Probabilistic analysis of recurrence plots generated by fractional Gaussian noise.

Recurrence plots of time series generated by discrete fractional Gaussian noise (fGn) processes are analyzed. We compute the probabilities of occurrence of consecutive recurrence points forming diagonals and verticals in the recurrence plot constructed without embedding. We focus on two recurrence quantification analysis measures related to these lines, respectively, the percent determinism and the laminarity ( LAM ). The behavior of these two measures as a function of the fGn's Hurst exponent H is investigated. We show that the dependence of the laminarity with respect to H is monotonic in contrast to the percent determinism. We also show that the length of the diagonal and vertical lines involved in the computation of percent determinism and laminarity has an influence on their dependence on H . Statistical tests performed on the LAM measure support its utility to discriminate fGn processes with respect to their H values. These results demonstrate that recurrence plots are suitable for the extraction of quantitative information on the correlation structure of these widespread stochastic processes.

Influence of noise on the sample entropy algorithm.

We study the effect of static additive noise on the sample entropy (SampEn) algorithm [J. S. Richman and J. R. Moorman, Am. J. Physiol. Heart Circ. Physiol. 278, 2039 (2000); R. B. Govindan et al., Physica A 376, 158 (2007)] for analyzing time series. Using surrogate data tests, we empirically investigate the ability of the SampEn index to detect nonlinearity in simulated time series corrupted by increased amounts of noise. Discrete and continuous chaotic and nonchaotic systems are included in the numerical experiments. Both Gaussian and uniformly distributed noises are considered. The results indicate that the SampEn statistic is a robust index for detecting nonlinearity in time series corrupted by observational noise.

Detecting determinism in short time series using a quantified averaged false nearest neighbors approach.

We propose a criterion to detect determinism in short time series. This criterion is based on the estimation of the parameter E2 defined by the averaged false neighbors method for analyzing time series [Cao, Physica D 110, 43 (1997)]. Using surrogate data testing with several chaotic and stochastic simulated time series, we show that the variation coefficient of E2 over a few values of the embedding dimension d defines a suitable statistic to detect determinism in short data sequences. This result holds for a time series generated by a high-dimensional chaotic system such as the Mackey-Glass one. Different decreasing lengths of the time series are included in the numerical experiments for both synthetic and real-world data. We also investigate the robustness of the criterion in the case of deterministic time series corrupted by additive noise.

FAIR: a fast algorithm for document image restoration.

We present, in this paper, the FAIR algorithm: a fast algorithm for document image restoration. This algorithm has been submitted to different contests where it showed good performance in comparison to the state of the art. In addition, this method is scale invariant and fast enough to be used in real-time applications. The method is based on a double-threshold edge detection approach that makes it possible to detect small details while remaining robust against noise. The performance of the proposition is evaluated on several types of degraded document images where considerable background noise or variation in contrast and illumination exist.

Characterizing the dynamics of postural sway in humans using smoothness and regularity measures.

We investigate human postural sway velocity time series by computing two dynamical statistics quantifying the smoothness (the central tendency measure or CTM) and the regularity (the sample entropy or SampEn) of their underlying dynamics. The purpose of the study is to investigate the effect of aging and vision on the selected measures and to explore the nature of postural dynamics by performing surrogate data tests. A group of 14 young subjects was compared to a group of 11 older healthy subjects in two visual conditions: with eyes open (EO) and with eyes closed (EC). The results suggest that vision and age do not influence the two statistics of the velocity data in the same way. More specifically, the smoothness statistic is able to detect the aging effect. The regularity measure is sensitive to the visual feedback removal. In contrast with some findings in the literature, the results of the surrogate data tests indicate that the center of pressure velocity dynamics are stochastic and are not produced by a purely deterministic behavior. Finally, we discuss some potential implications of our results in terms of postural control mechanisms.

Subpixel edge refinement using deformable models.

We propose an approach for subpixel edge refinement based on deformable models. In our approach, the result is constrained by two kinds of information: orientation information derived from the gradient and position information. The problem is formulated in a statistical framework: the likelihood function of the observations is computed and used in a classical maximum a posteriori estimator. Two different models are proposed: a parametric model based on B-spline functions and a sampled model. Experiments on both synthetic and natural images are described that show the adequacy and effectiveness of these algorithms.

On the use of sample entropy to analyze human postural sway data.

We analyze the irregularity of human postural sway data during quiet standing using the sample entropy (SampEn) algorithm. By considering recent methodological developments, we show that the SampEn parameter is able to characterize the irregularity of the center of pressure fluctuations through the analysis of the velocity variable. We present a practical method to select the input parameters of the SampEn algorithm. We show that the computed SampEn successfully discriminates two sensory conditions (eyes-open and eyes-closed) in a group of healthy young adults. We also perform surrogate data tests to investigate the nature of the underlying dynamics of our experimental data. Finally, the results of the proposed approach are compared to those obtained with the multiscale entropy algorithm.

Efficient algorithm for computation of the second-order moment of the subpixel-edge position.

Subpixel-edge detection is the first stage in processing many high-level vision algorithms. However, the study of the statistical properties of such data has remained incomplete in most research. We present a method for estimating the second-order moments of the subpixel-edge position, computed by a deterministic algorithm based on three quadratic interpolations. The algorithm is tested on different types of noise (Gaussian, impulse, colored) and compared with two methods in the literature. The results show that this approach remains accurate even at high noise levels.