Djemel Ziou

Aicha Baya Goumeidane, Djemel Ziou, Nafaa Nacereddine

Using integral transforms to the end of lines detection in images with complex background, makes the detection a hard task needing additional processing to manage the detection. As an integral transform, the Scale Space Radon Transform (SSRT) suffers from such drawbacks, even with its great abilities for thick lines detection. In this work, we propose a method to address this issue for automatic detection of thick linear structures in gray scale and binary images using the SSRT, whatever the image background content. This method involves the calculated Hessian orientations of the investigated image while computing its SSRT, in such a way that linear structures are emphasized in the SSRT space. As a consequence, the subsequent maxima detection in the SSRT space is done on a modified transform space freed from unwanted parts and, consequently, from irrelevant peaks that usually drown the peaks representing lines. Besides, highlighting the linear structure in the SSRT space permitting, thus, to efficiently detect lines of different thickness in synthetic and real images, the experiments show also the method robustness against noise and complex background.

Nafaa Nacereddine, Djemel Ziou, Aicha Baya Goumeidane

Since the Radon transform (RT) consists in a line integral function, some modeling assumptions are made on Computed Tomography (CT) system, making image reconstruction analytical methods, such as Filtered Backprojection (FBP), sensitive to artifacts and noise. In the other hand, recently, a new integral transform, called Scale Space Radon Transform (SSRT), is introduced where, RT is a particular case. Thanks to its interesting properties, such as good scale space behavior, the SSRT has known number of new applications. In this paper, with the aim to improve the reconstructed image quality for these methods, we propose to model the X-ray beam with the Scale Space Radon Transform (SSRT) where, the assumptions done on the physical dimensions of the CT system elements reflect better the reality. After depicting the basic properties and the inversion of SSRT, the FBP algorithm is used to reconstruct the image from the SSRT sinogram where the RT spectrum used in FBP is replaced by SSRT and the Gaussian kernel, expressed in their frequency domain. PSNR and SSIM, as quality measures, are used to compare RT and SSRT-based image reconstruction on Shepp-Logan head and anthropomorphic abdominal phantoms. The first findings show that the SSRT-based method outperforms the methods based on RT, especially, when the number of projections is reduced, making it more appropriate for applications requiring low-dose radiation, such as medical X-ray CT. While SSRT-FBP and RT-FBP have utmost the same runtime, the experiments show that SSRT-FBP is more robust to Poisson-Gaussian noise corrupting CT data.

Aicha Baya Goumeidane, Djemel Ziou, Nafaa Nacereddine

Inertia Axes are involved in many techniques for image content measurement when involving information obtained from lines, angles, centroids... etc. We investigate, here, the estimation of the main axis of inertia of an object in the image. We identify the coincidence conditions of the Scale Space Radon Transform (SSRT) maximum and the inertia main axis. We show, that by choosing the appropriate scale parameter, it is possible to match the SSRT maximum and the main axis of inertia location and orientation of the embedded object in the image. Furthermore, an example of use case is presented where binary objects central symmetry computation is derived by means of SSRT projections and the axis of inertia orientation. To this end, some SSRT characteristics have been highlighted and exploited. The experimentations show the SSRT-based main axis of inertia computation effectiveness. Concerning the central symmetry, results are very satisfying as experimentations carried out on randomly created images dataset and existing datasets have permitted to divide successfully these images bases into centrally symmetric and non-centrally symmetric objects.

Elvis Togban, Djemel Ziou

This paper presents a discriminative classifier for compositional data. This classifier is based on the posterior distribution of the Generalized Dirichlet which is the discriminative counterpart of Generalized Dirichlet mixture model. Moreover, following the mixture of experts paradigm, we proposed a hierarchical mixture of this classifier. In order to learn the models parameters, we use a variational approximation by deriving an upper-bound for the Generalized Dirichlet mixture. To the best of our knownledge, this is the first time this bound is proposed in the literature. Experimental results are presented for spam detection and color space identification.

Nafaa Nacereddine, Aicha Baya Goumeidane, Djemel Ziou

Accurate detection of the centerline of a thick linear structure and good estimation of its thickness are challenging topics in many real-world applications such X-ray imaging, remote sensing and lane marking detection in road traffic. Model-based approaches using Hough and Radon transforms are often used but, are not recommended for thick line detection, whereas methods based on image derivatives need further step-by-step processing making their efficiency dependent on each step outcome. In this paper, a novel paradigm to better detect thick linear objects is presented, where the 3D image gray level representation is considered as a finite mixture model of a statistical distribution, called linear anchored Gaussian distribution and parametrized by a scale factor to describe the structure thickness and radius and angle parameters to localize the structure centerline. Expectation-Maximization algorithm (Algo1) using the original image as input data is used to estimate the model parameters. To rid the data of irrelevant information brought by nonuniform and noisy background, a modified EM algorithm (Algo2) is detailed. In Experiments, the proposed algorithms show promising results on real-world images and synthetic images corrupted by blur and noise, where Algo2, using Hessian-based angle initialization, outperforms Algo1 and Algo2 with random angle initialization, in terms of running time and structure location and thickness computation accuracy.

Hadia Mecheri, Islam Benamirouche, Feriel Fass et al.

In this study, we propose an approach for predicting rare events by exploiting time series in coevolution. Our approach involves a weighted autologistic regression model, where we leverage the temporal behavior of the data to enhance predictive capabilities. By addressing the issue of imbalanced datasets, we establish constraints leading to weight estimation and to improved performance. Evaluation on synthetic and real-world datasets confirms that our approach outperform state-of-the-art of predicting home equipment failure methods.

Elvis Togban, Djemel Ziou

To display an image, the color space in which the image is encoded is assumed to be known. Unfortunately, this assumption is rarely realistic. In this paper, we propose to identify the color space of a given color image using pixel embedding and the Gaussian process. Five color spaces are supported, namely Adobe RGB, Apple RGB, ColorMatch RGB, ProPhoto RGB and sRGB. The results obtained show that this problem deserves more efforts.

Djemel Ziou, Issam Fakir

The links between the mean families of Lehmer and Hölder and the weighted maximum likelihood estimator have recently been established in the case of a regular univariate exponential family. In this article, we will extend the outcomes obtained to the multivariate case. This extension provides a probabilistic interpretation of these families of means and could therefore broaden their uses in various applications.

Djemel Ziou

In this report, we explore the data selection leading to a family of estimators maximizing a centrality. The family allows a nice properties leading to accurate and robust probability density function fitting according to some criteria we define. We establish a link between the centrality estimator and the maximum likelihood, showing that the latter is a particular case. Therefore, a new probability interpretation of Fisher maximum likelihood is provided. We will introduce and study two specific centralities that we have named Hölder and Lehmer estimators. A numerical simulation is provided showing the effectiveness of the proposed families of estimators opening the door to development of new concepts and algorithms in machine learning, data mining, statistics, and data analysis.