Similarity and symmetry measures for convex sets based on Minkowski addition

This paper discusses similarity and symmetry measures for convex shapes. Their definition is based on Minkowski addition and the Brunn-Minkowski inequality. All measures considered are invariant under translations; furthermore, they may also be invariant under rotations, multiplications, reflections, or the class of all affine transformations. The examples discussed in this paper allow efficient algorithms if one restricts oneselves to convex polygons. Although it deals exclusively with the 2-dimensional case, many of the theoretical results carry over almost directly to higher-dimensional spaces. Some results obtained in this paper are illustrated by experimental data

ON SYMMETRY: A FRAMEWORK FOR AUTOMATED SYMMETRY DETECTION

Symmetry has weaved itself into almost all fabrics of science, as well as in arts, and has left an indelible imprint on our everyday lives. And, in the same manner, it has pervaded a wide range of areas of computer science, especially computer vision area, and a copious amount of literature has been produced to seek an algorithmic way to identify symmetry in digital data. Notwithstanding decades of endeavor and attempt to have an efficient system that can locate and recover symmetry embedded in real-world images, it is still challenging to fully automate such tasks while maintaining a high level of efficiency. The subject of this thesis is symmetry of imaged objects. Symmetry is one of the non-accidental features of shapes and has long been (maybe mistakenly) speculated as a pre-attentive feature, which improves recognition of quickly presented objects and reconstruction of shapes from incomplete set of measurements. While symmetry is known to provide rich and useful geometric cues to computer vision, it has been barely used as a principal feature for applications because figuring out how to represent and recognize symmetries embedded in objects is a singularly difficult task, both for computer vision and for perceptual psychology. The three main problems addressed in the dissertation are: (i) finding approximate symmetry by identifying the most prominent axis of symmetry out of an entire region, (ii) locating bilaterally symmetrical areas from a scene, and (iii) automating the process of symmetry recovery by solving the problems mentioned above. Perfect symmetries are rare in the extreme in natural images and symmetry perception in humans allows for qualification so that symmetry can be graduated based on the degree of structural deformation or replacement error. There have been many approaches to detect approximate symmetry by searching an optimal solution in a form of an exhaustive exploration of the parameter space or surmising the center of mass. The algorithm set out in this thesis circumvents the computationally intensive operations by using geometric constraints of symmetric images, and assumes no prerequisite knowledge of the barycenter. The results from an extensive set of evaluation experiments on metrics for symmetry distance and a comparison of the performance between the method presented in this thesis and the state of the art approach are demonstrated as well. Many biological vision systems employ a special computational strategy to locate regions of interest based on local image cues while viewing a compound visual scene. The method taken in this thesis is a bottom-up approach that causes the observer favors stimuli based on their saliency, and creates a feature map contingent on symmetry. With the help of summed area tables, the time complexity of the proposed algorithm is linear in the size of the image. The distinguished regions are then delivered to the algorithm described above to uncover approximate symmetry

Deep learning of brain asymmetry digital biomarkers to support early diagnosis of cognitive decline and dementia

Early identification of degenerative processes in the human brain is essential for proper care and treatment. This may involve different instrumental diagnostic methods, including the most popular computer tomography (CT), magnetic resonance imaging (MRI) and positron emission tomography (PET) scans. These technologies provide detailed information about the shape, size, and function of the human brain. Structural and functional cerebral changes can be detected by computational algorithms and used to diagnose dementia and its stages (amnestic early mild cognitive impairment - EMCI, Alzheimer’s Disease - AD). They can help monitor the progress of the disease. Transformation shifts in the degree of asymmetry between the left and right hemispheres illustrate the initialization or development of a pathological process in the brain. In this vein, this study proposes a new digital biomarker for the diagnosis of early dementia based on the detection of image asymmetries and crosssectional comparison of NC (normal cognitively), EMCI and AD subjects. Features of brain asymmetries extracted from MRI of the ADNI and OASIS databases are used to analyze structural brain changes and machine learning classification of the pathology. The experimental part of the study includes results of supervised machine learning algorithms and transfer learning architectures of convolutional neural networks for distinguishing between cognitively normal subjects and patients with early or progressive dementia. The proposed pipeline offers a low-cost imaging biomarker for the classification of dementia. It can be potentially helpful to other brain degenerative disorders accompanied by changes in brain asymmetries

