Séminaire de recherche A3SI
(2011-2012)

Lundi 2 juillet 2012

Fusion and Enrichment of Medical Imaging for High Quality Diagnosis and Treatment (FERMI)
Tadashi Yamaguchi - Research Center for Frontier Medical Engineering, Chiba University, Japan
Abstract: Innovation of medical imaging in many aspects is required in order to improve the quality of diagnosis and treatment. FERMI project is proceeding the innovation in terms of new acquisition and improvement of high dimension, high definition, quantification of physical or physiological parameters of biological object and integration of multimodal medical images. This project consists of three sub projects: (1) development of essential imaging technology in medicine, (2) dynamic imaging technology, and (3) integration of spatial information of medicine. In this talk, brief overviews of FERMI project including the statistical echo analysis method for a quantitative diagnosis, the measurement and the estimation of organ motions using MRI and CT, the treatment navigation for brain and fetus surgery and the augmented reality for laparoscopic surgery. The details of two novel technologies for 2D/3D registration for fast knee motion with bi-gradient optimization algorithm, and laparoscopic surgery navigation system using three-dimensional ultrasonic image are also introduced.

Mardi 19 juin 2012

Nonlocal PDES on Graphs : from tug-of-war game to image processing and machine learning
Abderrahim Elmoataz - GREYC, Université de Caen Basse-Normandie
Abstract: In recent years, a game-theoretic approach, deterministic or stochastic, to various elliptic or parabolic equations attracted enormous attention.
These results provide representation theorems for the solutions through value functions of considered games. Example of this are p-harmonious functions which are value functions of certain random tug-of-war games. In particular, the infinity Laplace and p-Laplace equations can be obtained as limit when the parameter that controls the movement of the game goes to zero.
In this talk we propose an extension of these p-harmonious functions to weighted graphs, using the framework of Partial difference Equations.
This extension is introduced as a general Partial difference Equation on graphs which represents a wide class of nonlocal PDEs on graphs including: Laplacian, infinity Laplacian, p-Laplacian and p-Laplacian with drift.
Then, we will consider the Dirichlet problem involving these operators, and we will prove the existence and uniqueness of the solution.
We propose to use these operators as a unified framework for solution of many inverse problems in image processing and machine learning.

Vendredi 18 mai 2012

Laplace deconvolution in Regression - Application to angiogenosis follow-up in cancer
Yves Rozenholc - Université Paris Descartes
Abstract: In the context of cancer treatments, a major issue is to follow the effect of anti-angiogenesis drugs. If parametric models have been developed to achieve this goal, they suffer from being tissue-related and, moreover, if their pertinence is already questionable in heathy tissue, they are certainly wrong in tumors where the cell growth changes the nature of the tissue. In order to face these problems, nonparametric modeling of the blood flow exchanges has been imagined early in the 80's and started to be used in the second half of the 90's with the availability of high-frequency imaging techniques. Unfortunately, to date the estimation in such nonparametric models is highly unstable due to high level of ill-posedness.
After recalling the medical context which has motivated our study and describing the associated models, I will present a new nonparametric estimate for Laplace deconvolution in the regression setting. This estimate is derived from the statistical analysis of Volterra equations of the first type intimately linked to Laplace deconvolution. This estimate is shown to be adaptive in the sense that it achieves optimal rates of convergence up to the regularity of the unknown function even if this regularity is also unknown. This theoretical study is completed by simulations which show the proper behavior of this estimate.
Collaboration with Felix Abramovich (TAU) and Marianna Pensky (UCF)

Jeudi 10 mai 2012

Adaptive and nonlocal approaches in Mathematical Morphology
Olivier Lezoray - GREYC, Université de Caen Basse-Normandie
Abstract: Mathematical morphology (MM) offers a wide range of operators to address various image processing problems. These operators can be defined in terms of algebraic (discrete) sets or as partial differential equations (PDEs). We consider adaptive and nonlocal approaches in MM for both PDEs and Algebraic sets.
First, we introduce a nonlocal PDEs-based morphological framework defined on weighted graphs. We present and analyze a set of operators that leads to a family of discretized morphological PDEs on weighted graphs. Our formulation introduces nonlocal patch-based configurations for image processing and extends PDEs-based approach to the processing of arbitrary data such as nonuniform high dimensional data.
Second, we introduce a generalization of algebraic MM to multivariate images. The proposed approach is fully unsupervised and consists in constructing a complete lattice from an image as a rank transformation together with a learned ordering of vectors. This unsupervised ordering of vectors relies on three steps: dictionary learning, manifold learning and out of sample extension. In addition to providing an efficient way to construct a vectorial ordering, nonlocal configurations based on color patches can be easily handled and provide much better results than with classical local morphological approaches.

