Just noticeable differences for elbow joint torque feedback.

Joint torque feedback is a new and promising means of kinesthetic feedback imposed by a wearable device. The torque feedback provides the wearer temporal and spatial information during a motion task. Nevertheless, little research has been conducted on quantifying the psychophysical parameters of how well humans can perceive external torques under various joint conditions. This study aims to investigate the just noticeable difference (JND) perceptual ability of the elbow joint to joint torques. The paper focuses on the ability of two primary joint proprioceptors, the Golgi-tendon organ (GTO) and muscle spindle (MS), to detect elbow torques, since touch and pressure sensors were masked. We studied 14 subjects while the arm was isometrically contracted (static condition) and was moving at a constant speed (dynamic condition). In total there were 10 joint conditions investigated, which varied the direction of the arm's movement and the preload direction as well as torque direction. The JND torques under static conditions ranged from 0.097 Nm with no preload to 0.197 Nm with a preload of 1.28 Nm. The maximum dynamic JND torques were 0.799 Nm and 0.428 Nm, when the arm was flexing and extending at 213 degrees per second, respectively.

A note on detecting statistical outliers in psychophysical data.

This paper considers how to identify statistical outliers in psychophysical datasets where the underlying sampling distributions are unknown. Eight methods are described, and each is evaluated using Monte Carlo simulations of a typical psychophysical experiment. The best method is shown to be one based on a measure of spread known as Sn. This is shown to be more sensitive than popular heuristics based on standard deviations from the mean, and more robust than non-parametric methods based on percentiles or interquartile range. MATLAB code for computing Sn is included.

Performance metrics for an application-driven selection and optimization of psychophysical sampling procedures.

When estimating psychometric functions with sampling procedures, psychophysical assessments should be precise and accurate while being as efficient as possible to reduce assessment duration. The estimation performance of sampling procedures is commonly evaluated in computer simulations for single psychometric functions and reported using metrics as a function of number of trials. However, the estimation performance of a sampling procedure may vary for different psychometric functions. Therefore, the results of these type of evaluations may not be generalizable to a heterogeneous population of interest. In addition, the maximum number of trials is often imposed by time restrictions, especially in clinical applications, making trial-based metrics suboptimal. Hence, the benefit of these simulations to select and tune an ideal sampling procedure for a specific application is limited. We suggest to evaluate the estimation performance of sampling procedures in simulations covering the entire range of psychometric functions found in a population of interest, and propose a comprehensive set of performance metrics for a detailed analysis. To illustrate the information gained from these metrics in an application example, six sampling procedures were evaluated in a computer simulation based on prior knowledge on the population distribution and requirements from proprioceptive assessments. The metrics revealed limitations of the sampling procedures, such as inhomogeneous or systematically decreasing performance depending on the psychometric functions, which can inform the tuning process of a sampling procedure. More advanced metrics allowed directly comparing overall performances of different sampling procedures and select the best-suited sampling procedure for the example application. The proposed analysis metrics can be used for any sampling procedure and the estimation of any parameter of a psychometric function, independent of the shape of the psychometric function and of how such a parameter was estimated. This framework should help to accelerate the development process of psychophysical assessments.

Investigation of the perceptual thresholds of tooth whiteness.

