The effect of anisotropic systematic errors in estimating helical angles

A common question in movement studies is how the results should be interpreted with respect to systematic and random errors. In this study, simulations are made in order to see how a rigid body's orientation in space (i.e. helical angle between two orientations) is affected by (1) a systematic error added to a single marker (2) a combination of this systematic error and Gaussian white noise. The orientation was estimated after adding a systematic error to one marker within the rigid body. This procedure was repeated with Gaussian noise added to each marker. In conclusion, results show that the systematic error's effect on estimated orientation depends on number of markers in the rigid body and also on which direction the systematic error is added. The systematic error has no effect if the error is added along the radial axis (i.e. the line connecting centre of mass and the affected marker).     

Bayesian inverse kinematics vs. least-squares inverse kinematics in estimates of planar postures and rotations in the absence of soft tissue artifact

A variety of inverse kinematics (IK) algorithms exist for estimating postures and displacements from a set of noisy marker positions, typically aiming to minimize IK errors by distributing errors amongst all markers in a least-squares (LS) sense. This paper describes how Bayesian inference can contrastingly be used to maximize the probability that a given stochastic kinematic model would produce the observed marker positions. We developed Bayesian IK for two planar IK applications: (1) kinematic chain posture estimates using an explicit forward kinematics model, and (2) rigid body rotation estimates using implicit kinematic modeling through marker displacements. We then tested and compared Bayesian IK results to LS results in Monte Carlo simulations in which random marker error was introduced using Gaussian noise amplitudes ranging uniformly between 0.2 mm and 2.0 mm. Results showed that Bayesian IK was more accurate than LS-IK in over 92% of simulations, with the exception of one center-of-rotation coordinate planar rotation, for which Bayesian IK was more accurate in only 68% of simulations. Moreover, while LS errors increased with marker noise, Bayesian errors were comparatively unaffected by noise amplitude. Nevertheless, whereas the LS solutions required average computational durations of less than 0.5 s, average Bayesian IK durations ranged from 11.6 s for planar rotation to over 2000 s for kinematic chain postures. These results suggest that Bayesian IK can yield order-of-magnitude IK improvements for simple planar IK, but also that its computational demands may make it impractical for some applications.     

Asymptotic Properties of Pearson's Rank-Variate Correlation Coefficient under Contaminated Gaussian Model

This paper investigates the robustness properties of Pearson''s rank-variate correlation coefficient (PRVCC) in scenarios where one channel is corrupted by impulsive noise and the other is impulsive noise-free. As shown in our previous work, these scenarios that frequently encountered in radar and/or sonar, can be well emulated by a particular bivariate contaminated Gaussian model (CGM). Under this CGM, we establish the asymptotic closed forms of the expectation and variance of PRVCC by means of the well known Delta method. To gain a deeper understanding, we also compare PRVCC with two other classical correlation coefficients, i.e., Spearman''s rho (SR) and Kendall''s tau (KT), in terms of the root mean squared error (RMSE). Monte Carlo simulations not only verify our theoretical findings, but also reveal the advantage of PRVCC by an example of estimating the time delay in the particular impulsive noise environment.     

A new method for estimating the axis of rotation and the center of rotation.

A new method is presented for estimating the parameters of two different models of a joint. The two models are: (1) A rotational joint with a fixed axis of rotation, also referred to as a hinge joint and (2) a ball and socket model, corresponding to a spherical joint. Given the motion of a set of markers, it is shown how the parameters can be estimated, utilizing the whole data set. The parameters are estimated from motion data by minimizing two objective functions. The method does not assume a rigid body motion, but only that each marker rotates around the same fixed axis of rotation or center of rotation. Simulation results indicate that in situations where the rigid body assumption is valid and when measurement noise is present, the proposed method is inferior to methods that utilize the rigid body assumption. However, when there are large skin movement artefacts, simulation results show the proposed method to be more robust.     

