the internal models to the observed neural phenomena and mechanisms in the visual cortex.

[1]  R. Reid,et al.  Efficacy of Retinal Spikes in Driving Cortical Responses , 2003, The Journal of Neuroscience.

[2]  Christopher W Tyler,et al.  Recurrent Connectivity Can Account for the Dynamics of Disparity Processing in V1 , 2013, The Journal of Neuroscience.

[3]  Geoffrey E. Hinton,et al.  Modeling image patches with a directed hierarchy of Markov random fields , 2007, NIPS.

[4]  D. V. van Essen,et al.  Neuronal responses to static texture patterns in area V1 of the alert macaque monkey. , 1992, Journal of neurophysiology.

[5]  Geoffrey E. Hinton,et al.  ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.

[6]  Alexandre Pouget,et al.  Probabilistic Interpretation of Population Codes , 1996, Neural Computation.

[7]  James L. McClelland Integrating probabilistic models of perception and interactive neural networks: a historical and tutorial review , 2013, Front. Psychol..

[8]  P. Földiák,et al.  Forming sparse representations by local anti-Hebbian learning , 1990, Biological Cybernetics.

[9]  Long Zhu,et al.  Unsupervised Structure Learning: Hierarchical Recursive Composition, Suspicious Coincidence and Competitive Exclusion , 2008, ECCV.

[10]  Geoffrey E. Hinton,et al.  Modeling Natural Images Using Gated MRFs , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Michael N. Shadlen,et al.  Synchrony Unbound A Critical Evaluation of the Temporal Binding Hypothesis , 1999, Neuron.

[12]  H. Chick,et al.  The photosensitizing action of buckwheat (Fagopyrum esculentum) , 1941, The Journal of physiology.

[13]  A. Litwin-Kumar,et al.  Slow dynamics and high variability in balanced cortical networks with clustered connections , 2012, Nature Neuroscience.

[14]  James L. McClelland,et al.  Interactive Activation and Mutual Constraint Satisfaction in Perception and Cognition , 2014, Cogn. Sci..

[15]  J. Movshon,et al.  Nature and interaction of signals from the receptive field center and surround in macaque V1 neurons. , 2002, Journal of neurophysiology.

[16]  Carl R Olson,et al.  Statistical Learning of Serial Visual Transitions by Neurons in Monkey Inferotemporal Cortex , 2014, The Journal of Neuroscience.

[17]  J. Hegdé,et al.  A comparative study of shape representation in macaque visual areas v2 and v4. , 2007, Cerebral cortex.

[18]  Stephen Grossberg,et al.  Competitive Learning: From Interactive Activation to Adaptive Resonance , 1987, Cogn. Sci..

[19]  Andrew Y. Ng,et al.  Emergence of Object-Selective Features in Unsupervised Feature Learning , 2012, NIPS.

[20]  Steven W. Zucker,et al.  Differential Geometric Inference in Surface Stereo , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  D. Fitzpatrick,et al.  Orientation Selectivity and the Arrangement of Horizontal Connections in Tree Shrew Striate Cortex , 1997, The Journal of Neuroscience.

[22]  H. B. Barlow,et al.  Possible Principles Underlying the Transformations of Sensory Messages , 2012 .

[23]  Brian Potetz,et al.  Efficient Belief Propagation for Vision Using Linear Constraint Nodes , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[24]  Karl J. Friston The free-energy principle: a unified brain theory? , 2010, Nature Reviews Neuroscience.

[25]  D. V. van Essen,et al.  A neurobiological model of visual attention and invariant pattern recognition based on dynamic routing of information , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[26]  David Mumford,et al.  On the computational architecture of the neocortex , 2004, Biological Cybernetics.

[27]  T. Poggio,et al.  What and where: A Bayesian inference theory of attention , 2010, Vision Research.

[28]  Geoffrey E. Hinton,et al.  Learning to Represent Spatial Transformations with Factored Higher-Order Boltzmann Machines , 2010, Neural Computation.

[29]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[30]  Hualou Liang,et al.  Incremental Integration of Global Contours through Interplay between Visual Cortical Areas , 2014, Neuron.

[31]  R. Reid,et al.  Precisely correlated firing in cells of the lateral geniculate nucleus , 1996, Nature.

[32]  R. Born,et al.  Single-unit and 2-deoxyglucose studies of side inhibition in macaque striate cortex. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[33]  T. Wiesel,et al.  Columnar specificity of intrinsic horizontal and corticocortical connections in cat visual cortex , 1989, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[34]  Tim Gollisch,et al.  Eye Smarter than Scientists Believed: Neural Computations in Circuits of the Retina , 2010, Neuron.

[35]  Ulf Grenander,et al.  Lectures in pattern theory , 1978 .

[36]  Kunihiko Fukushima,et al.  Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position , 1980, Biological Cybernetics.

[37]  D. J. Felleman,et al.  Distributed hierarchical processing in the primate cerebral cortex. , 1991, Cerebral cortex.

[38]  Roozbeh Mottaghi,et al.  Complexity of Representation and Inference in Compositional Models with Part Sharing , 2013, J. Mach. Learn. Res..

[39]  D Marr,et al.  Cooperative computation of stereo disparity. , 1976, Science.

[40]  Victor A. F. Lamme,et al.  Contextual Modulation in Primary Visual Cortex , 1996, The Journal of Neuroscience.

[41]  D. Hubel,et al.  Ferrier lecture - Functional architecture of macaque monkey visual cortex , 1977, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[42]  D. Mumford,et al.  The role of the primary visual cortex in higher level vision , 1998, Vision Research.

[43]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[44]  David J. Jilk,et al.  Recurrent Processing during Object Recognition , 2011, Front. Psychol..

[45]  Wei Ji Ma,et al.  Bayesian inference with probabilistic population codes , 2006, Nature Neuroscience.

[46]  Gary L. Miller,et al.  Graph Partitioning by Spectral Rounding: Applications in Image Segmentation and Clustering , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[47]  Jeffrey S. Perry,et al.  Edge co-occurrence in natural images predicts contour grouping performance , 2001, Vision Research.

[48]  Tai Sing Lee,et al.  Decoding V1 Neuronal Activity using Particle Filtering with Volterra Kernels , 2003, NIPS.

[49]  Tai Sing Lee,et al.  Hierarchical Bayesian inference in the visual cortex. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[50]  Brian Potetz,et al.  Scene Statistics and 3D Surface Perception , 2011 .

[51]  Xiaolin Hu,et al.  Modeling response properties of V2 neurons using a hierarchical K-means model , 2014, Neurocomputing.

[52]  Aapo Hyvärinen,et al.  Interpreting Neural Response Variability as Monte Carlo Sampling of the Posterior , 2002, NIPS.

[53]  James J. DiCarlo,et al.  How Does the Brain Solve Visual Object Recognition? , 2012, Neuron.

[54]  Rodrigo F. Salazar,et al.  Content-Specific Fronto-Parietal Synchronization During Visual Working Memory , 2012, Science.

[55]  S. Zucker,et al.  Endstopped neurons in the visual cortex as a substrate for calculating curvature , 1987, Nature.

[56]  Tai Sing Lee,et al.  Cooperative and Competitive Interactions Facilitate Stereo Computations in Macaque Primary Visual Cortex , 2009, The Journal of Neuroscience.

[57]  Tai Sing Lee,et al.  Local field potentials indicate network state and account for neuronal response variability , 2010, Journal of Computational Neuroscience.

[58]  P. Milner A model for visual shape recognition. , 1974, Psychological review.

[59]  P. Cz. Handbuch der physiologischen Optik , 1896 .

[60]  C. Olson,et al.  Statistical learning of visual transitions in monkey inferotemporal cortex , 2011, Proceedings of the National Academy of Sciences.

[61]  Yoshua Bengio,et al.  Convolutional networks for images, speech, and time series , 1998 .

[62]  F FelzenszwalbPedro,et al.  Efficient Belief Propagation for Early Vision , 2006 .

[63]  David J. Field,et al.  Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.

[64]  Rajesh P. N. Rao Bayesian Computation in Recurrent Neural Circuits , 2004, Neural Computation.

