Quadratic time algorithm for inversion of binary permutation polynomials

International audienceIn this paper, we propose a new version of the Lagrangian interpolation applied to binary permutation polynomials and, more generally , permutation polynomials over prime power modular rings. We discuss its application to obfuscation and reverse engineering.Quadratic time algorithm for inversion of binary permutation polynomial

Pléiades project: Assessment of georeferencing accuracy, image quality, pansharpening performence and DSM/DTM quality

Pléiades 1A and 1B are twin optical satellites of Optical and Radar Federated Earth Observation (ORFEO) program jointly running by France and Italy. They are the first satellites of Europe with sub-meter resolution. Airbus DS (formerly Astrium Geo) runs a MyGIC (formerly Pléiades Users Group) program to validate Pléiades images worldwide for various application purposes. The authors conduct three projects, one is within this program, the second is supported by BEU Scientific Research Project Program, and the third is supported by TÜBİTAK. Assessment of georeferencing accuracy, image quality, pansharpening performance and Digital Surface Model/Digital Terrain Model (DSM/DTM) quality subjects are investigated in these projects. For these purposes, triplet panchromatic (50 cm Ground Sampling Distance (GSD)) and VNIR (2 m GSD) Pléiades 1A images were investigated over Zonguldak test site (Turkey) which is urbanised, mountainous and covered by dense forest. The georeferencing accuracy was estimated with a standard deviation in X and Y (SX, SY) in the range of 0.45m by bias corrected Rational Polynomial Coefficient (RPC) orientation, using ~170 Ground Control Points (GCPs). 3D standard deviation of ±0.44m in X, ±0.51m in Y, and ±1.82m in Z directions have been reached in spite of the very narrow angle of convergence by bias corrected RPC orientation. The image quality was also investigated with respect to effective resolution, Signal to Noise Ratio (SNR) and blur coefficient. The effective resolution was estimated with factor slightly below 1.0, meaning that the image quality corresponds to the nominal resolution of 50cm. The blur coefficients were achieved between 0.39-0.46 for triplet panchromatic images, indicating a satisfying image quality. SNR is in the range of other comparable space borne images which may be caused by de-noising of Pléiades images. The pansharpened images were generated by various methods, and are validated by most common statistical metrics and also visual interpretation. The generated DSM and DTM were achieved with ±1.6m standard deviation in Z (SZ) in relation to a reference DTM.Airbus Defence and SpaceBEU/2014-47912266-01TÜBİTAK/114Y38

Recent progress on univariate and multivariate polynomial and spline quasi-interpolants

Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to solve), uniform boundedness independently of the degree (polynomials) or of the partition (splines), good approximation order. We shall emphasize new results on various types of univariate and multivariate polynomial or spline QIs, depending on the nature of coefficient functionals, which can be differential, discrete or integral. We shall also present some applications of QIs to numerical methods

Continuous Evolution of Statistical Estimators for Optimal Decision-Making

In many everyday situations, humans must make precise decisions in the presence of uncertain sensory information. For example, when asked to combine information from multiple sources we often assign greater weight to the more reliable information. It has been proposed that statistical-optimality often observed in human perception and decision-making requires that humans have access to the uncertainty of both their senses and their decisions. However, the mechanisms underlying the processes of uncertainty estimation remain largely unexplored. In this paper we introduce a novel visual tracking experiment that requires subjects to continuously report their evolving perception of the mean and uncertainty of noisy visual cues over time. We show that subjects accumulate sensory information over the course of a trial to form a continuous estimate of the mean, hindered only by natural kinematic constraints (sensorimotor latency etc.). Furthermore, subjects have access to a measure of their continuous objective uncertainty, rapidly acquired from sensory information available within a trial, but limited by natural kinematic constraints and a conservative margin for error. Our results provide the first direct evidence of the continuous mean and uncertainty estimation mechanisms in humans that may underlie optimal decision making

A nonlinear updating algorithm captures suboptimal inference in the presence of signal-dependent noise

Bayesian models have advanced the idea that humans combine prior beliefs and sensory observations to optimize behavior. How the brain implements Bayes-optimal inference, however, remains poorly understood. Simple behavioral tasks suggest that the brain can flexibly represent probability distributions. An alternative view is that the brain relies on simple algorithms that can implement Bayes-optimal behavior only when the computational demands are low. To distinguish between these alternatives, we devised a task in which Bayes-optimal performance could not be matched by simple algorithms. We asked subjects to estimate and reproduce a time interval by combining prior information with one or two sequential measurements. In the domain of time, measurement noise increases with duration. This property takes the integration of multiple measurements beyond the reach of simple algorithms. We found that subjects were able to update their estimates using the second measurement but their performance was suboptimal, suggesting that they were unable to update full probability distributions. Instead, subjects’ behavior was consistent with an algorithm that predicts upcoming sensory signals, and applies a nonlinear function to errors in prediction to update estimates. These results indicate that the inference strategies employed by humans may deviate from Bayes-optimal integration when the computational demands are high

First- and second-order contributions to depth perception in anti-correlated random dot stereograms.

The binocular energy model of neural responses predicts that depth from binocular disparity might be perceived in the reversed direction when the contrast of dots presented to one eye is reversed. While reversed-depth has been found using anti-correlated random-dot stereograms (ACRDS) the findings are inconsistent across studies. The mixed findings may be accounted for by the presence of a gap between the target and surround, or as a result of overlap of dots around the vertical edges of the stimuli. To test this, we assessed whether (1) the gap size (0, 19.2 or 38.4 arc min) (2) the correlation of dots or (3) the border orientation (circular target, or horizontal or vertical edge) affected the perception of depth. Reversed-depth from ACRDS (circular no-gap condition) was seen by a minority of participants, but this effect reduced as the gap size increased. Depth was mostly perceived in the correct direction for ACRDS edge stimuli, with the effect increasing with the gap size. The inconsistency across conditions can be accounted for by the relative reliability of first- and second-order depth detection mechanisms, and the coarse spatial resolution of the latter

Imaging of subsurface lineaments in the southwestern part of the Thrace Basin from gravity data

Linear anomalies, as an indicator of the structural features of some geological bodies, are very important for the interpretation of gravity and magnetic data. In this study, an image processing technique known as the Hough transform (HT) algorithm is described for determining invisible boundaries and extensions in gravity anomaly maps. The Hough function implements the Hough transform used to extract straight lines or circles within two-dimensional potential field images. It is defined as image and Hough space. In the Hough domain, this function transforms each nonzero point in the parameter domain to a sinusoid. In the image space, each point in the Hough space is transformed to a straight line or circle. Lineaments are depicted from these straight lines which are transformed in the image domain. An application of the Hough transform to the Bouguer anomaly map of the southwestern part of the Thrace Basin, NW Turkey, shows the effectiveness of the proposed approach. Based on geological data and gravity data, the structural features in the southwestern part of the Thrace Basin are investigated by applying the proposed approach and the Blakely and Simpson method. Lineaments identified by these approaches are generally in good accordance with previously-mapped surface faults