OBJECTIVE: To investigate the tooth whiteness perceptibility thresholds of the average observer to changes in the CIELAB values and an optimised whiteness Index for dentistry (WIO) based on psychophysical studies. METHODS: A psychophysical experiment based on visual assessments of digital images of teeth on a calibrated display with a group of observers (n=32) has been conducted to determine the perceptual thresholds in tooth whiteness. Digital simulations of a tooth that is identical in shape to the left incisor in the image of teeth were superimposed on to images. The colour of the simulated tooth was varied and observers were asked to respond whether there was a difference in whiteness between the left incisor and the simulated tooth. Thresholds for detection of differences in whiteness were independently determined in four conditions: ΔL*, Δa*, Δb* and a blue optical whitening direction. Raw data were fitted using a non-parametric approach and thresholds of CIELAB and WIO for each conditions were calculated. RESULTS: Estimates of the threshold of the four conditions of ΔL*, Δa*, Δb* and a blue covarine optical tooth whitening direction were 1.14, 3.24, 1.11 and 1.51 respectively, with the corresponding WIO thresholds of 2.77, 6.52, 3.09 and 1.99 respectively. CONCLUSIONS: The thresholds for tooth whiteness perception in CIELAB space and WIO space were determined. The findings demonstrate that for a whitening treatment with a blue covarine optical technology, a colour change of about 2 WIO units would be noticeable. CLINICAL SIGNIFICANCE: This study gives a better understanding of the tooth whiteness perception threshold, and will help clinicians identify perceivable differences in tooth colour during matching and whitening procedures.

Cognitive state prediction using an EM algorithm applied to Gamma distributed data.

Behavioral tests are widely used to quantify features of cognitive processing. For a large class of behavioral signals, the observed variables are non-Gaussian and dynamic; classical estimation algorithms are ill-suited to modeling such data. In this research, we propose a mathematical framework to predict a cognitive state variable related to behavioral signals, which are best modeled using a Gamma distribution. The proposed algorithm combines a Gamma Smoother and EM algorithm in the prediction process. The algorithm is applied to reaction time recorded from subjects performing a Multi-Source Interference Task (MSIT) to dynamically quantify their cognitive flexibility through the course of the experiment.

A threshold theory account of psychometric functions with response confidence under the balance condition.

The study of thresholds for discriminability has been of long-standing interest in psychophysics. While threshold theories embrace the concept of discrete-state thresholds, signal detection theory discounts such a concept. In this paper we concern ourselves with the concept of thresholds from the discrete-state modelling viewpoint. In doing so, we find it necessary to clarify some fundamental issues germane to the psychometric function (PF), which is customarily constructed using psychophysical methods with a binary-response format. We challenge this response format and argue that response confidence also plays an important role in the construction of PFs, and thus should have some impact on threshold estimation. We motivate the discussion by adopting a three-state threshold theory for response confidence proposed by Krantz (1969, Psychol. Rev., 76, 308-324), which is a modification of Luce's (1963, Psychol. Rev., 70, 61-79) low-threshold theory. In particular, we discuss the case in which the practice of averaging over order (or position) is enforced in data collection. Finally, we illustrate the fit of the Luce-Krantz model to data from a line-discrimination task with response confidence.

How the 2SLS/IV estimator can handle equality constraints in structural equation models: a system-of-equations approach.

Parameters in structural equation models are typically estimated using the maximum likelihood (ML) approach. Bollen (1996) proposed an alternative non-iterative, equation-by-equation estimator that uses instrumental variables. Although this two-stage least squares/instrumental variables (2SLS/IV) estimator has good statistical properties, one problem with its application is that parameter equality constraints cannot be imposed. This paper presents a mathematical solution to this problem that is based on an extension of the 2SLS/IV approach to a system of equations. We present an example in which our approach was used to examine strong longitudinal measurement invariance. We also investigated the new approach in a simulation study that compared it with ML in the examination of the equality of two latent regression coefficients and strong measurement invariance. Overall, the results show that the suggested approach is a useful extension of the original 2SLS/IV estimator and allows for the effective handling of equality constraints in structural equation models.

Olp: an R package for optimal linear partitions of finite sets of points on the plane.

Given a set of points on the plane and an assignment of values to them, an optimal linear partition is a division of the set into two subsets which are separated by a straight line and maximally contrast with each other in the values assigned to their points. We present a method for inspecting and rating all linear partitions of a finite set, and a package of three functions in the R language for executing the computations. One function is for finding the optimal linear partitions and corresponding separating lines, another for graphically representing the results, and a third for testing how well the data comply with the linear separability condition. We illustrate the method on possible data from a psychophysical experiment (concerning the size-weight illusion) and compare its performance with that of linear discriminant analysis and multiple logistic regression, adapted to dividing linearly a set of points on the plane.

