Director Field Model of the Primary Visual Cortex for Contour Detection

We aim to build the simplest possible model capable of detecting long, noisy contours in a cluttered visual scene. For this, we model the neural dynamics in the primate primary visual cortex in terms of a continuous director field that describes the average rate and the average orientational preference of active neurons at a particular point in the cortex. We then use a linear-nonlinear dynamical model with long range connectivity patterns to enforce long-range statistical context present in the analyzed images. The resulting model has substantially fewer degrees of freedom than traditional models, and yet it can distinguish large contiguous objects from the background clutter by suppressing the clutter and by filling-in occluded elements of object contours. This results in high-precision, high-recall detection of large objects in cluttered scenes. Parenthetically, our model has a direct correspondence with the Landau - de Gennes theory of nematic liquid crystal in two dimensions.Comment: 9 pages, 7 figure

Real-time lattice boltzmann shallow waters method for breaking wave simulations

We present a new approach for the simulation of surfacebased fluids based in a hybrid formulation of Lattice Boltzmann Method for Shallow Waters and particle systems. The modified LBM can handle arbitrary underlying terrain conditions and arbitrary fluid depth. It also introduces a novel method for tracking dry-wet regions and moving boundaries. Dynamic rigid bodies are also included in our simulations using a two-way coupling. Certain features of the simulation that the LBM can not handle because of its heightfield nature, as breaking waves, are detected and automatically turned into splash particles. Here we use a ballistic particle system, but our hybrid method can handle more complex systems as SPH. Both the LBM and particle systems are implemented in CUDA, although dynamic rigid bodies are simulated in CPU. We show the effectiveness of our method with various examples which achieve real-time on consumer-level hardware.Peer ReviewedPostprint (author's final draft

A feedback model of visual attention

Feedback connections are a prominent feature of cortical anatomy and are likely to have significant functional role in neural information processing. We present a neural network model of cortical feedback that successfully simulates neurophysiological data associated with attention. In this domain our model can be considered a more detailed, and biologically plausible, implementation of the biased competition model of attention. However, our model is more general as it can also explain a variety of other top-down processes in vision, such as figure/ground segmentation and contextual cueing. This model thus suggests that a common mechanism, involving cortical feedback pathways, is responsible for a range of phenomena and provides a unified account of currently disparate areas of research

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335