Indexation d'images texturées fondée sur le modèle multivarié de la Gaussienne généralisée asymétrique à copule Gaussienne

National audienceDans ce papier, nous nous intéressons à l'indexation d'images texturées dans le contexte des modèles probabilistes multivariés. En utilisant une transformée en ondelettes, la dépendance entre les coefficients des sous-bandes peut être caractérisée à l'aide d'un modèle stochastique multivarié. Nous introduisons le modèle multivarié de la Gaussienne généralisée asymétrique à copule Gaussienne (GC-MAGG) pour la caractérisation de la dépendance spatiale des coefficients d'ondelettes en prenant en compte l'éventuelle asymétrie de leurs distributions marginales. Le modèle proposé est validé en utilisant un test statistique d'adéquation aux statistiques jointes observées. L'expression analytique de la divergence de Jeffreys entre deux distributions à copule Gaussienne est calculée afin de mesurer la similarité et utiliser le modèle proposé dans une application de classification d'images. En comparaison avec d'autres modèles de la littérature, des bonnes performances sont obtenues en recherche d'images par contenu textural en utilisant le modèle proposé GC-MAGG

Performance of the maximum likelihood estimators for the parameters of multivariate generalized Gaussian distributions

International audienceThis paper studies the performance of the maximum likelihood estimators (MLE) for the parameters of multivariate generalized Gaussian distributions. When the shape parameter belongs to ]0,1[, we have proved that the scatter matrix MLE exists and is unique up to a scalar factor. After providing some elements about this proof, an estimation algorithm based on a Newton-Raphson recursion is investigated. Some experiments illustrate the convergence speed of this algorithm. The bias and consistency of the scatter matrix estimator are then studied for different values of the shape parameter. The performance of the shape parameter estimator is finally addressed by comparing its variance to the Cramér-Rao bound

Modélisation stochastique pour l'analyse d'images texturées (approches Bayésiennes pour la caractérisation dans le domaine des transformées)

Le travail présenté dans cette thèse s inscrit dans le cadre de la modélisation d images texturées à l aide des représentations multi-échelles et multi-orientations. Partant des résultats d études en neurosciences assimilant le mécanisme de la perception humaine à un schéma sélectif spatio-fréquentiel, nous proposons de caractériser les images texturées par des modèles probabilistes associés aux coefficients des sous-bandes. Nos contributions dans ce contexte concernent dans un premier temps la proposition de différents modèles probabilistes permettant de prendre en compte le caractère leptokurtique ainsi que l éventuelle asymétrie des distributions marginales associées à un contenu texturée. Premièrement, afin de modéliser analytiquement les statistiques marginales des sous-bandes, nous introduisons le modèle Gaussien généralisé asymétrique. Deuxièmement, nous proposons deux familles de modèles multivariés afin de prendre en compte les dépendances entre coefficients des sous-bandes. La première famille regroupe les processus à invariance sphérique pour laquelle nous montrons qu il est pertinent d associer une distribution caractéristique de type Weibull. Concernant la seconde famille, il s agit des lois multivariées à copules. Après détermination de la copule caractérisant la structure de la dépendance adaptée à la texture, nous proposons une extension multivariée de la distribution Gaussienne généralisée asymétrique à l aide de la copule Gaussienne. L ensemble des modèles proposés est comparé quantitativement en terme de qualité d ajustement à l aide de tests statistiques d adéquation dans un cadre univarié et multivarié. Enfin, une dernière partie de notre étude concerne la validation expérimentale des performances de nos modèles à travers une application de recherche d images par le contenu textural. Pour ce faire, nous dérivons des expressions analytiques de métriques probabilistes mesurant la similarité entre les modèles introduits, ce qui constitue selon nous une troisième contribution de ce travail. Finalement, une étude comparative est menée visant à confronter les modèles probabilistes proposés à ceux de l état de l art.In this thesis we study the statistical modeling of textured images using multi-scale and multi-orientation representations. Based on the results of studies in neuroscience assimilating the human perception mechanism to a selective spatial frequency scheme, we propose to characterize textures by probabilistic models of subband coefficients.Our contributions in this context consist firstly in the proposition of probabilistic models taking into account the leptokurtic nature and the asymmetry of the marginal distributions associated with a textured content. First, to model analytically the marginal statistics of subbands, we introduce the asymmetric generalized Gaussian model. Second, we propose two families of multivariate models to take into account the dependencies between subbands coefficients. The first family includes the spherically invariant processes that we characterize using Weibull distribution. The second family is this of copula based multivariate models. After determination of the copula characterizing the dependence structure adapted to the texture, we propose a multivariate extension of the asymmetric generalized Gaussian distribution using Gaussian copula. All proposed models are compared quantitatively using both univariate and multivariate statistical goodness of fit tests. Finally, the last part of our study concerns the experimental validation of the performance of proposed models through texture based image retrieval. To do this, we derive closed-form metrics measuring the similarity between probabilistic models introduced, which we believe is the third contribution of this work. A comparative study is conducted to compare the proposed probabilistic models to those of the state-of-the-art.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF

