Local and global gestalt laws: A neurally based spectral approach

A mathematical model of figure-ground articulation is presented, taking into account both local and global gestalt laws. The model is compatible with the functional architecture of the primary visual cortex (V1). Particularly the local gestalt law of good continuity is described by means of suitable connectivity kernels, that are derived from Lie group theory and are neurally implemented in long range connectivity in V1. Different kernels are compatible with the geometric structure of cortical connectivity and they are derived as the fundamental solutions of the Fokker Planck, the Sub-Riemannian Laplacian and the isotropic Laplacian equations. The kernels are used to construct matrices of connectivity among the features present in a visual stimulus. Global gestalt constraints are then introduced in terms of spectral analysis of the connectivity matrix, showing that this processing can be cortically implemented in V1 by mean field neural equations. This analysis performs grouping of local features and individuates perceptual units with the highest saliency. Numerical simulations are performed and results are obtained applying the technique to a number of stimuli.Comment: submitted to Neural Computatio

Local and global gestalt laws: A neurally based spectral approach

This letter presents a mathematical model of figure-ground articulation that takes into account both local and global gestalt laws and is compatiblewith the functional architecture of the primary visual cortex (V1). The local gestalt law of good continuation is described by means of suitable connectivity kernels that are derived from Lie group theory and quantitatively compared with long-range connectivity in V1. Global gestalt constraints are then introduced in terms of spectral analysis of a connectivity matrix derived from these kernels. This analysis performs grouping of local features and individuates perceptual units with the highest salience. Numerical simulations are performed, and results are obtained by applying the technique to a number of stimuli

Modèles formels de la perception visuelle basés sur des architectures corticales

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...L’objectif de cette thèse est de développer des modèles mathématiques de perception visuelle basés sur des architectures corticales et de les appliquer pour reproduire des expériences phénoménologiques ainsi que pour traiter des images naturelles. Nous nous concentrons sur les tâches de vision de bas niveau et nous sommes intéressés par le problème du groupement et de l’individuation des unités perceptives. Nous ferons face au problème de la reconstruction des figures illusoires et de la détection des vaisseaux rétiniens dans les images optiques. Ensuite, nous considérerons le problème du codage et du décodage de l’activité cérébrale du cortex visuel obtenue par Imagerie par Résonance Magnétique fonctionnelle (IRMf). Ceci permet d’estimer la structure du cortex d’un patient spécifique et éventuellement de reconstruire le stimulus visuel de l’activité IRMf, dans une stratégie “de lecture du cerveau”. La distinction entre notre approche et l’état de la littérature consiste à utiliser des modèles neuromathématiques du cortex comme connaissance a priori pour régulariser la structure estimée. Même si c’est un objectif à long terme, nous proposons une première approche pour améliorer les résultats dans ce domaine. L’ensemble du travail de cette thèse a été développé en tenant compte des résultats de la phénoménologie de la perception et des résultats de la neurophysiologie. Dans le domaine de la phénoménologie de la perception, au début du siècle dernier, la théorie de la psychologie de la Gestalt a défini l’intégration des contours et en particulier Wertheimer [1938], Kohler [1947], Kofka [1935] ont défini le regroupement des lois de perception. Celles-ci sont cruciales dans la construction d’objets visuels : les éléments avec des caractéristiques en commun peuvent être regroupés pour former un nouvel objet visuel plus grand. Des expériences psychophysiques ont été proposées pour mesurer les paramètres quantitatifs de ces lois. Un intérêt particulier de cette thèse est le concept de champ d’association introduit par Field et al. [1993] lequel code différents principes de la Gestalt (dont la bonne continuation et la proximité).Ces auteurs ont montré que la co-linéarité de stimulus et la co-circularité jouent un rôle important dans la caractéristique du groupement. Leur étude a montré comment les chances de percevoir un chemin curviligne étaient élevées si l’orientation de ses éléments était tangente à ce chemin. D’autre part, en neurophysiologie, une grande quantité d’expériences confirment que le problème du groupement et de détection des contours est effectué par le cortex visuel primaire (V1) [Hubel, 1995]. Un cadre mathématique, basé sur les instruments différentiels, a été introduit pour formaliser ces résultats. Les premiers modèles géométriques sont dus à Koenderink and van Doorn..

Studio e applicazione di tecniche di riduzione di dimensionalita a modelli geometrici di percezione visiva

