Geodesic
Geometria differenziale per il completamento percettivo
La Matematica nella società e nella cultura, Série 1, Tome 1 (2008) no. 1, pp. 107-130.

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In questo lavoro richiamiamo alcuni esperimenti classici di psicologia della percezione dovuti a Kanizsa e a Heiss, Fields e Hess, che indicano l'importanza del concetto di direzione nei processi percettivi. Poi presentiamo un modello di corteccia, che descrive la corteccia visiva con strumenti di geometria differenziale e analisi in gruppi di Lie. È basato sulla modellazione di alcuni meccanismi neurali, ed in particolare sulla capacità delle cellule semplici di individuare in ogni punto la direzione dei bordi degli oggetti, e giustifica da un punto di vista microscopico, i fenomeni percettivi precedentemente descritti.
In this paper we recall some classical experiments of cognitivive psycology due to Kanizsa and to Heiss, Fields and Hess, which allow to undestand the role of the orientation and distance in perceptive phenomena. Then we model the visual cortex with instruments of differential geometry and Analysis in Lie groups. The model is based on some neural mechanism, and in particular on the ability of the simple cells of detect at every point of an image the direction of level lines. In this way we justify from a microscopical point of view the perceptive phenomena just described. 
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Citti, G.; Sarti, A. Geometria differenziale per il completamento percettivo. La Matematica nella società e nella cultura, Série 1, Tome 1 (2008) no. 1, pp. 107-130. http://geodesic.mathdoc.fr/item/RIUMI_2008_1_1_1_a5/

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