Jeudi 12 avril 2012

Atelier doctotants

L'optimisation et les hiérarchies dans les SIG (Systèmes d'information géographique)
Ravi Kiran, LIGM-ESIEE-A3SI
Abstract: Ma thèse a pour objet l'étude des variables de type INSEE (graphes planaires) et de type IGN (données raster). Je cherche à les décrire et à essayer de modéliser des prédictions au moyen de la morphologie mathématique. Ce travail se poursuit actuellement sur deux plans :
1- Recherche des informations disponibles, et mise en forme pour des traitements morphologiques ultérieurs. Apprentissage des logiciels de type GIS. Bibliographie.
2- Développement d'algorithmes pour les optimisations des coupes dans des hiérarchies par des énergies ascendantes.
Dans l'exposé, je présenterai le logiciel (ARCGIS) avec lequel je travaille, ainsi que des exemples de traitement des données démographiques dans la région PACA. J'exposerai la méthode des coupes par énergies ascendantes.

Efficient 4th Order Match Propagation
David Ok, LIGM-ENPC-IMAGINE-A3SI
Abstract: We propose a robust method to match image feature points taking into account geometric consistency. It is a simple but careful adaptation of the match propagation principle to 4th-order geometric constraints (feature quadruple matching). With our method, a set of matches is explained by a network of locally-similar affinities. This approach is useful when simple matching strategies (based on descriptors only) fail, in particular for highly ambiguous data, e.g., for repetitive patterns or when texture is lacking. As it scales easily to hundreds of thousands of matches, it is also useful when denser point distributions are sought, e.g., for high-precision rigid model estimation. Experiments show that our method is competitive (efficient, accurate, robust) against state-of-the-art methods in deformable object matching, camera calibration and pattern detection.

Filtrage morphologique dans des espaces de formes
Yongchao Xu, LIGM-EPITA-ESIEE-A3SI
Résumé : Les opérateurs connexes sont des outils de filtrage qui agissent en fusionnant des régions élémentaires appelées zones plates. Une stratégie populaire se fonde sur une représentation arborescente des régions de l'image: par exemple, on peut calculer un attribut pour chacun des noeuds de l'arbre, et ne garder que les noeuds pour lequel l'attribut est suffisamment fort. Cette opération est équivalente à faire un seuillage sur l'arbre dont les noeuds sont pondérés par l'attribut. Plutôt que de se contenter du seuillage, nous proposons d'aller plus loin, et de faire un filtrage connexe du graphe formé par l'arbre aux noeuds pondérés. Ainsi, le filtrage se fait non pas dans l'espace de l'image, mais dans l'espace des formes construit sur l'image.
En procédant de cette manière, nous généralisons les filtres connexes existants: on peut montrer ce nouveau cadre de travail inclus les filtres connexes classiques par attribut croissant ou non. Ce cadre nous permet de proposer de nouveaux filtres connexes de la famille des nivellements, fondés sur un attribut (non-croissant) de forme. Enfin, nous proposons une nouvelle classe de filtres connexes, également fondés sur un critère de forme, mais qui ne sont pas des nivellements.
Le cadre sera illustré par quelques exemples de filtrages avec une variété d'attributs de forme. En particulier, on introduira un critère original de forme, fondé sur une énergie de type snake.

