Cortical Spatiotemporal Dimensionality Reduction for Visual Grouping

The visual systems of many mammals, including humans, are able to integrate the geometric information of visual stimuli and perform cognitive tasks at the first stages of the cortical processing. This is thought to be the result of a combination of mechanisms, which include feature extraction at the single cell level and geometric processing by means of cell connectivity. We present a geometric model of such connectivities in the space of detected features associated with spatiotemporal visual stimuli and show how they can be used to obtain low-level object segmentation. The main idea is to define a spectral clustering procedure with anisotropic affinities over data sets consisting of embeddings of the visual stimuli into higher-dimensional spaces. Neural plausibility of the proposed arguments will be discussed.

[1]  Giovanna Citti,et al.  A Cortical-Inspired Geometry for Contour Perception and Motion Integration , 2013, Journal of Mathematical Imaging and Vision.

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

[3]  Timothy Ledgeway,et al.  The detection of direction-defined and speed-defined spatial contours: one mechanism or two? , 2003, Vision Research.

[4]  Luigi F. Cuturi,et al.  The effect of spatial orientation on detecting motion trajectories in noise , 2011, Vision Research.

[5]  Y. Frégnac,et al.  Orientation dependent modulation of apparent speed: a model based on the dynamics of feed-forward and horizontal connectivity in V1 cortex , 2002, Vision Research.

[6]  Ann B. Lee,et al.  Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  W. Singer,et al.  Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[8]  I. Ohzawa,et al.  Receptive-field dynamics in the central visual pathways , 1995, Trends in Neurosciences.

[9]  M. London,et al.  Dendritic computation. , 2005, Annual review of neuroscience.

[10]  A. Sarti,et al.  A model of natural image edge co-occurrence in the rototranslation group. , 2010, Journal of vision.

[11]  J. Koenderink,et al.  Representation of local geometry in the visual system , 1987, Biological Cybernetics.

[12]  J. P. Jones,et al.  An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex. , 1987, Journal of neurophysiology.

[13]  Marina Meila,et al.  Clustering by weighted cuts in directed graphs , 2007, SDM.

[14]  Bartlett W. Mel,et al.  On the Fight Between Excitation and Inhibition: Location Is Everything , 2004, Science's STKE.

[15]  Ulrike von Luxburg,et al.  A tutorial on spectral clustering , 2007, Stat. Comput..

[16]  D. Hubel Eye, brain, and vision , 1988 .

[17]  Lance R. Williams,et al.  Stochastic Completion Fields: A Neural Model of Illusory Contour Shape and Salience , 1997, Neural Computation.

[18]  Jianbo Shi,et al.  A Random Walks View of Spectral Segmentation , 2001, AISTATS.

[19]  H. Rodman,et al.  Coding of visual stimulus velocity in area MT of the macaque , 1987, Vision Research.

[20]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[21]  D. Mumford Elastica and Computer Vision , 1994 .

[22]  D. Fitzpatrick,et al.  A systematic map of direction preference in primary visual cortex , 1996, Nature.

[23]  Ohad Ben-Shahar,et al.  Geometrical Computations Explain Projection Patterns of Long-Range Horizontal Connections in Visual Cortex , 2004, Neural Computation.

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

[25]  Giovanna Citti,et al.  A Cortical Based Model of Perceptual Completion in the Roto-Translation Space , 2006, Journal of Mathematical Imaging and Vision.

[26]  C. K. Ogden A Source Book Of Gestalt Psychology , 2013 .

[27]  D C Van Essen,et al.  Functional properties of neurons in middle temporal visual area of the macaque monkey. I. Selectivity for stimulus direction, speed, and orientation. , 1983, Journal of neurophysiology.

[28]  S. Palmer,et al.  A century of Gestalt psychology in visual perception: I. Perceptual grouping and figure-ground organization. , 2012, Psychological bulletin.

[29]  Scott N J Watamaniuk,et al.  The predictive power of trajectory motion , 2005, Vision Research.

[30]  E. Platen An introduction to numerical methods for stochastic differential equations , 1999, Acta Numerica.

[31]  W JacobsDavid,et al.  Stochastic completion fields , 1997 .

[32]  R B Tootell,et al.  Organization of intrinsic connections in owl monkey area MT. , 1997, Cerebral cortex.

[33]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.

[34]  Santosh S. Vempala,et al.  On clusterings-good, bad and spectral , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[35]  W. Hoffman The visual cortex is a contact bundle , 1989 .

[36]  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.

[37]  J. B. Levitt,et al.  Circuits for Local and Global Signal Integration in Primary Visual Cortex , 2002, The Journal of Neuroscience.

