A Model for Image Segmentation in Retina

While traditional feed-forward filter models can reproduce the rate responses of retinal ganglion neurons to simple stimuli, they cannot explain why synchrony between spikes is much higher than expected by Poisson firing [6], and can be sometimes rhythmic [25, 16]. Here we investigate the hypothesis that synchrony in periodic retinal spike trains could convey contextual information of the visual input, which is extracted by computations in the retinal network. We propose a computational model for image segmentation consisting of a Kuramoto model of coupled oscillators whose phases model the timing of individual retinal spikes. The phase couplings between oscillators are shaped by the stimulus structure, causing cells to synchronize if the local contrast in their receptive fields is similar. In essence, relaxation in the oscillator network solves a graph clustering problem with the graph representing feature similarity between different points in the image. We tested different model versions on the Berkeley Image Segmentation Data Set (BSDS). Networks with phase interactions set by standard representations of the feature graph (adjacency matrix, Graph Laplacian or modularity) failed to exhibit segmentation performance significantly over the baseline, a model of independent sensors. In contrast, a network with phase interactions that takes into account not only feature similarities but also geometric distances between receptive fields exhibited segmentation performance significantly above baseline.

[1]  M. Tachibana,et al.  Synchronized retinal oscillations encode essential information for escape behavior in frogs , 2005, Nature Neuroscience.

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

[3]  F. Werblin,et al.  Rapid global shifts in natural scenes block spiking in specific ganglion cell types , 2003, Nature Neuroscience.

[4]  R. Masland Cell populations of the retina: the Proctor lecture. , 2011, Investigative ophthalmology & visual science.

[5]  Alex Arenas,et al.  Synchronization reveals topological scales in complex networks. , 2006, Physical review letters.

[6]  Tim Gollisch,et al.  Rapid Neural Coding in the Retina with Relative Spike Latencies , 2008, Science.

[7]  Joseph J. Atick,et al.  What Does the Retina Know about Natural Scenes? , 1992, Neural Computation.

[8]  D. Ruderman The statistics of natural images , 1994 .

[9]  Stephen A. Baccus,et al.  Segregation of object and background motion in the retina , 2003, Nature.

[10]  U. Feige,et al.  Spectral Graph Theory , 2015 .

[11]  S. Osher,et al.  Total Variation Based Image Cartoon-Texture Decomposition , 2005 .

[12]  Xin Wang,et al.  Exploring the Function of Neural Oscillations in Early Sensory Systems , 2009, Frontiers in neuroscience.

[13]  Kim L. Boyer,et al.  Quantitative measures of change based on feature organization: eigenvalues and eigenvectors , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

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

[15]  M. Newman,et al.  Finding community structure in networks using the eigenvectors of matrices. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  A. Díaz-Guilera,et al.  Synchronization and modularity in complex networks , 2007 .

[17]  Jitendra Malik,et al.  A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[18]  Charless C. Fowlkes,et al.  Contour Detection and Hierarchical Image Segmentation , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Günther Zeck,et al.  Network Oscillations in Rod-Degenerated Mouse Retinas , 2011, The Journal of Neuroscience.

[20]  Iman H. Brivanlou,et al.  Mechanisms of Concerted Firing among Retinal Ganglion Cells , 1998, Neuron.

[21]  R. Leahy,et al.  Modularity-based graph partitioning using conditional expected models. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  R. Masland The tasks of amacrine cells , 2012, Visual Neuroscience.

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

[24]  Xin Wang,et al.  Statistical Wiring of Thalamic Receptive Fields Optimizes Spatial Sampling of the Retinal Image , 2014, Neuron.

[25]  Frank S Werblin,et al.  The retinal hypercircuit: a repeating synaptic interactive motif underlying visual function , 2011, The Journal of physiology.

[26]  W. Singer,et al.  Long-range synchronization of oscillatory light responses in the cat retina and lateral geniculate nucleus , 1996, Nature.

[27]  Leo Grady,et al.  Random Walks for Image Segmentation , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  L. Croner,et al.  Receptive fields of P and M ganglion cells across the primate retina , 1995, Vision Research.

[29]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[30]  W. Singer,et al.  Synchronous oscillations in the cat retina , 1999, Vision Research.

[31]  Michael J. Berry,et al.  Weak pairwise correlations imply strongly correlated network states in a neural population , 2005, Nature.

[32]  W. Gerstner,et al.  The temporal paradox of Hebbian learning and homeostatic plasticity , 2017, Current Opinion in Neurobiology.

[33]  Eero P. Simoncelli,et al.  Testing pseudo-linear models of responses to natural scenes in primate retina , 2016, bioRxiv.

[34]  Xin Wang,et al.  Retinal Oscillations Carry Visual Information to Cortex , 2008, Front. Syst. Neurosci..

[35]  S. W. Kuffler Discharge patterns and functional organization of mammalian retina. , 1953, Journal of neurophysiology.

[36]  Eero P. Simoncelli,et al.  Spatio-temporal correlations and visual signalling in a complete neuronal population , 2008, Nature.

[37]  Eero P. Simoncelli,et al.  Spike-triggered neural characterization. , 2006, Journal of vision.

[38]  T. Ogden,et al.  The oscillatory waves of the primate electroretinogram. , 1973, Vision research.