Anomaly Detection on Textured Images with Convolutional Neural Network for Quality Control of Micrometric Woven Meshes

International audienceIndustrial woven meshes are composed of metal material and are often used in construction, industrial and residential industries. The context of this work is defect detection in industrial fabrics in the quality control process. It is often performed with a manual method and could be quite tedious and time-consuming. We propose here a method to automatically detect defects in micrometric steel meshes using a Convolutional Neural Network. The database used for this work comes from the real problem of anomaly detection on micrometric woven meshes. This detection is performed through supervised classification with Convolutional Neural Network using a VGG19 architecture. To this aim, we propose a pipeline and a strategy to tackle the small amount of data. It includes i) augmenting the database with translation, rotation and symmetry, ii) using pre-trained weights and iii) checking the learning curve behaviour through cross-validation. The proposed method has been evaluated by automatically detecting if metallic fabrics has defects. Obtain results show that, despite the small size of our databases, detection accuracy of 96% was reached

Decision-Making with Heterogeneous Sensors - A Copula Based Approach

Statistical decision making has wide ranging applications, from communications and signal processing to econometrics and finance. In contrast to the classical one source-one receiver paradigm, several applications have been identified in the recent past that require acquiring data from multiple sources or sensors. Information from the multiple sensors are transmitted to a remotely located receiver known as the fusion center which makes a global decision. Past work has largely focused on fusion of information from homogeneous sensors. This dissertation extends the formulation to the case when the local sensors may possess disparate sensing modalities. Both the theoretical and practical aspects of multimodal signal processing are considered. The first and foremost challenge is to \u27adequately\u27 model the joint statistics of such heterogeneous sensors. We propose the use of copula theory for this purpose. Copula models are general descriptors of dependence. They provide a way to characterize the nonlinear functional relationships between the multiple modalities, which are otherwise difficult to formalize. The important problem of selecting the `best\u27 copula function from a given set of valid copula densities is addressed, especially in the context of binary hypothesis testing problems. Both, the training-testing paradigm, where a training set is assumed to be available for learning the copula models prior to system deployment, as well as generalized likelihood ratio test (GLRT) based fusion rule for the online selection and estimation of copula parameters are considered. The developed theory is corroborated with extensive computer simulations as well as results on real-world data. Sensor observations (or features extracted thereof) are most often quantized before their transmission to the fusion center for bandwidth and power conservation. A detection scheme is proposed for this problem assuming unifom scalar quantizers at each sensor. The designed rule is applicable for both binary and multibit local sensor decisions. An alternative suboptimal but computationally efficient fusion rule is also designed which involves injecting a deliberate disturbance to the local sensor decisions before fusion. The rule is based on Widrow\u27s statistical theory of quantization. Addition of controlled noise helps to \u27linearize\u27 the higly nonlinear quantization process thus resulting in computational savings. It is shown that although the introduction of external noise does cause a reduction in the received signal to noise ratio, the proposed approach can be highly accurate when the input signals have bandlimited characteristic functions, and the number of quantization levels is large. The problem of quantifying neural synchrony using copula functions is also investigated. It has been widely accepted that multiple simultaneously recorded electroencephalographic signals exhibit nonlinear and non-Gaussian statistics. While the existing and popular measures such as correlation coefficient, corr-entropy coefficient, coh-entropy and mutual information are limited to being bivariate and hence applicable only to pairs of channels, measures such as Granger causality, even though multivariate, fail to account for any nonlinear inter-channel dependence. The application of copula theory helps alleviate both these limitations. The problem of distinguishing patients with mild cognitive impairment from the age-matched control subjects is also considered. Results show that the copula derived synchrony measures when used in conjunction with other synchrony measures improve the detection of Alzheimer\u27s disease onset