Non-linear stimulus-response behavior of the human stance control system is predicted by optimization of a system with sensory and motor noise

We developed a theory of human stance control that predicted (1) how subjects re-weight their utilization of proprioceptive and graviceptive orientation information in experiments where eyes closed stance was perturbed by surface-tilt stimuli with different amplitudes, (2) the experimentally observed increase in body sway variability (i.e. the “remnant” body sway that could not be attributed to the stimulus) with increasing surface-tilt amplitude, (3) neural controller feedback gains that determine the amount of corrective torque generated in relation to sensory cues signaling body orientation, and (4) the magnitude and structure of spontaneous body sway. Responses to surface-tilt perturbations with different amplitudes were interpreted using a feedback control model to determine control parameters and changes in these parameters with stimulus amplitude. Different combinations of internal sensory and/or motor noise sources were added to the model to identify the properties of noise sources that were able to account for the experimental remnant sway characteristics. Various behavioral criteria were investigated to determine if optimization of these criteria could predict the identified model parameters and amplitude-dependent parameter changes. Robust findings were that remnant sway characteristics were best predicted by models that included both sensory and motor noise, the graviceptive noise magnitude was about ten times larger than the proprioceptive noise, and noise sources with signal-dependent properties provided better explanations of remnant sway. Overall results indicate that humans dynamically weight sensory system contributions to stance control and tune their corrective responses to minimize the energetic effects of sensory noise and external stimuli.     

Determination of rigid body registration marker error from edge error

Registration markers affixed to rigid bodies (fixed to bone as opposed to skin) are commonly used when tracking 3D rigid body motion. The measured positions of registration markers are subject to unavoidable errors, both systematic and non-systematic. Prior studies have investigated the error propagated to such derived properties as rigid body positions and helical axes, while others have focused on the error associated with a specific position tracking system under restricted conditions. Theoretical and simulation-based error propagation requires knowledge of the variation due to individual registration markers; however, the variation in registration marker position measurement has previously been either assumed or determined from static cases. The objective of this paper is the introduction of a method for determining individual marker variation irrespective of change in rigid body position or motion by utilizing the distances between the markers (edge lengths), which are invariant under rotation and translation. Simulations were used to validate and characterize the introduced technique, demonstrating that the predictions improve with greater edge length and additional markers, converge on reference values where the edge length is at least 4 times the magnitude of the maximum vertex variation, and that under ideal conditions the confidence interval about the predicted variation is within 7% of the maximum variation associated with that marker set. The introduced technique was tested on the results of a motion tracking experiment to demonstrate the wide disparity in vertex variation between static and non-static measurements of the same registration markers, where the non-static variation exceeded the static variation by an average factor of 12.7.     

Moving the Weber Fraction: The Perceptual Precision for Moment of Inertia Increases with Exploration Force

How does the magnitude of the exploration force influence the precision of haptic perceptual estimates? To address this question, we examined the perceptual precision for moment of inertia (i.e., an object''s “angular mass”) under different force conditions, using the Weber fraction to quantify perceptual precision. Participants rotated a rod around a fixed axis and judged its moment of inertia in a two-alternative forced-choice task. We instructed different levels of exploration force, thereby manipulating the magnitude of both the exploration force and the angular acceleration. These are the two signals that are needed by the nervous system to estimate moment of inertia. Importantly, one can assume that the absolute noise on both signals increases with an increase in the signals'' magnitudes, while the relative noise (i.e., noise/signal) decreases with an increase in signal magnitude. We examined how the perceptual precision for moment of inertia was affected by this neural noise. In a first experiment we found that a low exploration force caused a higher Weber fraction (22%) than a high exploration force (13%), which suggested that the perceptual precision was constrained by the relative noise. This hypothesis was supported by the result of a second experiment, in which we found that the relationship between exploration force and Weber fraction had a similar shape as the theoretical relationship between signal magnitude and relative noise. The present study thus demonstrated that the amount of force used to explore an object can profoundly influence the precision by which its properties are perceived.     

