q-Bernstein polynomials and Bézier curves

AbstractWe define q-Bernstein polynomials, which generalize the classical Bernstein polynomials, and show that the difference of two consecutive q-Bernstein polynomials of a function f can be expressed in terms of second-order divided differences of f. It is also shown that the approximation to a convex function by its q-Bernstein polynomials is one sided.A parametric curve is represented using a generalized Bernstein basis and the concept of total positivity is applied to investigate the shape properties of the curve. We study the nature of degree elevation and degree reduction for this basis and show that degree elevation is variation diminishing, as for the classical Bernstein basis

Cross-orientation transfer of adaptation for facial identity is asymmetric: A study using contrast-based recognition thresholds

AbstractRecent studies suggest that adaptation effects for face shape and gender transfer from upright to inverted faces more than the reverse. We investigated whether a similar asymmetry occurred for face identity, using a recently developed adaptation method based on contrast-recognition thresholds. When adapting and test stimuli shared the same orientation, aftereffects were similar for upright and inverted faces. When orientation differed, there was significant transfer of aftereffects from upright adapting to inverted test faces, but none from inverted to upright faces. We show that asymmetric cross-orientation transfer of face aftereffects generalize across two distinct face adaptation paradigms: the previously used perceptual-bias methodology and the recently introduced contrast-threshold based adaptation paradigm. These results also represent a generalization from aftereffects for face shape and gender to aftereffects for face identity. While these results are consistent with the dual-mode hypothesis, they can also be accounted for by a single population of units of varying orientation selectivity

2-Methyl-5-[(3-methyl-4-nitro­benz­yl)sulfan­yl]-1,3,4-thia­diazole

The mol­ecule of the title thia­diazole derivative, C11H11N3O2S2, has a butterfly-like structure and the whole mol­ecule is disordered with a site-occupancy ratio of 0.629 (4):0.371 (4). The mol­ecule is disordered in such a way that the 3-methyl-4-nitro­phenyl units of the major and minor components are approximately related by 180° rotation around the C—N bond axis. The dihedral angle between the 1,3,4-thia­diazole and benzene rings is 70.8 (4)° in the major component and 74.9 (6)° in the minor component. In the crystal, mol­ecules are arranged into screw chains along the c axis. These chains are stacked along the b axis. Weak inter­molecular C—H⋯O and C—H⋯π inter­actions and a short C⋯O contact [3.005 (7) Å] are present

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

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

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

The Mere Exposure Effect in the Domain of Haptics

Background: Zajonc showed that the attitude towards stimuli that one had been previously exposed to is more positive than towards novel stimuli. This mere exposure effect (MEE) has been tested extensively using various visual stimuli. Research on the MEE is sparse, however, for other sensory modalities. Methodology/Principal Findings: We used objects of two material categories (stone and wood) and two complexity levels (simple and complex) to test the influence of exposure frequency (F0 = novel stimuli, F2 = stimuli exposed twice, F10 = stimuli exposed ten times) under two sensory modalities (haptics only and haptics & vision). Effects of exposure frequency were found for high complex stimuli with significantly increasing liking from F0 to F2 and F10, but only for the stone category. Analysis of ‘‘Need for Touch’ ’ data showed the MEE in participants with high need for touch, which suggests different sensitivity or saturation levels of MEE. Conclusions/Significance: This different sensitivity or saturation levels might also reflect the effects of expertise on the haptic evaluation of objects. It seems that haptic and cross-modal MEEs are influenced by factors similar to those in the visual domain indicating a common cognitive basis

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