On the limitations of fixed-step-size adaptive methods with response confidence.

The family of (non-parametric, fixed-step-size) adaptive methods, also known as 'up-down' or 'staircase' methods, has been used extensively in psychophysical studies for threshold estimation. Extensions of adaptive methods to non-binary responses have also been proposed. An example is the three-category weighted up-down (WUD) method (Kaernbach, 2001) and its four-category extension (Klein, 2001). Such an extension, however, is somewhat restricted, and in this paper we discuss its limitations. To facilitate the discussion, we characterize the extension of WUD by an algorithm that incorporates response confidence into a family of adaptive methods. This algorithm can also be applied to two other adaptive methods, namely Derman's up-down method and the biased-coin design, which are suitable for estimating any threshold quantiles. We then discuss via simulations of the above three methods the limitations of the algorithm. To illustrate, we conduct a small scale of experiment using the extended WUD under different response confidence formats to evaluate the consistency of threshold estimation.

Sources of uncertainty in intuitive physics.

Recent work suggests that people predict how objects interact in a manner consistent with Newtonian physics, but with additional uncertainty. However, the sources of uncertainty have not been examined. In this study, we measure perceptual noise in initial conditions and stochasticity in the physical model used to make predictions. Participants predicted the trajectory of a moving object through occluded motion and bounces, and we compared their behavior to an ideal observer model. We found that human judgments cannot be captured by simple heuristics and must incorporate noisy dynamics. Moreover, these judgments are biased consistently with a prior expectation on object destinations, suggesting that people use simple expectations about outcomes to compensate for uncertainty about their physical models.

Complexity of images: experimental and computational estimates compared.

We tested whether visual complexity can be modeled through the use of parameters relevant to known mechanisms of visual processing. In psychophysical experiments observers ranked the complexity of two groups of stimuli: 15 unfamiliar Chinese hieroglyphs and 24 outline images of well-known common objects. To predict image complexity, we considered: (i) spatial characteristics of the images, (ii) spatial-frequency characteristics, (iii) a combination of spatial and Fourier properties, and (iv) the size of the image encoded as a JPEG file. For hieroglyphs the highest correlation was obtained when complexity was calculated as the product of the squared spatial-frequency median and the image area. This measure accounts for the larger number of lines, strokes, and local periodic patterns in the hieroglyphs. For outline objects the best predictor of the experimental data was complexity estimated as the number of turns in the image, as Attneave (1957 Journal of Experimental Psychology 53 221-227) obtained for his abstract outlined images. Other predictors of complexity gave significant but lower correlations with the experimental ranking. We conclude that our modeling measures can be used to estimate the complexity of visual images but for different classes of images different measures of complexity may be required.

The role of spatial switching in the attentional blink

The attentional blink (AB) is a well-established paradigm in which identification of a target T2 is reduced shortly after presentation of an earlier target T1. An important question concerns the importance of backward masking during the AB. While task switching has been found to be a strong modulator mediating the AB without any masking of T2, the present study investigated whether spatial switching could similarly produce an AB without masking. Using a spatial AB paradigm in which items appeared at different locations; we found (a) a significant AB without backward masking of T2 but no AB when no distractors followed T2, (b) no evidence for Lag 1 sparing. These findings show that when there is a spatial switch between the targets, presenting the distractor following T2 at the same location than T2 (backward masking) is not a necessary condition for the AB to occur, but T2 has to be followed by surrounding distractors (appearing at different locations than T2). This pattern of data confirms that spatial switching is a robust modulator of the AB, but to a less extent than task switching (AU)

El parpadeo atencional (PA) es un paradigma muy utilizado cuyo principal resultado se traduce en una reducción temporal en la identificación de un target (T2) que se presenta seguido de otro target (T1). Una de las claves que provoca este efecto es el enmascaramiento hacia atrás que tiene lugar durante el PA. Sin embargo, estudios previos asumen que el cambio de tarea es uno de los moduladores más potentes en la aparición de PA sin enmascaramiento del T2; el objetivo de este trabajo se centró en probar si otro tratamiento, el cambio espacial podría dar lugar a un efecto de PA similar, esto es, sin enmascaramiento. Un paradigma de PA con presentación de los ítems en diferentes localizaciones condujo a los siguientes resultados: (a) efecto significativo de PA sin enmascaramiento hacia atrás de T2, pero no PA sin la presencia de distractores después de T2; (b) esto no se confirmó en la posición 1; los resultados sugieren que si hay un cambio espacial entre los targets, presentar un distractor seguido de T2 y en su mismo lugar (enmascaramiento hacia atrás) no necesariamente va a facilitar la aparición de PA, sino que es necesario que T2 vaya seguido de distractores pero presentados en diferentes localizaciones. Este patrón de datos confirma que el cambio espacial es un importante modulador en la aparición de PA, aunque en menor medida que el cambio de tarea (AU)

Predictions about bisymmetry and cross-modal matches from global theories of subjective intensities.

The article first summarizes the assumptions of Luce (2004, 2008) for inherently binary (2-D) stimuli (e.g., the ears and eyes) that lead to a "p-additive," order-preserving psychophysical representation. Next, a somewhat parallel theory for unary (1-D) signals is developed for intensity attributes such as linear extent, vibration to finger, and money. The 3rd section studies the property of bisymmetry in these 2 cases. For the 2-D case and the nontrivial p-additive forms, Proposition 3 shows that bisymmetry implies commutativity of the presentations. Bisymmetry has been empirically well sustained, whereas commutativity has been rejected for loudness, brightness, and perceived contrast, thus implying that pure additivity must obtain in the 2-D context. By contrast, bisymmetry and commutativity are automatically satisfied by the p-additive 1-D theory. The 4th section explores the resulting complex of cross-modal predictions. For the additive 1-D case and the 2-D case, the predictions are power functions. For the nonadditive 1-D cases, other relations are predicted (see Table 2). Some parameter estimation issues are taken up in Appendices B and C.

Anticipation from biological motion: the goalkeeper problem.

People can often anticipate the outcome of another person's actions based on visual information available in the movements of the other person's body. We investigated this problem by studying how goalkeepers anticipate the direction of a penalty kick in soccer. The specific aim was to determine whether the information used to anticipate kick direction is best characterized as local to a particular body segment or distributed across multiple segments. In Experiment 1, we recorded the movements of soccer players as they kicked balls into a net. Using a novel method for analyzing motion capture data, we identified sources of local and distributed information that were reliable indicators of kick direction. In Experiments 2 and 3, subjects were presented with animations of kickers' movements prior to foot-to-ball contact and instructed to judge kick direction. Judgments were consistent with the use of distributed information, with a possible small contribution of local information.

When viewing natural scenes, do abnormal colors impact on spatial or temporal parameters of eye movements?

Since Treisman's theory, it has been generally accepted that color is an elementary feature that guides eye movements when looking at natural scenes. Hence, most computational models of visual attention predict eye movements using color as an important visual feature. In this paper, using experimental data, we show that color does not affect where observers look when viewing natural scene images. Neither colors nor abnormal colors modify observers' fixation locations when compared to the same scenes in grayscale. In the same way, we did not find any significant difference between the scanpaths under grayscale, color, or abnormal color viewing conditions. However, we observed a decrease in fixation duration for color and abnormal color, and this was particularly true at the beginning of scene exploration. Finally, we found that abnormal color modifies saccade amplitude distribution.

The law of categorical judgment (corrected) extended: a note on Rosner and Kochanski (2009).

Rosner and Kochanski (2009) noticed an inconsistency in the mathematical statement of the Law of Categorical Judgment and derived "the valid equation, the Law of Categorical Judgment (Corrected)" (p. 125). The purpose of this comment is to point out that the law can be corrected in many different ways, leading to substantially different equations. The different versions have different consequences for the predicted distributions of the responses and, hence, for fitting real data. Some of these consequences are unexpected and sometimes undesirable. Researchers should be aware of the different possibilities as they may lead to pronouncedly different accounts of given data.

