Séminaire de recherche A3SI

Jeudi 11 mai 2017

Atelier doctorants

Kacper Pluta, LIGM, A3SI, ESIEE Honeycomb geometry: Rigid Motions on the Hexagonal Grid Abstract: Euclidean rotations in R^2 are bijective and isometric maps, but they lose generally theseproperties when digitized in discrete spaces. In particular, the topological and geometrical defects of digitized rigid motions on the square grid have been studied. In this context, the main problem is related to the incompatibility between the square grid and rotations; in general, one has to accept either relatively high loss of information or non-exactness of the applied digitized rigid motion. Motivated by these considerations, we study digitized rigid motions on the hexagonal grid. We establish a framework for studying digitized rigid motions in the hexagonal grid---previously proposed for the square grid and known as neighborhood motion maps. This allows us to study non-injective digitized rigid motions on the hexagonal grid and to compare the loss of informationbetween digitized rigid motions defined on the two grids. Marina Vinyes, LIGM, A3SI, IMAGINE Fast column generation for atomic norm regularization Abstract: We consider optimization problems that consist in minimizing a quadratic function under an atomic norm regularization or constraint. In the line of work on conditional gradient algorithms, we show that the fully corrective Frank-Wolfe (FCFW) algorithm - which is most naturally reformulated as a column generation algorithm in the regularized case - can be made particularly efficient for difficult problems in this family by solving the simplicial or conical subproblems produced by FCFW using a special instance of a classical active set algorithm for quadratic programming that generalizes the min-norm point algorithm. Diane Genest, LIGM, A3SI, ESIEE An automated assay for the assessment of cardiac arrest in fish embryo Abstract: Studies on fish embryo models are widely developed in research. They are used in several research field such as drug discovery or environmental toxicology. In this article, we propose an entirely automated assay to detect cardiac arrest in Medaka (Oryzias latipes) based on image analysis. We propose a multi-scale pipeline based on mathematical morphology. Starting from video sequences of entire wells in 24-well plates, we focus on the embryo, detect its heart, and ascertain whether or not the heart is beating based on intensity variation analysis. Our image analysis pipeline only uses commonly available operators. It has a low computational cost, allowing analysis at the same rate as acquisition. From an initial dataset of 3,192 videos, 660 were discarded as unusable (20.7%), 655 of them correctly so (99.25%) and only 5 incorrectly so (0.75%). The 2,532 remaining videos were used for our test. On these, 45 errors were made, leading to a success rate of 98.23%. Bruno Jartoux, LIGM, A3SI, ESIEE




Mnets, epsilon-nets: combinatorics of geometric regions
Abstract: We investigate the behaviour of incidence relations between points and geometric shapes (i.e., geometric set systems). Using recent advances on 'shallow packings', we develop the theory of Mnets. Those are a combinatorial analogue of Macbeath regions in convex geometry. We obtain asymptotically tight bounds on the size of Mnets for common shapes. Our results on Mnets imply all classical bounds on epsilon-nets, a staple of computational geometry.

Mercredi 26 avril 2017

An Adversarial Regularization for Semi-Supervised Training of Structured Output Neural Networks
Mateusz Kozinski, GREYC, Université de Caen
Abstract: My talk is is going to be focused on semi-supervised training of structured-output neural networks. The problem is of broad interest, because training deep neural networks requires large amounts of annotated data, and producing structured annotations is costly. On the other hand, unannotated input data is often cheap to acquire. I will show that this unannotated data can be used for training structured-output models in a semi-supervised scenario. The idea is inspired by the Generative Adversarial Networks, and consists in generating an error signal for the unlabelled data by means of a discriminator neural network. To be source of a useful error signal, the discriminator needs to capture quality of the structured output. This can be achieved by training the discriminator to differentiate between structured outputs obtained for the labelled training data (qualitatively better) and the outputs obtained for unlabelled data, not used for training (qualitatively worse). Initial experiments suggest that this approach may lead to decreasing the volume of labels required to attain a given precision by a significant factor.

