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Cortical based mathematical models of geometric optical illusions

Abstract : This thesis presents mathematical models for visual perception and deals with such phenomena in which there is a visible gap between what is represented and what we perceive. A phenomenon which drew the interest most is amodal completion, consisting in perceiving a completion of a partially occluded object, in contrast with the modal completion, where we perceive an object even though its boundaries are not present [Gestalt theory, 99]. Such boundaries reconstructed by our visual system are called illusory contours, and their neural processing is performed by the primary visual cortices (V1/V2), [93]. Geometric models of the functional architecture of primary visual areas date back to Hoffman [86]. In [139] Petitot proposed a model of single boundaries completion through constraint minimization, neural counterpart of the model of Mumford [125]. In this setting Citti and Sarti introduced a cortical based model [28], which justifies the illusions at a neural level and provides a neurogeometrical model for V1. Another class of phenomena are Geometric optical illusions (GOIs), discovered in the XIX century [83, 190], arising in presence of a mismatch of geometrical properties between an item in object space and its associated percept. The fundamental idea developed here is these phenomena arise due to a polarization of the connectivity of V1/V2, responsible for the misperception. Starting from [28] in which the connectivity building contours in V1 is modeled as a sub-Riemannian metric, we extend it claiming that in GOIs the cortical response to the stimulus modulates the connectivity of the cortex, becoming a coefficient for the metric. GOIs will be tested through this model.
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Submitted on : Monday, November 13, 2017 - 10:15:14 AM
Last modification on : Thursday, December 10, 2020 - 11:06:36 AM
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  • HAL Id : tel-01633515, version 1


Benedetta Franceschiello. Cortical based mathematical models of geometric optical illusions. Neurons and Cognition [q-bio.NC]. Université Pierre et Marie Curie - Paris VI; Università degli studi (Bologne, Italie). Dipartimento di matematica, 2017. English. ⟨NNT : 2017PA066131⟩. ⟨tel-01633515⟩



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