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Are cortical feature maps complete?| old_uid | 19886 |
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| title | Are cortical feature maps complete? |
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| start_date | 2021/12/07 |
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| schedule | 14h30-16h30 |
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| online | no |
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| summary | One of the most studied neural structures in brain’s visual cortex is area V1, where neurons perform a wavelet-like analysis that is generally considered to be associated with the group of rotations and translations of the plane. It is indeed possible to model part of the (classical) behavior of V1 cells in terms of a projection of the image onto one, or more, orbits of that group, and consequently to associate to each neuron in V1 a parameter of the group. However, as a consequence of the physical displacement of neurons onto the characteristic geometric structures of cortical feature maps, this modelling group is not fully represented in V1. A natural question arising from this model is whether the missing part of the group, and of the corresponding wavelet coefficients, has perceptual consequences, or if, on the contrary, it is possible to recover or estimate in some stable way the missing information. The purpose of this talk is to propose an iterative mechanism able to reconstruct the exact image, or equivalently the full group wavelet transform, starting from the knowledge of only the coefficients stored on pinwheel-shaped subsets of the group. The iteration is based on the group reproducing kernel, and on the projection onto the sampling surface. We will show an elementary proof of convergence in the finite setting, and discuss numerical simulations on natural images. |
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| responsibles | Sarti, Petitot, Nadal |
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