Object Recognition

Vision-based object recognition tasks are very familiar in our everyday activities, such as driving our car in the correct lane. We do these tasks effortlessly in real-time. In the last decades, with the advancement of computer technology, researchers and application developers are trying to mimic the human's capability of visually recognising. Such capability will allow machine to free human from boring or dangerous jobs

Traitement des configurations spatiales dans le cortex visuel chez le primate non-humain

Le traitement des configurations spatiales est un mécanisme qui intervient en permanence au sein du cortex visuel. Dans ce monde emplit de régularités qui est le nôtre, il tient une place prépondérante dans l'analyse des objets de notre environnement en nous permettant d'établir des relations spatiales entre des ensembles d'éléments pour aboutir à une perception globale. Si certaines caractéristiques de ces mécanismes ont été étudiés chez les primate humain et non-humain, les observations issues de ces études ont été majoritairement portées par des approches différentes dont les méthodes non-invasives en neuroimagerie sont privilégiées chez l'humain et les méthodes plus invasives tel que l'électrophysiologie sont favorisées chez le singe. Bien qu'elles soient un support critique dans la compréhension des mécanismes neuronaux, les connaissances issues d'enregistrements unitaires chez le singe ne peuvent être transposées à l'humain qu'une fois l'identification d'homologies et de différences fonctionnelles établie à partir des mêmes approches expérimentales. Pour ce faire, nous proposons dans cette thèse de répondre aux besoins d'études comparatives entre les deux espèces dans le cadre du traitement visuel des configurations spatiales portant sur le traitement de la symétrie et le traitement configural des visages par une approche en IRMf. Une première étude menée en collaboration avec des chercheurs de l'Université de Stanford nous a permis d'étudier les réponses à des stimuli texturaux englobant des motifs de symétrie chez le macaque. Nous avons pu mettre en évidence (1) un réseau cortical de traitement de la symétrie par rotation similaire entre les primates humains et non-humains, (2) des réponses augmentant de manière paramétrique avec l'ordre de symétrie présenté (n rotations) (3) un réseau similaire de traitement de la symétrie par rotation et par réflexion chez le macaque (4) des réponses plus fortes pour des motifs symétriques à deux axes (horizontale et verticale) plutôt qu'un seul axe (horizontal). Nous avons ainsi observé que les réponses à la symétrie chez le macaque débutaient au-delà de V1, dans un réseau comprenant les aires V2, V3, V3A, V4 semblablement à l'humain mais également des réponses paramétriques à l'ordre de symétrie par rotation dans les aires V3, V4 et PITd tout comme reporté chez les sujets humains. En somme, l'ensemble de ces résultats ont mis en évidence le réseau cortical du traitement de la symétrie jusqu'alors jamais observé chez le macaque, supporté par des aires visuelles homologues à celles de l'humain. Ces résultats ouvrent de nouvelles pistes quant à la compréhension des mécanismes neuronaux unitaires par des approches plus invasives chez le singe, tout particulièrement dans l'aire V3 qui semble jouer un rôle important dans le traitement sophistiqué des paramètres de configurations spatiales. La secondé étude de ce projet de thèse visait à étudier les mécanismes de reconnaissance de l'identité faciale chez le singe à travers l'orientation configurale des visages porté par l'objectif de réaliser une comparaison inter-espèces du traitement holistique des visages. S'il est largement admis que l'humain est un expert de l'identification des visages dont les mécanismes dépendent de l'orientation dans laquelle ils sont présentés, les résultats sont bien plus contradictoires chez le singe. Pour résoudre ces contradictions, nous avons mis en place un protocole innovant visant à mesurer l'effet d'inversion chez les deux espèces qui ne nécessitait ni entrainement ni tâche comportementale. Cette étude menée en collaboration avec B. Rossion demeure en cours d'acquisition. Néanmoins, les données pourraient fournir des preuves de mécanismes fonctionnels distincts entre celles-ci, appelant à une potentielle réévaluation de l'utilisation du macaque dans l'étude et la compréhension des processus de reconnaissance de l'identité faciale chez l'humain.The processing of spatial configurations is a mechanism that constantly intervenes within the visual cortex. In this world full of regularities that are ours, it holds a prominent place in the analysis of objects in our environment, allowing us to establish spatial relationships between sets of elements to reach a global perception. While characteristics of these mechanisms have been studied in human and non-human primates, the resulting observations depend on different methodologies. In human studies, non-invasive neuroimaging methods are privileged, while more invasive technics (i.e electrophysiology) are favored in monkeys. Despite being critical in understanding neuronal mechanisms, outcomes from unit recordings in monkeys can only be transposed to humans once the identification of functional homologies and differences are established from the same experimental approaches. Tn this thesis, we propose to meet the needs of comparative studies between the two species within the visual treatment of spatial configurations framework relating to the processing of symmetry and the configural processing of faces by an fMRI approach. A first study conducted in collaboration with researchers at Stanford University allows us to investigate the responses to textural stimuli encompassing patterns of symmetry in the macaque brain. The study demonstrates (1) a similar cortical rotational symmetry processing network between human and non-human primates (2) responses increasing parametrically with the order of symmetry presented (n rotations) (3) a similar network for processing of rotational and reflection symmetry in the macaque (4) stronger responses for symmetrical patterns with two axes (horizontal and vertical) rather than a single axis (horizontal). We also observe that the responses to symmetry in the macaque begin beyond V1, in a network comprising the areas V2, V3, V3A, V4 similar to humans but also parametric responses to the order of rotation in symmetry in areas V3, V4, and PITd as reported in human subjects. Overall, all of these results highlight the cortical network of symmetry processing never observed in macaques so far, supported by visual areas homologous to those of humans. These results open up new possibilities for the understanding of unitary neuronal mechanisms by more invasive approaches in monkeys, especially in the V3 area which seems to play an important role in the sophisticated processing of spatial configuration parameters. The second study of this thesis project aims to investigate the mechanisms of facial identity recognition in monkeys through the configural orientation of faces, and carry out an interspecies comparison of holistic facial processing. It is widely accepted that humans are experts at identifying faces whose mechanisms depend on the orientation in which they are presented. However, results are much more contradictory in the monkey. To resolve these contradictions, we implement an innovative protocol to measure the face inversion effect in the two species that require no training or behavioral tasks. This study, conducted in collaboration with B. Rossion, is still in progress. Nonetheless, the futur data could provide evidence of distinct functional mechanisms between human and non-human species, calling for a potential reassessment of the use of the macaque in the study and understanding of facial identity recognition processes in humans