[65]  Ohad Ben-Shahar,et al.  Cortical connections and early visual function: intra- and inter-columnar processing , 2003, Journal of Physiology-Paris.

[66]  M. Bar The proactive brain: using analogies and associations to generate predictions , 2007, Trends in Cognitive Sciences.

[67]  John W. Clark,et al.  Neural Representation of Probabilistic Information , 2001, Neural Computation.

[68]  H. Barlow,et al.  Three factors limiting the reliable detection of light by retinal ganglion cells of the cat , 1969, The Journal of physiology.

[69]  J. Elder,et al.  Ecological statistics of Gestalt laws for the perceptual organization of contours. , 2002, Journal of vision.

[70]  Geoffrey E. Hinton,et al.  The Helmholtz Machine , 1995, Neural Computation.

[71]  Tai Sing Lee,et al.  Relating functional connectivity in V1 neural circuits and 3D natural scenes using Boltzmann machines , 2016, Vision Research.

[72]  D. Hubel,et al.  Receptive fields, binocular interaction and functional architecture in the cat's visual cortex , 1962, The Journal of physiology.

[73]  D. Heeger Normalization of cell responses in cat striate cortex , 1992, Visual Neuroscience.

[74]  T. S. Lee,et al.  A Bayesian framework for understanding texture segmentation in the primary visual cortex , 1995, Vision Research.

[75]  S. Grossberg,et al.  Pattern formation, contrast control, and oscillations in the short term memory of shunting on-center off-surround networks , 1975, Biological Cybernetics.

[76]  W Singer,et al.  Visual feature integration and the temporal correlation hypothesis. , 1995, Annual review of neuroscience.

[77]  T. Sanger,et al.  Probability density estimation for the interpretation of neural population codes. , 1996, Journal of neurophysiology.

[78]  James L. McClelland,et al.  An interactive activation model of context effects in letter perception: I. An account of basic findings. , 1981 .

[79]  P. Berkes,et al.  Statistically Optimal Perception and Learning: from Behavior to Neural Representations , 2022 .

[80]  Daniel P. Huttenlocher,et al.  Efficient Belief Propagation for Early Vision , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[81]  Geoffrey E. Hinton,et al.  Reducing the Dimensionality of Data with Neural Networks , 2006, Science.

[82]  C. Gilbert,et al.  Spatial distribution of contextual interactions in primary visual cortex and in visual perception. , 2000, Journal of neurophysiology.

[83]  Tai Sing Lee,et al.  Predictive Encoding of Contextual Relationships for Perceptual Inference, Interpolation and Prediction , 2014, ICLR.

[84]  T. Wiesel,et al.  Functional architecture of macaque monkey visual cortex , 1977 .

[85]  J. M. Hupé,et al.  Cortical feedback improves discrimination between figure and background by V1, V2 and V3 neurons , 1998, Nature.

[86]  Victor A. F. Lamme,et al.  Neuronal synchrony does not represent texture segregation , 1998, Nature.

[87]  Rob Fergus,et al.  Visualizing and Understanding Convolutional Networks , 2013, ECCV.

[88]  Nicolas Pinto,et al.  Beyond simple features: A large-scale feature search approach to unconstrained face recognition , 2011, Face and Gesture 2011.

[89]  E. Maris,et al.  Prior Expectation Mediates Neural Adaptation to Repeated Sounds in the Auditory Cortex: An MEG Study , 2011, The Journal of Neuroscience.

[90]  Geoffrey E. Hinton,et al.  Learning and relearning in Boltzmann machines , 1986 .

[91]  T. Poggio,et al.  Hierarchical models of object recognition in cortex , 1999, Nature Neuroscience.

[92]  József Fiser,et al.  Spontaneous Cortical Activity Reveals Hallmarks of an Optimal Internal Model of the Environment , 2011, Science.

[93]  C. Gray The Temporal Correlation Hypothesis of Visual Feature Integration Still Alive and Well , 1999, Neuron.

[94]  Steven W. Zucker,et al.  Stereo, Shading, and Surfaces: Curvature Constraints Couple Neural Computations , 2014, Proceedings of the IEEE.