Jeudi 30 mars 2017

Homologie algorithmique appliquée aux objets discrets
Aldo Gonzalez Lorenzo, LSIS, Polytech' Marseille
Résumé : La théorie de l'homologie formalise la notion de trou dans un espace. Pour un sous-ensemble de l'espace Euclidien, on définit une séquence de groupes d'homologie, dont leurs rangs sont interprétés comme le nombre de trous de chaque dimension. Ainsi, b0, le rang du groupe d'homologie de dimension zéro, est le nombre de composantes connexes, b1 est le nombre de tunnels ou anses et b2 est le nombre de cavités. Ces groupes sont calculables quand l'espace est décrit d'une façon combinatoire, comme c'est le cas pour les complexes simpliciaux ou cubiques. À partir d'un objet discret (un ensemble de pixels, voxels ou leur analogue en dimension supérieure) nous pouvons construire un complexe cubique et donc calculer ses groupes d'homologie.
Je vais présenter trois approches relatives au calcul de l'homologie sur des objets discrets. En premier lieu, j'introduirai le champ de vecteurs discret homologique, une structure combinatoire généralisant les champs de vecteurs gradients discrets, qui permet de calculer les groupes d'homologie. Cette notion permet de voir la relation entre plusieurs méthodes existantes pour le calcul de l'homologie et révèle également des notions subtiles associés. Je présenterai ensuite un algorithme linéaire pour calculer les nombres de Betti dans un complexe cubique 3D, ce qui peut être utilisé pour les volumes binaires. Enfin, je vais présenter deux mesures (l'épaisseur et la largeur) associées aux trous d'un objet discret, ce qui permet d'obtenir une signature topologique et géométrique plus intéressante que les simples nombres de Betti. Cette approche fournit aussi quelques heuristiques permettant de localiser les trous, d'obtenir des générateurs d'homologie ou de cohomologie minimaux, d'ouvrir et de fermer les trous.

Lundi 27 mars 2017

Approche double dual pour la reconnaissance de courbe polynomiale
Gaëlle Largeteau-Skapin, XLIM, Université de Poitiers
Résumé : Nous proposons une méthode basée sur un espace dual pour reconnaître des courbes polynomiales implicites C(x,y): x^i y^j - B x^k y^l - A = 0 dans des images digitales. Utiliser la pre-image classique (définie dans le cadre de la reconnaissance de droite discrète) amène à intersecter des polygones non-convexes. Pour éviter cela, nous proposons un second espace dual dans lequel nous obtenons des polygones convexes. Nous utilisons ensuite des algorithmes de calcule de ligne transversales et de la programmation linéaire pour résoudre le problème de la reconnaissance.
Le principal avantage de ce travail est que nous transformons le problème de trouver les paramètres A et B de la courbe C(x,y) dont la discrétisation contient l'ensemble de pixel donné en un problème linéaire de calcul de droite transversale à des polygones convexes.
Le modèle discret que nous considérons est le modèle 1-Flake (similaire au modèle Naïf dans la plupart des cas).

Vendredi 3 février 2017

Discrete polynomial curve fitting in the presence of outlier
Akihiro Sugimoto, National Institute of Informatics, Japan
Abstract: This presentation deals with the problem of fitting a discrete polynomial curve to 2D data in the presence of outliers. We use a discrete polynomial curve model achieving connectivity in the discrete space. We formulate the fitting as the problem to find parameters of this model maximizing the number of inliers i.e., data points contained in the discrete polynomial curve. We propose a method guaranteeing inclusion-wise maximality of its obtained inlier set.

Jeudi 19 janvier 2017

Surgical Data Science for Decision Making Support and Knowledge Discovery in Deep Brain Stimulation
Pierre Jannin, MediCIS, INSERM, Université de Rennes
Abstract:High frequency and continuous electrical stimulation of deep brain structures (DBS) has been demonstrated as an efficient minimally invasive surgical treatment for motor related diseases and recently for severe neuropsychological diseases. The quality of the clinical improvement, as well as the occurrence of motor, neuropsychological or psychiatric side effects strongly depend on the location of the electrodes. However, even though DBS provides excellent clinical results, there is no consensus in the neurosurgical community about the optimal location of the area to be stimulated as well as corresponding electrical parameters. It is also expected that this is different among patients. The choice of the best target is usually based on a combination of patient specific and generic anatomical, functional and clinical information and knowledge. Patient specific data and information are based on multimodal medical images, clinical and electrophysiological data, whereas most of the generic information and knowledge are implicit. To make it explicit, some groups suggested digital atlases; some atlases were computed from population analysis.

In this talk, I will introduce the surgical data science approach we studied, implemented and validated in the context of Deep Brain Stimulation. The main characteristics of our approach include: 1) computation of pre, intra and post-operative patient-specific models from multimodal medical images, clinical and electrophysiological data, 2) analysis of patient population for outlining common patterns and outcome, and 3) computation of generic models from population analysis to help pre, intra and post operative decisions and actions. It aims both at assisting surgical planning, performance and post operative programming and evaluation, as well as better understanding neurological phenomenon for knowledge discovery. Our approach is based on numeric and symbolic surgical data analysis. The clinical motivation is to improve targeting and post operative evaluation for better outcome and reduced side effects.

Lundi 9 janvier 2017

Multi A(ge)nt Systems
Alfred M. Bruckstein, Ollendorff Professor of Science, The Technion
Abstract: We discuss a paradigm of ant-robotics, based on ideas from ant-colony behavior. Lots of identical agents in interaction can achieve amazing feats due to carefully programmed rules of local interaction. We shall present some of the mathematical methods for analysis of such multi-agent systems.

Jeudi 8 décembre 2016

Atelier doctorants

A Deep Metric for Multimodal Registration
Martin Simonovsky, LIGM, A3SI, IMAGINE
Abstract: Multimodal registration is a challenging problem in medical imaging due the high variability of tissue appearance under different imaging modalities. The crucial component here is the choice of the right similarity measure. We make a step towards a general learning-based solution that can be adapted to specific situations and present a metric based on a convolutional neural network. Our network can be trained from scratch even from a few aligned image pairs. The metric is validated on intersubject deformable registration on a dataset different from the one used for training, demonstrating good generalization. In this task, we outperform mutual information by a significant margin.

Towards PCI procedure modelling: empty catheter segmentation
Ketan Bacchuwar, LIGM, A3SI, ESIEE
Abstract: We present empty guiding catheter segmentation, a preliminary result in the development of a complete framework of Percutaneous Coronary Intervention (PCI) procedure modelling (analysis of image stream in term of clinical activities). In number of clinical situations, the guiding catheter, a commonly visible landmark is empty and appears as a low contrasted structure with two parallel and partially disconnected edges. To segment it, we work on the level-set (non-linear) scale-space of image, the min tree, to extract curve blobs. We then propose a novel structural scale-space, a hierarchy built on these curve blobs. The deep connected component, i.e. the cluster of curve blobs on this hierarchy, that maximizes the likelihood to be an empty catheter is retained as final segmentation. We develop a novel structural scale-space to segment out a structured object, the empty catheter in challenging imaging situations where the information content is very sparse.

An efficient implementation of geometric algebra to handle high and low dimensional spaces
Stéphane Breuils, LIGM, A3SI, ESIEE
Abstract: Geometric algebras can be understood as a set of very intuitive tools to represent, construct and manipulate geometric objects. There already exists some methods to represent and compute geometric algebra elements but none of them can handle efficiently high dimensional spaces. During this talk, I will present a method based on binary trees and table to efficiently compute Geometric algebra. The key feature of our approach is to optimize the complexity of the products. In order to achieve this, we exploit the particular structure of geometric algebra products. The resulting implementations are usable for any dimensions, including high dimensions. The tests show that our implementation is faster for high dimensional spaces and at least as fast as for low dimensional spaces.

Jeudi 1 décembre 2016

Distributed modeling of visual perception
Chaohui Wang, UPEM, A3SI, LIGM
Abstract: Distributed modeling, which formulates the problem of interest via a sum of energy terms each involving a small subset of variables, is one main methodology for addressing visual perception problems. We have been investigating such a methodology, particularly in the contexts of joint modeling for complementary tasks, 3D shape matching and inference, and developed distributed models for several important 2D, 2.5D, 3D, 2D-3D visual perception problems, including object detection, segmentation, tracking, 3D shape matching, 3D scene/surface inference and illumination estimation, etc. Recently, following the success of deep modeling in related research fields, we have been exploring the deep-learning-based techniques within the distributed modeling methodology for addressing challenging problems like occlusion boundary detection. In this talk, I will present the related research via several representative works.

