Improved image display by identifying the RGB family color space

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.

Deriving Lehmer and Hölder means as maximum weighted likelihood estimates for the multivariate exponential family

The links between the mean families of Lehmer and H\"older 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.

Hierarchical mixture of discriminative Generalized Dirichlet classifiers

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.

Centrality Estimators for Probability Density Functions

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 H\"older 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.

Linear Anchored Gaussian Mixture Model for Location and Width Computation of Objects in Thick Line Shape

An accurate detection of the centerlines of linear objects is a challenging topic in many sensitive 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 approaches based on image derivatives need further step-by-step processing, making their efficiency dependent on each step outcomes. In this paper, we aim to detect linear structures found in images by considering the 3D representation of the image gray levels as a finite mixture model of statistical distribution. The latter, which we named linear anchored Gaussian distribution could be parametrized by a scale value ${\sigma}$ describing the linear structure thickness and a line equation, parametrized, in turn, by a radius ${\rho}$ and an orientation angle ${\theta}$, describing the linear structure centerline location. Expectation-Maximization (EM) algorithm is used for the mixture model parameter estimation, where a new paradigm, using the background subtraction for the likelihood function computation, is proposed. For the EM algorithm, two ${\theta}$ parameter initialization schemes are used: the first one is based on a random choice of the first component of ${\theta}$ vector, whereas the second is based on the image Hessian with a simultaneous computation of the mixture model components number. Experiments on real world images and synthetic images corrupted by blur and additive noise show the good performance of the proposed methods, where the algorithm using background subtraction and Hessian-based ${\theta}$ initialization provides an outstanding accuracy of the linear structure detection despite irregular image background and presence of blur and noise.

Prediction of rare events in the operation of household equipment using co-evolving time series

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.

Guided Scale Space Radon Transform for linear structures detection

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.

Scale space radon transform-based inertia axis and object central symmetry estimation

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.

On Scale Space Radon Transform, Properties and Image Reconstruction

Aware of the importance of the good behavior in the scale space that a mathematical transform must have, we depict, in this paper, the basic properties and the inverse transform of the Scale Space Radon Transform (SSRT). To reconstruct the image from SSRT sinogram, the Filtered backprojection (FBP) technique is used in two different ways: (1) Deconvolve SSRT to obtain the estimated Radon transform (RT) and then, reconstruct image using classical FBP or (2) Adapt FBP technique to SSRT so that the Radon projections spectrum used in classical FBP is replaced by SSRT and Wiener filtering, expressed in the frequency domain. Comparison of image reconstruction techniques using SSRT and RT are performed on Shepp-Logan head phantom image. Using the Mean Absolute Error (MAE) as image reconstruction quality measure, the preliminary results present an outstanding performance for SSRT-based image reconstruction techniques compared to the RT-based one. Furthermore, the method (2) outperforms the method (1) in terms of computation time and adaptability for high level of noise when fairly large Gaussian kernel is used.