Team NeuroMathComp

Overall Objectives
Scientific Foundations
New Results
Other Grants and Activities

Section: New Results

Visual perception modeling

A new twist on the ring model of orientation perception

Keywords : Stationary solutions, neural field equation, bifurcation, Leray-Schauder degree, hypercolumn, ring model.

Participants : Olivier Faugeras, Romain Veltz.

Our goal is to understand the dynamics of the cortical states of parts of the primate visual cortex when stationary (independent of time) stimuli are presented. A first step to achieve this goal is to understand the stationary cortical states. We do this in the framework of a mesoscopic neural network model also called a neural mass model. These neural mass models have been used to describe the activity of neural populations that are found in the visual cortex of primates. They feature stationary solutions, when submitted to a stationary input. These solutions depend quite sensitively on such parameters of the model as the stiffness of the nonlinearity and the contrast of the external input. We characterize this sensitivity by using degree theory and bifurcation theory in the context of functional, in particular infinite dimensional, spaces. The joint use of these two theories allows us to make new detailed predictions about the global and local behaviours of the solutions. We apply these results to the study of a neural mass model of a cortical hypercolumn of orientation sensitive neurons called the ring model [47] .

This work has appeared in Neuroimage

This work was partially funded by the ERC advanced grant NerVi number 227747.

Hyperbolic planforms in relation to visual edges and textures perception

Keywords : Bifurcation theory, pattern formation, hyperbolic geometry, Fuchsian groups, edges, textures, structure tensor.

Participants : Pascal Chossat, Olivier Faugeras.

We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g. optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in previous work to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.

This work has been accepted in Plos Computional Biology [15] and is available on arXiv, [34] (in press)

Model and large-scale simulator of a biological retina with contrast gain control

Keywords : Retina, simulator, spikes.

Participants : Pierre Kornprobst [ correspondant ] , Adrien Wohrer.

This work was partially supported by the EC IP project FP6-015879, FACETS and the Fondation d'Entreprise EADS.

Precise, integrated models of retinal processing are relatively rare in the visual neuroscience community. Also, the models which do exist are not widely used as input to higher level models of visual processing, because potential users are generally not convinced of the need to use such a detailed model. Instead, modelers of thalamo-cortical areas often use over-simplified retina models, because they either ignore subtle features of retinal processing, or do not wish to spend time on re-implementing an existing retina model. These considerations led Adrien Wohrer, during his PhD  [51] , us to implement a retina simulation platform. This research was part of our lab's contribution to the FACETS European research project. The resulting simulator, termed Virtual Retina and distributed as an open-source software (See section 5.1 ), intends to fulfill the requirements of thalamo-cortical modelers through three particular points: Increased biological precision, Large-scale simulations and Convenient usage.

The underlying model is mostly state-of-the-art, with formulations adapted to large-scale simulation and nonlinearities which include Y cells, spike generation and an original model for contrast gain control. We insured ourselves of its good behavior by reproducing different experimental measurements on real ganglion cells, from the literature.

Contrast gain control, more precisely, has been implemented in an original framework (although bearing similarities with pre-existing models). The proposed mechanism is based on a very simple feedback loop, whose general formulation could also be used elsewhere than in the retina. To better assess its behavior, we have led a mathematical analysis of this feedback loop  [50] . This analysis revealed more arduous than could be expected from the simple form of the system, but we proved some interesting results, which confirm the gain control properties of our feedback loop.

This work has appeared in Journal of Computational Neuroscience  [27]


V1-MT models for action recognition in natural scenes

Keywords : Motion analysis, V1, MT, action recognition, biological motion, motion integration, spiking networks.

Participants : Maria-Jose Escobar, Pierre Kornprobst, Guillaume Masson [ Centre de Recherche en Neurosciences Cognitives, CNRS, FRE2098, 13402 Marseille, France ] , Thierry Viéville.

This work was partially supported by the EC IP project FP6-015879, FACETS and the Fondation d'Entreprise EADS.

In her PhD, Maria-Jose Escobar started from a classical view of the brain areas V1-MT and proposed several "implementations" depending on the objectives. The model is a feedforward model restricted to V1-MT cortical layers and cortical cells cover the visual space with a foveated structure. Interestingly, as observed in neurophysiology, our MT cells not only behave like simple velocity detectors, but also respond to several kinds of motion contrasts.

Our major achievment here was to show how such a bio-inspired model could be the heart of an action recognition model which could have some interest for the computer vision community. Two main results were obtained. The first resultis that better modeling functional properties of the visual system can improve the performance of a algorithmic model. In particular, we showed that reproducing some of the richness of center-surround interactions of MT cells allows recognition rates to be significantly improved. Defining motion maps as our feature vectors, we used a standard classification method on the Weizmann database: We obtained an average recognition rate of 98.9%, which is superior to the recent results by Jhuang et al. [45] . These promising results published at ECCV 2008  [41] encourage us to further develop bio–inspired models incorporating other brain mechanisms and cortical layers in order to deal with more complex videos. Note that this model here was completely analogue. But if one is able to simulate properly a spiking signal out of a visual entry, the second resultis that the analysis of spike trains may bring extra improvement in the performance. Considering a spiking version of the V1-MT model, we showed that the correlation information between neurons tuned for the same orientations also improve motion recognition in a complementray way than just the mean firing rate.

Based on the same motion architecture, we consider now the problem of motion integration for the solution of the aperture problem. We investigate the role of delayed V1 surround suppression, and how the 2D information extracted through this mechanism can be integrated to propose a solution for the aperture problem (see  [42] for some preliminary results).

This work has appeared in ECCV [41] , ICCV  [17]

Functional bio-inspired motion model for motion perception

Keywords : Motion analysis, V1, MT.

Participants : Pierre Kornprobst, Guillaume Masson [ Institut de Neurosciences Cognitives de la Méditerranée, UMR 6193, CNRS, Marseille, France ] , Emilien Tlapale.

This work was partially supported by the EC IP project FP6-015879 (FACETS), the EC ICT project No. 215866 (SEARISE) and the Région Provence-Alpes-Côte d'Azur.

In his PhD, Emilien Tlapale proposed a model of motion integration where diffusion is modulated by luminance. This model incorporates feedforward, feedback and inhibitive lateral connections and is inspired by the motion processing cortical areas. Our main contribution is to propose an anisotropic integration model where motion diffusion is gated by the luminance distribution in the image. The proposed approach produces results compatible with several psychophysical experiments concerning not only the resulting global motion percept but also the motion integration dynamics (see [48] and [35] ). It can also explain several properties of MT neurons regarding the dynamics of selective motion integration, a fundamental property of object motion segmentation.

This work has appeared in Vision Research, available as an INRIA research report [35]


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