Jeudi 17 novembre 2016

Illuminating a convex body
Márton Naszódi, EPFL (Suisse), Eötvös University (Hongrie)
Abstract: A light source p in the d-dimensional real space illuminates a boundary point b of a convex body K, if the ray emanating from b in the direction pb intersects the interior of K. As is easy to see, the minimum number of light sources needed so that each boundary point is illuminated is the same as the minimum number of translates of the interior of K that cover K.
A famous open problem in discrete geometry is the Boltjanskii-Hadwiger conjecture, according to which, for every convex body, this number is at most 2d. In this introductory talk, we will discuss different approaches to the problem, and its relationship with other questions.

Jeudi 10 novembre 2016

Graph-based deformable image registration: an application for optimized estimation of diffusion in DW-MR
Evangelia Zacharaki, Center for Visual Computing, CentraleSupelec - Galen Team, INRIA, Paris
Abstract: During the past two decades, much of the research in image analysis was devoted to image registration, producing a large number of free software solutions. Most applications, mainly in the biomedical domain, require deformable image registration, in which a nonlinear dense transformation is sought (as opposed to a linear or global one) due to the fact that almost all anatomical parts, or organs of the human body are deformable structures. In this talk, a joint deformable registration and diffusion modeling approach will be presented, which aims to improve estimation of the apparent diffusion coefficient (ADC) in diffusion-weighted (DW) magnetic resonance imaging (MRI). Over the last years, ADC computed from DW-MRI has become an important imaging biomarker for evaluating and managing patients with neoplastic or cerebrovascular disease. Standard methods for the calculation of ADC ignore the presence of noise and motion between successive (in time) DW-MR images acquired by changing the (operator-selected) b-value parameter. In order to accurately quantify the diffusion process during image acquisition, a registration method is introduced that is based on a high-order Markov Random Fields (MRF) formulation. In this formulation, inference is expressed as a (undirected) graph optimization problem acting on a predefined graph structure associated with a discrete number of variables.

Jeudi 27 octobre 2016

Représentation compacte d'image pour l'indexation par le contenu
Romain Negrel, ESIEE, LIGM
Résumé : Depuis plusieurs années, le nombre d'images stockées dans les bases d'images augmente rapidement. Il est aujourd'hui impossible d'effectuer une indexation manuelle de ces images et cela limite fortement l'exploitation de ces bases. Pour indexer et rendre accessible facilement les images, des méthodes d'indexation automatique et d'aide à l'indexation par le contenu se sont développées depuis plusieurs années.
Dans ce séminaire nous nous intéressons aux représentations vectorielles d'image basées sur l'agrégation de descripteurs locaux (HOG, SIFT, SURF, ...) et la réduction de dimension de ces signatures d'images.
La première partie de ce séminaire est consacrée aux signatures d'images et plus particulièrement à la signature VLAT (Vectors of Locally Aggregated Tensors) et ces améliorations permettent de la rendre plus discriminante tout en réduisant sa dimension.
La deuxième partie de ce séminaire est consacrée aux méthodes de réduction de dimension par projection linéaire et plus particulièrement à une méthode non supervisée basée sur la conservation du produit scalaire ainsi qu'une amélioration de cette méthode pour obtenir des projecteurs creux à faible cout.
Les performances de ces signatures sont évaluées en classification (VOC 2007 dataset) et en recherche par similarité (Holidays dataset).

Jeudi 15 septembre 2016

Using statistics to justify vision algorithms
Michael Lindenbaum, Technion, Israel
Abstract: Many of the most successful vision algorithms are based on clever heuristics. We study two algorithms and show that, under certain statistical models, they correspond to common statistical decisions. The first is the local variation (LV) algorithm (LV) (Efficient graph-based image segmentation, by Felzenszwalb and Huttenlocher). We show that algorithms similar to LV can be devised by applying different statistical models and decisions, some of which are based on statistics of natural images and on a hypothesis testing decision. We we denote these algorithms probabilistic local variation (pLV). The best pLV algorithm, which relies on censored estimation, yields state-of-the-art results while preserving the computational complexity of the LV algorithm. We then turn to the SIFT matching algorithm (Object recognition from local scale-invariant features, by Lowe). Here we study the ratio criterion and show that this criterion could be a result of using various statistical decisions and, in particular, could correspond to minimizing the conditional probability of a false match. In both cases, the analysis provides further theoretical justification and well-founded explanations for the unexpected high performance of these two algorithms. It also provides statistically based versions of these algorithms that are at least as good as, and sometimes better than, the originals.
Joint work with Michael Baltaxe, Peter Meer, Avi Kaplan, and Tammy Avraham.

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