This work presents a comparison of results about the accuracy of statistical routines from four statistical software packages that are freely used: Octave, academic Ox, Python, and R. Having extensive functional libraries for statistical computing with applications in image processing, these software packages are useful for data analysis and visualization. The National Institute of Standards and Technology datasets and McCullough’s methodology are used for assessing these packages. As to the statistical analysis herein performed, R yielded the best results and had the most comprehensive library.

This paper presents analytical pseudo-likelihood (PL) equations for Potts Markov random field (MRF) model parameter estimation on higher-order neighborhood systems by expanding the derivative of the log-PL function based on the enumeration of all possible contextual configuration patterns given a neighborhood system. The proposed equations allow the modeling of less restrictive neighborhood systems in a large number of MRF applications in a computationally feasible way. To evaluate the proposed estimation method we propose a hypothesis testing approach, derived by approximating the asymptotic variance of MPL parameter estimators using the observed Fisher information. The definition of the asymptotic variance, together with the test size α and p-values, provide a complete framework for quantitative analysis. Experiments with synthetic images generated by Markov chain Monte Carlo simulation methods assess the accuracy of the proposed estimation method, indicating that higher-order neighborhood systems reduce the MPL estimator asymptotic variance and improve estimation performance.

The objective of this review paper is to summarize the main properties of the spatial ARMA models and describe some of the well-known methods used in image filtering based on estimation of spatial autoregressive models. A new proposal based on robust RA estimation is also presented. Previous studies have shown that under additive outliers the RA estimator is resistant to a small percentage of contamination and behaves better than the LS, M, and GM estimators. A discussion about how well these models fit to a digital image is presented. Some applications using real images are presented to illustrate how an image is filtered in practice.

When processing synthetic aperture radar (SAR) images, there is a strong need for statistical models of scattering to take into account multiplicative noise. For instance, the classification process needs to be based on the use of statistics. Our main contribution is the choice of an accurate model for SAR images over urban areas and its use in a Markovian classification algorithm. Clutter in SAR images becomes non-Gaussian when the resolution is high or when the area is manmade. Many models have been proposed to fit with non-Gaussian scattering statistics (K, Weibull, Log-normal, etc.), but none of them is flexible enough to model all kinds of surfaces. Frery et al. [IEEE Transactions on Geoscience and Remote Sensing 35 (1997) 648–659] proposed a new class of distributions, $\mathcal{G}$ distribution, arising from the multiplicative model. Classical distributions such as $\mathcal{K}$ are particular cases of this new class. A special case of this class called $\mathcal{G}^{0}$ is shown able to model extremely heterogeneous clutter, such as that of urban areas. The quality of the classification obtained by mixing this model and a Markovian segmentation is high.

Face detection has been an important research topic over the last 20 years. It is commonly used as a first step in face recognition and several techniques were applied in face detection, going from geometrical methods such as model matching to connectionist methods such as neural networks. This work presents a face detection system that uses a Bayesian network to combine information from different computational cheap visual operators, and is part of an ongoing project that uses a webcam to perform a reliable and accurate eye tracking. The face detection is the first step in this project. The aim in this work is to show that combining simple features in a Bayesian network helps improving the performance in a face detector system, increasing the detection rate and speeding up the face detection process.

This paper focuses on testing composite hypotheses about parameters of s independent samples of different sizes. With this purpose, it introduces test statistics based on the family of Rényi divergences between likelihoods. The asymptotic distributions of the proposed test statistics and of the likelihood ratio statistic are derived under standard regularity assumptions. An application to test the homogeneity of variances in data from families belonging to different populations is described and, under this setup, a simulation experiment compares the small sample performance of the likelihood ratio test and some members of the Rényi family of tests. The experiment indicates that some of the Rényi tests perform better under null hypothesis.

The usual finite population model—where information provided by a subset of units is used to reduce uncertainty about functions of the complete population list of values—is explored from a predictivistic point of view. Under this approach, only operationally meaningful quantities (operational parameters) are considered and therefore no superpopulation parameters are involved. This paper addresses the estimation of both population total and maximum based on uniformity and/or exchangeability judgments on finite sequences of random variables. A central point of this paper is that there are contexts in which the superpopulation approach cannot be employed in inferential problems in finite populations. There are circumstances in which the prior distributions for the operational parameters cannot be obtained from any superpopulation model. Conditions for the extendibility to infinite populations are also established for some models, as this approach may ease the inferential problem.