La tesi affronta il tema della neuromatematica della visione, in particolare l’integrazione di modelli geometrici di percezione visiva con tecniche di riduzione di dimensionalità. Dall’inizio del secolo scorso, la corrente ideologica della Gestalt iniziò a definire delle regole secondo le quali stimoli visivi distinti tra loro possono essere percepiti come un’unica unità percettiva, come ad esempio i principi di prossimità, somiglianza o buona continuazione. Nel tentativo di quantificare ciò che gli psicologi avevano definito in maniera qualitativa, Field, Hayes e Hess hanno descritto, attraverso esperimenti psicofisiologici, dei campi di associazione per stimoli orientati, che definiscono quali caratteristiche due segmenti dovrebbero avere per poter essere associati allo stesso gruppo percettivo. Grazie alle moderne tecniche di neuroimaging che consentono una mappatura funzionale dettagliata della corteccia visiva, è possibile giustificare su basi neurofisiologiche questi fenomeni percettivi. Ad esempio è stato osservato come neuroni sensibili ad una determinata orientazione siano preferenzialmente connessi con neuroni aventi selettività in posizione e orientazione coerenti con le regole di prossimità e buona continuazione. Partendo dal modello di campi di associazione nello spazio R^2xS^1 introdotto da Citti e Sarti, che introduce una giustificazione del completamento percettivo sulla base della funzionalità della corteccia visiva primaria (V1), è stato possibile modellare la connettività cellulare risolvendo un sistema di equazioni differenziali stocastiche. In questo modo si sono ottenute delle densità di probabilità che sono state interpretate come probabilità di connessione tra cellule semplici in V1. A queste densità di probabilità è possibile collegare direttamente il concetto di affinità tra stimoli visivi, e proprio sulla costruzione di determinate matrici di affinità si sono basati diversi metodi di riduzione di dimensionalità. La fenomenologia del grouping visivo descritta poco sopra è, di fatto, il risultato di un procedimento di riduzione di dimensionalità. I risultati ottenuti da questa analisi e gli esempi applicativi sviluppati si sono rivelati utili per comprendere più nel dettaglio la possibilità di poter riprodurre, attraverso l’analisi spettrale di matrici di affinità calcolate utilizzando i modelli geometrici di Citti-Sarti, il fenomeno percettivo di grouping nello spazio R^2xS^1

Curvature Integration in a 5D Kernel for Extracting Vessel Connections in Retinal Images

Tree-like structures, such as retinal images, are widely studied in computer-aided diagnosis systems for large-scale screening programs. Despite several segmentation and tracking methods proposed in the literature, there still exist several limitations specifically when two or more curvilinear structures cross or bifurcate, or in the presence of interrupted lines or highly curved blood vessels. In this paper, we propose a novel approach based on multi-orientation scores augmented with a contextual affinity matrix, which both are inspired by the geometry of the primary visual cortex (V1) and their contextual connections. The connectivity is described with a 5D kernel obtained as the fundamental solution of the Fokker-Planck equation modeling the cortical connectivity in the lifted space of positions, orientations, curvatures, and intensity. It is further used in a self-tuning spectral clustering step to identify the main perceptual units in the stimuli. The proposed method has been validated on several easy as well as challenging structures in a set of artificial images and actual retinal patches. Supported by quantitative and qualitative results, the method is capable of overcoming the limitations of current state-of-the-art techniques

Hydrogen peroxide localization and antioxidant status in the recovery of apricot plants from European Stone Fruit Yellows

Hydrogen peroxide (H2O2) localization and roles of peroxidases, malondialdehyde and reduced glutathione were compared in leaves of apricot (Prunus armeniaca) plants asymptomatic, European Stone Fruits Yellows (ESFY)-symptomatic and recovered. Nested PCR analysis revealed that Candidatus Phytoplasma prunorum, is present in asymptomatic, symptomatic and recovered apricot trees, confirming previous observations on this species, in which recovery does not seem to be related to the disappearance of phytoplasma from the plant. H2O2was detected cytochemically by its reaction with cerium chloride, which produces electron-dense deposits of cerium perhydroxides. H2O2was present in the plasmalemma of the phloem cells of recovered apricot plant leaves, but not in the asymptomatic or symptomatic material. Furthermore, by labelling apricot leaf tissues with diaminobenzidine DAB, no differences were found in the localization of peroxidases. Protein content in asymptomatic, symptomatic and recovered leaves was not significantly different from one another. In contrast, guaiacol peroxidase activity had the following trend: symptomatic > recovered > asymptomatic, whereas reduced glutathione content followed the opposite trend: asymptomatic > recovered > symptomatic. Moreover, no differences were observed in malondialdehyde concentrations between asymptomatic, symptomatic and recovered leaves. The overall results suggest that H2O2 and related metabolites and enzymes appear to be involved in lessening both pathogen virulence and disease symptom expression in ESFY-infected apricot plants

Activation of Phosphatidylinositol 3-Kinase/Akt and Impairment of Nuclear Factor-κB : Molecular Mechanisms Behind the Arrested Maturation/Activation State of Leishmania infantum-Infected Dendritic Cells

Understanding the complex interactions between Leishmania and dendritic cells (DCs) is central to the modulation of the outcome of this infection, given that an effective immune response against Leishmania is dependent on the successful activation and maturation of DCs. We report here that Leishmania infantum promastigotes successfully infect mouse bone marrow-derived DCs without triggering maturation, as shown by a failure in the up-regulation of CD40 and CD86 expression, and that parasites strongly counteract the lipopolysaccharide-triggered maturation of DCs. A small increase in interleukin (IL)-12 and IL-10 transcription and secretion and a decrease in IL-6 were observed in infected cells. This arrested DC maturation state is actively promoted by parasites because heat-killed or fixed parasites increased cytokine and costimulatory molecule expression. At a molecular level, L. infantum rapidly induced activation of phosphatidylinositol 3-kinase/Akt and extracellular signal-regulated kinase 1/2, whereas no effect was observed in the c-Jun N-terminal kinase and p38 mitogen-activated protein kinase proinflammatory pathways. Moreover, parasites actively promoted cleavage of the nuclear factor-κB p65RelA subunit, causing its impairment. The blockade of phosphatidylinositol 3-kinase/Akt by either treatment of bone marrow-derived DCs with wortmannin or transfection with an Akt dominant-negative mutant resulted in a strong decrease in infection rates, revealing for the first time a crucial role of this pathway on Leishmania engulfment by DCs. Overall, our data indicate that activation of Akt and impairment of nuclear factor-κB are responsible for immunogenicity subversion of L. infantum-infected DCs