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Simple cells receptive fields and orientation preference maps:
A Lie group approach for the analysis of fundamental morphologies of V1 (Work in collaboration with G. Citti, G. Sanguinetti and A. Sarti)| old_uid | 14748 |
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| title | Simple cells receptive fields and orientation preference maps:
A Lie group approach for the analysis of fundamental morphologies of V1 (Work in collaboration with G. Citti, G. Sanguinetti and A. Sarti) |
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| start_date | 2014/12/02 |
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| schedule | 14h30-16h30 |
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| online | no |
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| location_info | salle de conférence |
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| summary | Simple cells classical receptive fields can be accurately modeled by Gaussian Gabor functions. However, this a-priori 6 parameters family (including positions, frequencies and scales) is represented on an essentially two dimensional cortical layer. This implies that only a subset of the parameter space is actually available to the linear filtering of visual stimuli performed by V1.
We will first discuss a fundamental property of the family of implemented parameters, namely the distribution of the shape index, which measures the number of on and off regions of receptive fields by relating frequencies to scales. We will show that it can be effectively quantified in terms of the uncertainty principle associated to the complementary symmetries of the parameter space, that are given by the group of translations and rotations of the Euclidean plane SE(2). The main argument is the effort to keep the highest possible resolution in the detection of position and orientation allowed by the dimensional constraint.
Then we will enter a more detailed study of the SE(2) group, and show that its irreducible representations can be used to provide an accurate model for orientation preference maps. In particular, we will see that the associated continuous wavelet transform allows to effectively reproduce the maps of activation of V1 in response to gratings, whenever the mother wavelet is a fundamental minumum of the uncertainty principle and the analyzed signal is white noise. In this case we can also prove that the wavelet transform is injective, which implies uniqueness of the white noise source, despite not being square integrable. Moreover, its complex regularity inherited by the uncertainty principle allows to obtain it as the two dimensional Bargmann transform of a purely directional signal, hence characterizing all possible configurations of such activated regions. |
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| responsibles | Citti, Nadal, Faugeras |
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