Probabilistic Atlas and Geometric Variability Estimation to Drive Tissue Segmentation

International audienceComputerized anatomical atlases play an important role in medical image analysis. While an atlas usually refers to a standard or mean image also called template, that presumably represents well a given population, it is not enough to characterize the observed population in detail. A template image should be learned jointly with the geometric variability of the shapes represented in the observations. These two quantities will in the sequel form the atlas of the corresponding population. The geometric variability is modelled as deformations of the template image so that it fits the observations. In this paper, we provide a detailed analysis of a new generative statistical model based on dense deformable templates that represents several tissue types observed in medical images. Our atlas contains both an estimation of probability maps of each tissue (called class) and the deformation metric. We use a stochastic algorithm for the estimation of the probabilistic atlas given a dataset. This atlas is then used for atlas-based segmentation method to segment the new images. Experiments are shown on brain T1 MRI datasets

Image registration via stochastic gradient markov chain monte carlo

We develop a fully Bayesian framework for non-rigid registration of three-dimensional medical images, with a focus on uncertainty quantification. Probabilistic registration of large images along with calibrated uncertainty estimates is difficult for both computational and modelling reasons. To address the computational issues, we explore connections between the Markov chain Monte Carlo by backprop and the variational inference by backprop frameworks in order to efficiently draw thousands of samples from the posterior distribution. Regarding the modelling issues, we carefully design a Bayesian model for registration to overcome the existing barriers when using a dense, high-dimensional, and diffeomorphic parameterisation of the transformation. This results in improved calibration of uncertainty estimates

Modèles de recalage classifiant pour l'imagerie médicale

Dans cette thèse, nous avons traité un problème rencontré en recalage d'images médicales. Il s'agit de la présence de plusieurs classes de pixels ayant des propriétés de changement de niveau de gris différentes (lorsqu'on injecte un agent de contraste par exemple). Ceci n'est pas conforme aux hypothèses sur lesquelles reposent la majorité des termes de similarité utilisés dans la littérature. Pour résoudre ce problème, nous avons proposé trois modèles. Pour recaler deux images, les deux premiers modèles reposent sur la description des variations des niveaux de gris entre les deux images par un mélange de deux distributions de probabilité, qui correspondent à deux classes de pixels. La pondération entre les deux composantes du mélange est faite à l'aide d'une carte de probabilité décrivant la localisation spatiale des pixels de la deuxième classe. Cette carte de probabilité est fixée dans le premier modèle, ce qui permet d'avoir un modèle de recalage qui tient compte de la présence de deux classes. Dans le deuxième modèle, la carte de probabilité est estimée en même temps que le recalage, conduisant ainsi à la combinaison de la détection (ou segmentation) et du recalage. Le troisième modèle concerne les séquences d'images dynamiques d'agent de contraste. Le modèle proposé se base sur une classification des pixels en fonction de leur courbes de rehaussement dynamiques et l'estimation de ces dernières pour chaque classe. Les trois modèles ont été appliqués à des images réelles et simulées.This thesis addresses a specific issue encountered in medical image registration. It concerns the presence of many classes of pixels having different properties of intensity change (when a contrast agent is injected for example). This is inconsistent with some hypotheses on which depend most similarity criteria used in the literature. To solve this problem, we developed three models. To register two images, the first two models rely on the description of intensity variation by a mixture of two probability distributions corresponding to two classes of pixels. A probability map describing spatial localization of the second class is used to weight the two components. This map is set constant in the first model to get a registration model which takes into account the presence of two classes. In the second model, the probability map is estimated together with the registration transformation, leading to a model which combines detection (or segmentation) and registration. The third model deals with Dynamic Contrast-Enhanced sequences. This last model is based upon pixel classification and contrast enhancement curve estimation in each class. Multiple applications of these models have been conducted on simulated and real images.PARIS5-BU Saints-Pères (751062109) / SudocSudocFranceF

Path integral treatment of the deformed Schioberg-type potential for some diatomic molecules

The bound state solution of the Feynman propagator with the deformed generalized Schiöberg potential is determined using an approximation of the centrifugal term. The energy eigenvalue expression is computed using Duru–Kleinert space–time transformation for both positive and negative deformation parameters of diatomic molecules. Besides, the rotation–vibration energy eigenvalues are numerically calculated for some diatomic molecules and compared with those given in the literature. The obtained results are in agreement with those given by state-of-the-art approximate and numerical methods.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author

Bayesian Technique for Image Classifying Registration

International audienceIn this paper, we address a complex image registration issue arising while the dependencies between intensities of images to be registered are not spatially homogeneous. Such a situation is frequently encountered in medical imaging when a pathology present in one of the images modifies locally intensity dependencies observed on normal tissues. Usual image registration models, which are based on a single global intensity similarity criterion, fail to register such images, as they are blind to local deviations of intensity dependencies. Such a limitation is also encountered in contrast-enhanced images where there exist multiple pixel classes having different properties of contrast agent absorption. In this paper, we propose a new model in which the similarity criterion is adapted locally to images by classification of image intensity dependencies. Defined in a Bayesian framework, the similarity criterion is a mixture of probability distributions describing dependencies on two classes. The model also includes a class map which locates pixels of the two classes and weighs the two mixture components. The registration problem is formulated both as an energy minimization problem and as a maximum a posteriori estimation problem. It is solved using a gradient descent algorithm. In the problem formulation and resolution, the image deformation and the class map are estimated simultaneously, leading to an original combination of registration and classification that we call image classifying registration. Whenever sufficient information about class location is available in applications, the registration can also be performed on its own by fixing a given class map. Finally, we illustrate the interest of our model on two real applications from medical imaging: template-based segmentation of contrast-enhanced images and lesion detection in mammograms. We also conduct an evaluation of our model on simulated medical data and show its ability to take into account spatial variations o- intensity dependencies while keeping a good registration accuracy