[95]  Jason M Samonds,et al.  Relative luminance and binocular disparity preferences are correlated in macaque primary visual cortex, matching natural scene statistics , 2012, Proceedings of the National Academy of Sciences.

[96]  Thomas Dean,et al.  A Computational Model of the Cerebral Cortex , 2005, AAAI.

[97]  Dumitru Erhan,et al.  Going deeper with convolutions , 2014, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[98]  Jianbo Shi,et al.  Segmentation given partial grouping constraints , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[99]  David J. Field,et al.  Contour integration by the human visual system: Evidence for a local “association field” , 1993, Vision Research.

[100]  Sophie Denève,et al.  Bayesian Spiking Neurons I: Inference , 2008, Neural Computation.

[101]  M. Alexander,et al.  Principles of Neural Science , 1981 .

[102]  J. Allman,et al.  Stimulus specific responses from beyond the classical receptive field: neurophysiological mechanisms for local-global comparisons in visual neurons. , 1985, Annual review of neuroscience.

[103]  Michael Isard,et al.  Statistical models of visual shape and motion , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[104]  S Ullman,et al.  Sequence seeking and counter streams: a computational model for bidirectional information flow in the visual cortex. , 1995, Cerebral cortex.

[105]  Stuart Geman,et al.  Invariance and selectivity in the ventral visual pathway , 2006, Journal of Physiology-Paris.

[106]  Christoph von der Malsburg,et al.  The What and Why of Binding The Modeler’s Perspective , 1999, Neuron.

[107]  D. Mumford,et al.  Neural activity in early visual cortex reflects behavioral experience and higher-order perceptual saliency , 2002, Nature Neuroscience.

[108]  G. I. Kustova,et al.  From the author , 2019, Automatic Documentation and Mathematical Linguistics.

[109]  George Papandreou,et al.  Modeling Image Patches with a Generic Dictionary of Mini-epitomes , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[110]  Long Zhu,et al.  Recursive Compositional Models for Vision: Description and Review of Recent Work , 2011, Journal of Mathematical Imaging and Vision.

[111]  T. Wiesel,et al.  Morphology and intracortical projections of functionally characterised neurones in the cat visual cortex , 1979, Nature.

[112]  Dileep George,et al.  Towards a Mathematical Theory of Cortical Micro-circuits , 2009, PLoS Comput. Biol..

[113]  T. Wiesel,et al.  Relationships between horizontal interactions and functional architecture in cat striate cortex as revealed by cross-correlation analysis , 1986, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[114]  Bartlett W. Mel,et al.  Computational subunits in thin dendrites of pyramidal cells , 2004, Nature Neuroscience.

[115]  Richard G. Baraniuk,et al.  Sparse Coding via Thresholding and Local Competition in Neural Circuits , 2008, Neural Computation.

[116]  Thomas L. Griffiths,et al.  Neural Implementation of Hierarchical Bayesian Inference by Importance Sampling , 2009, NIPS.

[117]  Long Zhu,et al.  Rapid Inference on a Novel AND/OR graph for Object Detection, Segmentation and Parsing , 2007, NIPS.

[118]  Geoffrey E. Hinton Learning multiple layers of representation , 2007, Trends in Cognitive Sciences.

[119]  HERBERT A. SIMON,et al.  The Architecture of Complexity , 1991 .

[120]  Rajesh P. N. Rao,et al.  Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. , 1999 .

[121]  Edward H. Adelson,et al.  The Laplacian Pyramid as a Compact Image Code , 1983, IEEE Trans. Commun..

[122]  P. Fries A mechanism for cognitive dynamics: neuronal communication through neuronal coherence , 2005, Trends in Cognitive Sciences.

[123]  C. Gross,et al.  Visuotopic organization and extent of V3 and V4 of the macaque , 1988, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[124]  Tai Sing Lee,et al.  Efficient belief propagation for higher-order cliques using linear constraint nodes , 2008, Comput. Vis. Image Underst..

[125]  C Koch,et al.  Analog "neuronal" networks in early vision. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[126]  H Sompolinsky,et al.  Simple models for reading neuronal population codes. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[127]  Eero P. Simoncelli,et al.  Implicit encoding of prior probabilities in optimal neural populations , 2010, NIPS.