Perceptual Compensation Is Correlated with Individuals' “Autistic” Traits: Implications for Models of Sound Change

Variation is a ubiquitous feature of speech. Listeners must take into account context-induced variation to recover the interlocutor''s intended message. When listeners fail to normalize for context-induced variation properly, deviant percepts become seeds for new perceptual and production norms. In question is how deviant percepts accumulate in a systematic fashion to give rise to sound change (i.e., new pronunciation norms) within a given speech community. The present study investigated subjects'' classification of /s/ and // before /a/ or /u/ spoken by a male or a female voice. Building on modern cognitive theories of autism-spectrum condition, which see variation in autism-spectrum condition in terms of individual differences in cognitive processing style, we established a significant correlation between individuals'' normalization for phonetic context (i.e., whether the following vowel is /a/ or /u/) and talker voice variation (i.e., whether the talker is male or female) in speech and their “autistic” traits, as measured by the Autism Spectrum Quotient (AQ). In particular, our mixed-effect logistic regression models show that women with low AQ (i.e., the least “autistic”) do not normalize for phonetic coarticulation as much as men and high AQ women. This study provides first direct evidence that variability in human''s ability to compensate for context-induced variations in speech perceptually is governed by the individual''s sex and cognitive processing style. These findings lend support to the hypothesis that the systematic infusion of new linguistic variants (i.e., the deviant percepts) originate from a sub-segment of the speech community that consistently under-compensates for contextual variation in speech.     

Statistical interpretation of the interplay between noise and chaos in the stochastic logistic map

A recurring problem in population biology - as well as other stochastic dynamical systems in biology, the physical and social sciences - is the distinction between the ‘true’ dynamics of a system and observational noise: i.e. can we from present data reliably infer e.g. biological mechanisms, or are signals swamped by noise.Here, we approach this problem using the canonical model for simple systems that exhibit complex behaviour, the logistic map. At each time-point noise is added, which allows us to study the long-term behaviour of a system which exhibits both non-linear dynamics and intrinsic noise.We show that the interplay between deterministic non-linear dynamics and simple Gaussian noise results in a perplexingly simple system when viewed statistically.In particular we show that for the case of Gaussian noise it is possible to derive at very reliable approximations for the time until the system has reached an absorbing state. This generic model allows us, for example, to study the life-time of molecular species involved in noisy feedback loops.     

A novel method for assessing the 3-D orientation accuracy of inertial/magnetic sensors

A novel method for assessing the accuracy of inertial/magnetic sensors is presented. The method, referred to as the “residual matrix” method, is advantageous because it decouples the sensor's error with respect to Earth's gravity vector (attitude residual error: pitch and roll) from the sensor's error with respect to magnetic north (heading residual error), while remaining insensitive to singularity problems when the second Euler rotation is close to ±90°. As a demonstration, the accuracy of an inertial/magnetic sensor mounted to a participant's forearm was evaluated during a reaching task in a laboratory. Sensor orientation was measured internally (by the inertial/magnetic sensor) and externally using an optoelectronic measurement system with a marker cluster rigidly attached to the sensor's enclosure. Roll, pitch and heading residuals were calculated using the proposed novel method, as well as using a common orientation assessment method where the residuals are defined as the difference between the Euler angles measured by the inertial sensor and those measured by the optoelectronic system. Using the proposed residual matrix method, the roll and pitch residuals remained less than 1° and, as expected, no statistically significant difference between these two measures of attitude accuracy was found; the heading residuals were significantly larger than the attitude residuals but remained below 2°. Using the direct Euler angle comparison method, the residuals were in general larger due to singularity issues, and the expected significant difference between inertial/magnetic sensor attitude and heading accuracy was not present.     

