Mattia Galeotti
@matematica.unibo.it
Postdoc, Dipartimento di Matematica
Università di Bologna
RESEARCH INTERESTS
differential geometry, geometric models of the visual cortex, topos theory
Scopus Publications
Scholar Citations
Scholar h-index
Scopus Publications
Mattia Galeotti, Giovanna Citti, and Alessandro Sarti
Springer Nature Switzerland
Mattia Galeotti, Giovanna Citti, and Alessandro Sarti
Springer Science and Business Media LLC
AbstractWe introduce a model for image morphing in the primary visual cortex V1 to perform completion of missing images in time. We model the output of simple cells through a family of Gabor filters and the propagation of the neural signal accordingly to the functional geometry induced by horizontal connectivity. Then we model the deformation between two images as a path relying two different outputs. This path is obtained by optimal transport considering the Wasserstein distance geodesics associated to some probability measures naturally induced by the outputs on V1. The frame of Gabor filters allows to project back the output path, therefore obtaining an associated image stimulus deformation. We perform a numerical implementation of our cortical model, assessing its ability in reconstructing rigid motions of simple shapes.
Mattia Galeotti
Cellule MathDoc/CEDRAM
Mattia Galeotti
Elsevier BV
Mattia Galeotti and Sara Perna
World Scientific Pub Co Pte Lt
In this paper, we investigate the construction of two moduli stacks of Kummer varieties. The first one is the stack [Formula: see text] of abstract Kummer varieties and the second one is the stack [Formula: see text] of embedded Kummer varieties. We will prove that [Formula: see text] is a Deligne-Mumford stack and its coarse moduli space is isomorphic to [Formula: see text], the coarse moduli space of principally polarized abelian varieties of dimension [Formula: see text]. On the other hand, we give a modular family [Formula: see text] of embedded Kummer varieties embedded in [Formula: see text], meaning that every geometric fiber of this family is an embedded Kummer variety and every isomorphic class of such varieties appears at least once as the class of a fiber. As a consequence, we construct the coarse moduli space [Formula: see text] of embedded Kummer surfaces and prove that it is obtained from [Formula: see text] by contracting the locus swept by a particular linear equivalence class of curves. We conjecture that this is a general fact: [Formula: see text] could be obtained from [Formula: see text] via a contraction for all [Formula: see text].