[38]  S P McKee,et al.  Stimulus configuration determines the detectability of motion signals in noise. , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[39]  D Barbieri,et al.  How Uncertainty Bounds the Shape Index of Simple Cells , 2014, The Journal of Mathematical Neuroscience.

[40]  Wilson S. Geisler,et al.  Grouping local orientation and direction signals to extract spatial contours: Empirical tests of “association field” models of contour integration , 2005, Vision Research.

[41]  Preeti Verghese,et al.  PII: S0042-6989(98)00033-9 , 1998 .

[42]  David Fitzpatrick,et al.  Emergent Properties of Layer 2/3 Neurons Reflect the Collinear Arrangement of Horizontal Connections in Tree Shrew Visual Cortex , 2003, The Journal of Neuroscience.

[43]  Yair Weiss,et al.  Segmentation using eigenvectors: a unifying view , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[44]  Stéphane Lafon,et al.  Diffusion maps , 2006 .

[45]  L Barnett,et al.  Neural complexity and structural connectivity. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  G. Edelman,et al.  A measure for brain complexity: relating functional segregation and integration in the nervous system. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[47]  Hugh R. Wilson,et al.  Global shape coding for motion-defined radial-frequency contours , 2005, Vision Research.

[48]  U. Eysel,et al.  Orientation-specific relationship between populations of excitatory and inhibitory lateral connections in the visual cortex of the cat. , 1997, Cerebral cortex.

[49]  A. Sarti,et al.  Spatiotemporal receptive fields of cells in V1 are optimally shaped for stimulus velocity estimation. , 2012, Journal of the Optical Society of America. A, Optics, image science, and vision.

[50]  Stephen R. Mitroff,et al.  Dynamics of Population Response to Changes of Motion Direction in Primary Visual Cortex , 2011, The Journal of Neuroscience.

[51]  Robert F Hess,et al.  Rules for combining the outputs of local motion detectors to define simple contours , 2002, Vision Research.

[52]  Mauro Maggioni,et al.  Geometric diffusions for the analysis of data from sensor networks , 2005, Current Opinion in Neurobiology.

[53]  Jitendra Malik,et al.  Normalized Cuts and Image Segmentation , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[54]  Giovanna Citti,et al.  The constitution of visual perceptual units in the functional architecture of V1 , 2014, Journal of Computational Neuroscience.

[55]  Martin Golubitsky,et al.  What Geometric Visual Hallucinations Tell Us about the Visual Cortex , 2002, Neural Computation.

[56]  J. Petitot,et al.  Vers une neurogéométrie. Fibrations corticales, structures de contact et contours subjectifs modaux , 1999 .

[57]  B. Nadler,et al.  Diffusion maps, spectral clustering and reaction coordinates of dynamical systems , 2005, math/0503445.

[58]  J. Kao,et al.  Organization of Intracortical Circuits in Relation to Direction Preference Maps in Ferret Visual Cortex , 1999, The Journal of Neuroscience.

[59]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[60]  Preeti Verghese,et al.  Motion grouping impairs speed discrimination , 2006, Vision Research.

[61]  Pietro Perona,et al.  A Factorization Approach to Grouping , 1998, ECCV.

[62]  J. Daugman Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[63]  Pietro Perona,et al.  Self-Tuning Spectral Clustering , 2004, NIPS.

[64]  Olivier D. Faugeras,et al.  Persistent Neural States: Stationary Localized Activity Patterns in Nonlinear Continuous n-Population, q-Dimensional Neural Networks , 2009, Neural Computation.

[65]  Marina Meila,et al.  Spectral Clustering of Biological Sequence Data , 2005, AAAI.

[66]  D. Talay,et al.  Stochastic simulation and Monte-Carlo methods , 2013 .

[67]  M. Wertheimer Laws of organization in perceptual forms. , 1938 .

[68]  R. Duits,et al.  The explicit solutions of linear left-invariant second order stochastic evolution equations on the 2D-Euclidean motion group , 2007 .

[69]  佐藤 健一 Lévy processes and infinitely divisible distributions , 2013 .

[70]  Steven W. Zucker,et al.  Sketches with Curvature: The Curve Indicator Random Field and Markov Processes , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

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

[72]  Dario L. Ringach,et al.  Reverse correlation in neurophysiology , 2004, Cogn. Sci..

[73]  U. Eysel,et al.  Cellular organization of reciprocal patchy networks in layer III of cat visual cortex (area 17) , 1992, Neuroscience.

[74]  A. Sarti,et al.  Neuromathematics of Vision , 2014 .

[75]  Remco Duits,et al.  Numerical Approaches for Linear Left-invariant Diffusions on SE(2), their Comparison to Exact Solutions, and their Applications in Retinal Imaging , 2014, Numerical Mathematics: Theory, Methods and Applications.