Combinatorial structure of rigid transformations in 2D digital images
Hoai Diem Phuc Ngo, LIGM-ESIEE-A3SI
Abstract: Rigid transformations are involved in a wide range of digital image processing applications. When applied on such discrete images, rigid transformations are however usually performed in their associated continuous space, then requiring a subsequent digitization of the result. In this article, we propose to study rigid transformations of digital images as a fully discrete process. In particular, we investigate a combinatorial structure modelling the whole space of digital rigid transformations on any subset of Z^2 of size N × N. We describe this combinatorial structure, which presents a space complexity O (N^9 ) and we propose an algorithm enabling to build it in linear time with respect to this space complexity. This algorithm, which handles real (i.e., non-rational) values related to the continuous transformations associated to the discrete ones, is however defined in a fully discrete form, leading to exact computation.

Jeudi 22 mars 2012

Identification of video subsequence using bipartite graph matching
Silvio Guimarães - PUC Minas, Brazil
Abstract: Subsequence identification consists in identifying real positions of a specific video clip in a video stream together with the operations that may be used to transform the former into a subsequence from the latter. To cope with this problem, we propose a new approach considering a bipartite graph matching to measure video clip similarity with a target video stream which has not been preprocessed. Main contributions of our work are the application of a simple and efficient distance to solve subsequence identification problem along with the definition of a hit function that identifies precisely which operations were used in query transformation. Experimental results demonstrate that our method performance achieve 93% recall with 93% precision, though it has a low computational cost since its classifications step is extremely simple.

Jeudi 9 février 2012

Atelier doctotants

A hybrid algorithm for automatic heart segmentation in CT angiography
Imen Melki - A3SI/LIGM/ESIEE - General Electric
Abstract: Volumetric Computed Tomography (CT) angiography has become a standard non-invasive routine procedure for cardiac imaging and coronary arteries pathology detection. However, before the diagnosis process, a preprocessing task is critical for an accurate examination of the vessels.In this work, we present a hybrid algorithm to automatically delineate the heart volume in 3D cardiac CT datasets for the visualization of coronary arteries. Our work eliminates the tedious and time consuming step of manual removing obscuring structures around the heart (ribs, sternum, liver...) and quickly provides a clear and well defined view of the coronaries. So far, works related to heart segmentation have mainly focused on heart cavities delineation, which is not suited for coronaries visualization. In contrast, our algorithm extracts the heart cavities, the myocardium and coronaries as a single object. The proposed approach is based on the fitting of a geometric model of the heart to a set of automatically extracted 3D points lying on the heart shell. A novel two-stage fitting scheme is used to improve the robustness to the outliers. The fitting result is refined using a Random Walker (RW) segmentation approach. Qualitative analysis of results obtained on a 70 exam database shows the efficiency and the accuracy of our approach.

Medial axis filtering for shapes with features at different scales
Michal Postolski - A3SI/LIGM/ESIEE - Technical University of Lodz
Abstract: The medial axis is a very useful representation of the object and plays a major role in shape analysis in numerous applications, for example object recognition, registration or compression. However it can be hard or even impossible to use this tool effectively without first dealing with some problems, especially in discrete spaces and with noisy objects. One of the most important one is that the medial axis is not stable under small perturbations of a shape: modifying a shape slightly can result in substantially different medial axes. This fact, among others, explains why it is usually necessary to add a filtering step (or pruning step) to any method that aims at computing the medial axis and a nonreversible but simplified description of binary objects is of interest. Different criteria can be used to locally threshold and discard spurious medial axis points or branches. In previously proposed methods local information (that is, geometric information extracted from a single medial ball) is compared to a global parameter value to determine the importance of the corresponding medial axis point. However, it is well known that this local filtering can lead to remove small branches which might be important for the shape understanding especially for shapes with features at different scales. In this presentation, we address this issue and propose two new different approaches which put in relation local information and regional information to make an effective medial axis filtering and overcome drawback noticed in previously presented methods. On a number of experiments we evaluate their stability, and compare they with the previously introduced methods.

Non-convex image restoration
Anna Jezierska - Signal et communications/A3SI/LIGM/UPEMLV
Abstract: We consider criteria for sparse image recovery problems, suitable for preserving edges between homogeneous regions. Our studies focus on the optimization of functions expressed as a sum of convex data fidelity term and a prior, which is either a truncated quadratic penalization or a smoothed version. Since the problem is non-convex, it is generally challenging. In this talk, a short review of existing methods is first given, and then we propose two approaches: a combinatorial Graph-Cut based algorithm, which we call Quantized-Convex Split Move and a continuous Majorise-Minimize Memory-Gradient optimization algorithm. We compare both methods in term of convergence properties, quality of the results and time efficiency.