On symmetry in visual perception

This thesis is concerned with the role of symmetry in low-level image segmentation. Early detection of local image properties that could indicate the presence of an object would be useful in segmentation, and it is proposed here that approximate bilateral symmetry, which is common to many natural and man made objects, is a candidate local property. To be useful in low-level image segmentation the representation of symmetry must be relatively robust to noise interference, and the symmetry must be detectable without prior knowledge of the location and orientation of the pattern axis. The experiments reported here investigated whether bilateral symmetry can be detected with and without knowledge of the axis of symmetry, in several different types of pattern. The pattern properties found to aid symmetry detection in random dot patterns were the presence of compound features, formed from locally dense clusters of dots, and contrast uniformity across the axis. In the second group of experiments, stimuli were designed to enhance the features found to be important for global symmetry detection. The pattern elements were enlarged, and grey level was varied between matched pairs, thereby making each pair distinctive. Symmetry detection was found to be robust to variation in the size of matched elements, but was disrupted by contrast variation within pairs. It was concluded that the global pattern structure is contained in the parallelism between extended, cross axis regions of uniform contrast. In the third group of experiments, detection performance was found to improve when the parallel structure was strengthened by the presence of matched strings, rather than pairs of elements. It is argued that elongation, parallelism, and approximate alignment between pattern constituents are visual properties that are both presegmentally detectable, and sufficient for the representation of global symmetric structure. A simple computational property of these patterns is described

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity