Statistical Models of Natural Images and Cortical Visual Representation

A fundamental question in visual neuroscience is: Why are the response properties of visual neurons as they are? A modern approach to this problem emphasizes the importance of adaptation to ecologically valid input, and it proceeds by modeling statistical regularities in ecologically valid visual input (natural images). A seminal model was linear sparse coding, which is equivalent to independent component analysis (ICA), and provided a very good description of the receptive fields of simple cells. Further models based on modeling residual dependencies of the ''independent" components have later been introduced. These models lead to emergence of further properties of visual neurons: the complex cell receptive fields, the spatial organization of the cells, and some surround suppression and Gestalt effects. So far, these models have concentrated on the response properties of neurons, but they hold great potential to model various forms of inference and learning.

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

[2]  Norbert Krüger,et al.  Collinearity and Parallelism are Statistically Significant Second-Order Relations of Complex Cell Responses , 1998, Neural Processing Letters.

[3]  I. Ohzawa,et al.  Functional Micro-Organization of Primary Visual Cortex: Receptive Field Analysis of Nearby Neurons , 1999, The Journal of Neuroscience.

[4]  N. Swindale.  The development of topography in the visual cortex: a review of models. , 1996, Network.

[5]  D. Ruderman,et al.  Independent component analysis of natural image sequences yields spatio-temporal filters similar to simple cells in primary visual cortex , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[6]  D. Ruderman,et al.  Independent component analysis of natural image sequences yields spatio-temporal filters similar to simple cells in primary visual cortex , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[7]  W. Hashimoto.  Quadratic forms in natural images , 2003, Network.

[8]  Erkki Oja,et al.  Independent Component Analysis , 2001 .

[9]  Aapo Hyvärinen,et al.  Estimating Markov Random Field Potentials for Natural Images , 2009, ICA.

[10]  Eero P. Simoncelli.  4.7 – Statistical Modeling of Photographic Images , 2005 .

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

[12]  Aapo Hyvärinen,et al.  Fast and robust fixed-point algorithms for independent component analysis , 1999, IEEE Trans. Neural Networks.

[13]  Aapo Hyv.  Fast and Robust Fixed-Point Algorithms for Independent Component Analysis , 1999 .

[14]  J. V. van Hateren,et al.  Independent component filters of natural images compared with simple cells in primary visual cortex , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[15]  David J. Field,et al.  What Is the Goal of Sensory Coding? , 1994, Neural Computation.

[16]  Aapo Hyvärinen,et al.  A two-layer sparse coding model learns simple and complex cell receptive fields and topography from natural images , 2001, Vision Research.

[17]  Aapo Hyvärinen,et al.  Sparse Code Shrinkage: Denoising of Nongaussian Data by Maximum Likelihood Estimation , 1999, Neural Computation.

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

[19]  Marco Buiatti,et al.  Variance normalisation: a key mechanism for temporal adaptation in natural vision? , 2003, Vision Research.

[20]  Eero P. Simoncelli,et al.  Natural image statistics and neural representation. , 2001, Annual review of neuroscience.

[21]  Eero P. Simoncelli,et al.  Natural signal statistics and sensory gain control , 2001, Nature Neuroscience.

[22]  Michael S. Lewicki,et al.  Emergence of complex cell properties by learning to generalize in natural scenes , 2009, Nature.

[23]  Aapo Hyvärinen,et al.  Learning Natural Image Structure with a Horizontal Product Model , 2009, ICA.

[24]  Peter Földiák,et al.  Learning Invariance from Transformation Sequences , 1991, Neural Comput..

[25]  G. Blasdel,et al.  Orientation selectivity, preference, and continuity in monkey striate cortex , 1992, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[26]  Aapo Hyvärinen,et al.  Emergence of Phase- and Shift-Invariant Features by Decomposition of Natural Images into Independent Feature Subspaces , 2000, Neural Computation.

[27]  Hyvarinen.  Sparse code shrinkage: denoising of nongaussian data by maximum likelihood estimation , 1999, Neural computation.

[28]  W. Geisler.  Visual perception and the statistical properties of natural scenes. , 2008, Annual review of psychology.

[29]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[30]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[31]  Geoffrey E. Hinton,et al.  Topographic Product Models Applied to Natural Scene Statistics , 2006, Neural Computation.

[32]  Terrence J. Sejnowski,et al.  Slow Feature Analysis: Unsupervised Learning of Invariances , 2002, Neural Computation.

[33]  J. H. Hateren,et al.  Independent component filters of natural images compared with simple cells in primary visual cortex , 1998 .

[34]  Aapo Hyvärinen,et al.  Natural Image Statistics - A Probabilistic Approach to Early Computational Vision , 2009, Computational Imaging and Vision.

[35]  C. Gilbert,et al.  On a common circle: natural scenes and Gestalt rules. , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Bruno A. Olshausen,et al.  Principles of Image Representation in Visual Cortex , 2003 .

[37]  Eero P. Simoncelli,et al.  On Advances in Statistical Modeling of Natural Images , 2004, Journal of Mathematical Imaging and Vision.

[38]  Terrence J. Sejnowski,et al.  The “independent components” of natural scenes are edge filters , 1997, Vision Research.

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

[40]  Pierre Comon.  Independent component analysis - a new concept? signal processing , 1994 .

[41]  Daniel A. Pollen,et al.  Visual cortical neurons as localized spatial frequency filters , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[42]  David J. Field,et al.  Sparse coding with an overcomplete basis set: A strategy employed by V1? , 1997, Vision Research.

[43]  Aapo Hyvärinen,et al.  Simple-Cell-Like Receptive Fields Maximize Temporal Coherence in Natural Video , 2003, Neural Computation.

[44]  Aapo Hyvärinen,et al.  A Two-Layer ICA-Like Model Estimated by Score Matching , 2007, ICANN.

[45]  Aapo Hyvärinen,et al.  Bubbles: a unifying framework for low-level statistical properties of natural image sequences. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[46]  Aapo Hyvärinen,et al.  Statistical model of natural stimuli predicts edge-like pooling of spatial frequency channels in V2 , 2004, BMC Neuroscience.

[47]  Eero P. Simoncelli,et al.  Natural image statistics and divisive normalization: Modeling nonlinearity and adaptation in cortical neurons , 2002 .