Jeudi 19 janvier 2012

Géostatistique linéaire - Partie II : krigeage, et méthodes qui en dérivent
Jean Serra - ESIEE, LIGM, équipe A3SI
Résumé des deux parties

Jeudi 12 janvier 2012

Géostatistique linéaire - Partie I : Variogrammes et variances d'estimation
Jean Serra - ESIEE, LIGM, équipe A3SI
Résumé des deux parties

Algorithmes pour la variation totale et problèmes similaires
Antonin Chambolle - CMAP, Ecole Polytechnique
Résumé : Dans cet exposé, nous illustrerons par quelques problèmes pratiques la nécessité d'introduire des algorithmes simples et efficaces pour minimiser la variation totale ou des problèmes convexes non-linéaires du même type. Nous montrerons qu'un algorithme simple du premier ordre basé sur une formulation primale-duale peut arriver, théoriquement, à une vitesse de convergence "optimale", et nous aborderons le problème du "préconditionnement" (diagonal) de cette approche.

Mardi 6 décembre 2011

Generalized Ordering Constraints for Multilabel Optimization
Evgeny Strekalovskiy - Technische Universität München
Abstract: We propose a novel framework for imposing label ordering constraints in multilabel optimization. In particular, label jumps can be penalized differently depending on the jump direction. In contrast to the recently proposed MRF-based approaches, the proposed method arises from the viewpoint of spatially continuous optimization.
It unifies and generalizes previous approaches to label ordering constraints:
Firstly, it provides a common solution to three different problems which are otherwise solved by three separate approaches. We provide an exact characterization of the penalization functions expressible with our approach.
Secondly, we show that it naturally extends to three and higher dimensions of the image domain.
Thirdly, it allows novel applications, such as the convex shape prior. Despite this generality, our model is easily adjustable to various label layouts and is also easy to implement. On a number of experiments we show that it works quite well, producing solutions comparable and superior to those obtained with previous approaches.

Mercredi 16 novembre 2011

Nonlocal Smoothing for Scalar- and Matrix-Valued Images
Luis Pizarro - Imperial College London, UK
Abstract: There exist numerous approaches to image smoothing emerging from statistical methods, information theory and variational methods, among others. Establishing equivalences and relations between the different approaches has been focus of intense research in recent years. In this talk we present a novel discrete variational approach with nonlocal constraints penalising general dissimilarity measures defined on image patches. This framework leads to a novel family of filters suitable for removing Gaussian and impulse noise in scalar-valued images. We further extend our approach to the setting of matrix fields in two different ways, isotropically and anisotropically, by allowing the energy penalisers to act on scalar- and matrix-valued similarity measures. We test our smoothing framework on synthetic data sets and on diffusion tensor magnetic resonance imaging (DT-MRI) data sets. We also discuss the conditions for preservation of positive semidefiniteness of DT-MRI fields. Finally, we establish connections between the proposed approaches and other recent smoothing methods for scalar and matrix fields.

PDE-based Adaptive Morphology for Matrix Fields
Bernhard Burgeth - Saarland University, Germany
Abstract: Matrix fields are the adequate means to describe anisotropic behaviour in image processing models and physical measurements. A prominent example is diffusion tensor magnetic resonance imaging (DT-MRI) which is a medical imaging technique useful for analysing the fibre structure in the brain. Morphological partial differential equations (PDEs) for dilation and erosion known for grey scale images have already been extended to three dimensional fields of symmetric positive definite matrices. In this talk we report on a method to incorporate adaptivity into the matrix-valued, PDE-driven dilation process. The approach uses a structure tensor concept for 3D matrix data to steer anisotropic morphological evolution in a way that enhances and completes line-like structures in matrix fields. Numerical upwind schemes are utilised only in their basic one-dimensional version. Experiments performed on synthetic and real-world data confirm the gap-closing and line-completing qualities of the method; properties it shares with matrix-valued coherence enhancing diffusion filtering.