Mathematical Models of Visual Perception Based on Cortical Architectures

We present a mathematical model of figure-ground articulation, which takes into account gestalt laws and is compatible with the functional architecture of the primary visual cortex (V1) to obtain low-level object segmentation. Connectivity kernels, derived from Lie group theory, are used to describe the gestalt law of good continuation. The spectral analysis of connectivity matrix derived from these kernels allows to individuates perceptual units with the highest saliency. Some applications of this model to the problem of individuation of perceptual units in illusory figures are presented, as clear examples of problems of visual perception.

[1]  A. Sarti,et al.  From neural oscillations to variational problems in the visual cortex , 2003, Journal of Physiology-Paris.

[2]  S. Zucker,et al.  The Curve Indicator Random Field: Curve Organization Via Edge Correlation , 2000 .

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

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

[5]  Michael Felsberg,et al.  Image Analysis and Reconstruction using a Wavelet Transform Constructed from a Reducible Representation of the Euclidean Motion Group , 2007, International Journal of Computer Vision.

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

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

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

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

[10]  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.

[11]  Chisachi Kato,et al.  Visualization of aerodynamic noise source in the wake of a rotating cylinder , 2007, J. Vis..

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

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

[14]  R. Duits,et al.  Left-invariant parabolic evolutions on SE(2) and contour enhancement via invertible orientation scores. Part II: Non-linear left-invariant diffusions on invertible orientation scores , 2010 .

[15]  R. Duits,et al.  Left-invariant parabolic evolutions on SE(2) and contour enhancement via invertible orientation scores. Part I: Linear left-invariant diffusion equations on SE(2) , 2010 .

[16]  Desmond J. Higham,et al.  An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations , 2001, SIAM Rev..

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

[18]  Giovanna Citti,et al.  Cortical Spatiotemporal Dimensionality Reduction for Visual Grouping , 2014, Neural Computation.

[19]  Jean-Paul Gauthier,et al.  Anthropomorphic Image Reconstruction via Hypoelliptic Diffusion , 2010, SIAM J. Control. Optim..

[20]  Giovanna Citti,et al.  The symplectic structure of the primary visual cortex , 2008, Biological Cybernetics.

[21]  L. Florack,et al.  Evolution equations on Gabor transforms and their applications , 2011, 1110.6087.

[22]  Giovanna Citti,et al.  Image Completion Using a Diffusion Driven Mean Curvature Flowin A Sub-Riemannian Space , 2008, VISAPP.

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

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

[25]  S. Zucker,et al.  Differential Geometry from the Frenet Point of View: Boundary Detection, Stereo, Texture and Color , 2006, Handbook of Mathematical Models in Computer Vision.

[26]  B. H. Romeny,et al.  Invertible Orientation Scores as an Application of Generalized Wavelet Theory , 2007, Pattern Recognition and Image Analysis.

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

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

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