INS/Epinext Topical Seminar – Marta Favali (Paris)
“Formal models of visual perception based on cortical architectures”
I will show the integration of geometric models of visual perception with dimensionality reduction techniques. Starting from the model of association fields introduced by Citti and Sarti , which gives a justification of perceptual completion based on the functionality of the primary visual cortex (V1), it is possible to model the cellular connectivity by solving systems of stochastic differential equations as described in  and , obtaining the probability density that is the probability of connection between simple cells in V1 . Starting from these kernels, the problem of grouping is faced by means of spectral analysis of suitable affinity matrices [2,7]. For the numerical simulations, I have consider particularly Kanizsa figures as clear examples of problems of visual perception , and retinal images, to afford problems of grouping during the tracking of blood vessels . Finally I will show a comparison between the results obtained through these models with functional data fMRI, in order to afford the problem of identification and reconstruction of images from fMRI activity [3,6,8].
 D. Barbieri, G. Citti, G. Cocci, A. Sarti, A cortical-inspired geometry for contour perception., 2013.
 G. Citti and A. Sarti, A cortical based model of perceptual completion in the roto-translation space., Journal of Mathematical Imaging and Vision, 24(3):307-326, 2006.
 K. N. Kay, T. Naselaris, R. J. Prenger, and J. L. Gallant. Identifying natural images from human brain activity. Nature, 452(7185): 352-355, 2008.
 M. Favali, S. Abbasi-Sureshjani, B. H. Romeny, and A. Sarti. Analysis of vessel connectivities in retinal images by cortically inspired spectral clustering. Journal of Mathematical Imaging and Vision, 56(1):158-172, 2016a.
 M. Favali, G. Citti, A. Sarti, Local and global gestalt laws: A neurally based spectral approach, Neural Computation, February 2017, Vol. 29, No. 2, Pages: 394-422.
 T. Naselaris, R. J. Prenger, K. N Kay, M. Oliver, and J. L. Gallant. Bayesian reconstruction of natural images from human brain activity. Neuron, 63(6):902-915, 2009.
 A. Sarti, G. Citti, The constitution of visual perceptual units in the functional architecture of V1, Journal of computational neuroscience, 38(2):285–300, 2015.
 B.Thirion, E. Duchesnay, E. Hubbard, J. Dubois, J. Poline, D. Lebihan, and S. Dehaene. Inverse retinotopy: inferring the visual content of images from brain activation patterns. Neuroimage, 33(4):1104-1116, 2006.
 L.R. Williams, D.W. Jacobs, Stochastic completion fields., ICCV Proceedings, 1995.
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