Animal detection and identification in natural scenes: image statistics and emotional valence.

Humans process natural scenes rapidly and accurately. Low-level image features and emotional valence affect such processing but have mostly been studied in isolation. At which processing stage these factors operate and how they interact has remained largely unaddressed. Here, we briefly presented natural images and asked observers to report the presence or absence of an animal (detection), species of the detected animal (identification), and their confidence. In a second experiment, the same observers rated images with respect to their emotional affect and estimated their anxiety when imagining a real-life encounter with the depicted animal. We found that detection and identification improved with increasing image luminance, background contrast, animal saturation, and luminance plus color contrast between target and background. Surprisingly, animals associated with lower anxiety were detected faster and identified with higher confidence, and emotional affect was a better predictor of performance than anxiety. Pupil size correlated with detection, identification, and emotional valence judgments at different time points after image presentation. Remarkably, images of threatening animals induced smaller pupil sizes, and observers with higher mean anxiety ratings had smaller pupils on average. In sum, rapid visual processing depends on contrasts between target and background features rather than overall visual context, is negatively affected by anxiety, and finds its processing stages differentially reflected in the pupillary response.

Extended Stevens' power law.

An extension of the Stevens' power law, widely used in psychophysics to relate a physical magnitude of a stimulus (e.g. taste, luminance, weight, sound pressure) with the corresponding experienced magnitude (saltiness, brightness, heaviness, loudness etc.) has been proposed. It takes into account the fact that psychophysical functions are basically of a sigmoid and not power-like type. To model the stimulus-response relationship the S-shaped Gompertz function converted to the power form by the mapping procedure is employed. It provides the extended Stevens' power law y(C) = k(C)C(n(C)) with the scaling factor k(C) and exponent n(C) as function of the stimulus magnitude C. The model will be used in determination of the saltiness and brightness stimulus-response power function correctly reproducing the experimental psychophysical data in a wide range of the stimuli applied. It will be proven that the extended Stevens' power law belongs to the class of self-similar and allometric processes of the fractal nature.

Evaluating a model of global psychophysical judgments for brightness: II. Behavioral properties linking summations and productions.

Steingrimsson (Attention, Perception, & Psychophysics, 71, 1916-1930, 2009) outlined Luce's (Psychological Review, 109, 520-532 2002, 111, 446-454 2004) proposed psychophysical theory and tested, for brightness, behavioral properties that, separately, gave rise to two psychophysical functions, Ψ (⊕) and [Formula: see text]. The function Ψ (⊕) maps pairs of physical intensities onto positive real numbers and represents subjective summation, and the function [Formula: see text] represents a form of ratio production. This article, the second in a series expected to consist of three articles, tests the properties linking summation and production such that it forces [Formula: see text]. The properties tested are a form of distributivity and, in three experiments, were subjected to an empirical evaluation. Considerable support is provided for the existence of a single function Ψ for both summation and ratio production. The scope of this series of articles is to establish the theory as a descriptive model of binocular brightness perception.

Extensions of Narens' theory of ratio magnitude estimation.

Stevens postulated that the responses of a participant in a ratio scaling experiment can be used directly to construct a psychophysical function. Today, it is generally accepted that the axioms of commutativity and multiplicativity are crucial for the interpretation of the subjects' ratio scaling behaviour. Empirical findings provide evidence that commutativity holds, whereas multiplicativity fails to hold across different sensory modalities. This shows that, in principle, Stevens' direct scaling methods yield measurements on a ratio scale level, but that the numerals occurring in a ratio scaling experiment cannot be taken at face value. Thus, Narens and others introduced a transformation function f, which converts the numerals used in an experiment into the latent mathematical numbers. The aim of the present paper is to specify the (unknown) shape of the transformation function f, by analysing different extensions of the multiplicative property. The results provide evidence that f is either a power function or a logarithmic function.