Formal models of visual perception based on cortical architectures

Abstract : The objective of this thesis is to develop mathematical models of visual perception based on cortical architectures and to apply them to reproduce phenomenological experiments and to process natural images. We primarly focus on low level vision tasks and in particular we are interested in the problem of grouping and of individuation of perceptual units. In this setting we will face the problem of the reconstruction of illusory figures and the detection of retinal vessels in optical images. Then we consider the problem of encoding and decoding of the fMRI signal from in vivo acquired brain activity of visual cortex. This allows to estimate the structure of the cortex of a specific human patient and eventually to reconstruct the visual stimulus from fMRI activity, in a so called “brain reading” strategy. The difference between our approach and the state of the art literature consists in using previously defined neuromathematical models of the cortices as a-priori knowledge to regularise in vivo estimated structure. Even if it is a long term objective, we propose a first approach to improve the results in this field. The entire work of this thesis has been developed taking into account results from phenomenology of perception and results of neurophysiology.In the field of the phenomenology of perception, at the beginning of the last century, the theory of the Gestalt psychology [Wertheimer, 1938, Kohler, 1947, Kofka, 1935] defined the integration of contours and in particular they defined grouping laws underlying perception. These are crucial in the construction of visual objects: points with characteristics in common can be grouped together to form a new visual object. Many psychophysical experiments have been proposed to measure the quantitative parameters of these laws. A particular interest of this thesis is the concept of association fields introduced by Field et al. [1993] which encodes different Gestalt principles (as good continuation, proximity). They showed that stimulus co-linearity and co-circularity play an important role for the feature of grouping. Their study showed how chances of perceiving the curvilinear path were high if the orientation of its features was the one tangent at that point and collapsed as their relative orientation deviated from being tangent...
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Marta Favali. Formal models of visual perception based on cortical architectures. Numerical Analysis [math.NA]. Université Pierre et Marie Curie - Paris VI; Università degli studi (Bologne, Italie). Dipartimento di matematica, 2017. English. ⟨NNT : 2017PA066094⟩. ⟨tel-02105088v1⟩

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