Numerical simulation of neuronal population coding: influences of noise and tuning width on the coding error

Performance of neuronal population coding is investigated numerically, in neurons with Gaussian tuning functions of various widths and noise ratios. The present model is applicable to both direction coding and orientation coding. It is shown that the coding error exhibits peculiar dependence on the width of the tuning function and that the dependence under the influence of noise is different from that of the noise-free case. In the absence of noise, the coding error increases monotonically with the width of the tuning function. The increment obeys the power law (the exponent estimated is 0.501) when the width is less than the critical value. In this region of the width a scaling law is obtained, which shows that the root-mean-square error is proportional to the square root of the ratio of the width of the tuning function to the population size. When the width exceeds the critical value, the coding error increases more rapidly than the power law. The reason for this anomalous increase, not seen previously, is argued. Existence of noise changes the dependence of the coding error on the width of the tuning function. Unlike the noise-free case, the error under the influence of noise becomes minimum at an intermediate value of the width. The width that gives the minimum coding error is termed the optimum width in this article. The numerical results suggest that the optimum width is roughly proportional to the square root of the noise ratio but has only a weak dependence on the population size. It is further shown that the coding error for the optimum width increases sharply when the noise ratio exceeds about 0.5 and is inversely proportional to the square root of the population size.     

Assessing the effect of sound file compression and background noise on measures of acoustic signal structure

The study of animal acoustic signals is a central tool for many fields in ecology and evolution, but the diversity of analytical methods and sources of animal sound recordings poses important challenges for carrying out robust acoustic analyses. Sound file compression and background noise may both affect acoustic analysis, although little attention has been paid to their respective effects. We evaluated the effect of these factors by assessing the systematic deviation (i.e. bias) and measurement error (i.e. precision) that they generate on spectrographic parameters and two (dis)similarity methods (dynamic time warping on frequency contours and cross-correlation), which represent the most common methods currently used for quantitative characterization of acoustic signals. Measurements were taken across a wide range of signals from a diverse group of bird species, and compared between uncompressed files and decompressed files obtained from mp3-encoded files generated using the two most common mp3 encoders (Fraunhofer and LAME). Measurements were also compared across a range of synthetically-generated background noise levels. Compression did not significantly bias any of the acoustic or similarity measurements. However, the precision of acoustic parameters representing single extreme values (e.g. peak frequency) as well as dynamic time warping distances, was strongly affected by compression. High background noise biased most energy distribution-related parameters (e.g. spectral entropy) and affected the precision of most acoustic parameters and dynamic time warping. Overall, compression and background noise did have considerable effects on acoustic analyses. We provide recommendations to avoid potential pitfalls and maximize the information that can be reliably obtained.     

A phase dynamic model of systematic error in simple copying tasks

A crucial insight into handwriting dynamics is embodied in the idea that stable, robust handwriting movements correspond to attractors of an oscillatory dynamical system. We present a phase dynamic model of visuomotor performance involved in copying simple oriented lines. Our studies on human performance in copying oriented lines revealed a systematic error pattern in orientation of drawn lines, i.e., lines at certain orientation are drawn more accurately than at other values. Furthermore, human subjects exhibit “flips” in direction at certain characteristic orientations. It is argued that this flipping behavior has its roots in the fact that copying process is inherently ambiguous—a line of given orientation may be drawn in two different (mutually opposite) directions producing the same end result. The systematic error patterns seen in human copying performance is probably a result of the attempt of our visuomotor system to cope with this ambiguity and still be able to produce accurate copying movements. The proposed nonlinear phase-dynamic model explains the experimentally observed copying error pattern and also the flipping behavior with remarkable accuracy.     

Analysis of variance for gene expression microarray data.

Spotted cDNA microarrays are emerging as a powerful and cost-effective tool for large-scale analysis of gene expression. Microarrays can be used to measure the relative quantities of specific mRNAs in two or more tissue samples for thousands of genes simultaneously. While the power of this technology has been recognized, many open questions remain about appropriate analysis of microarray data. One question is how to make valid estimates of the relative expression for genes that are not biased by ancillary sources of variation. Recognizing that there is inherent "noise" in microarray data, how does one estimate the error variation associated with an estimated change in expression, i.e., how does one construct the error bars? We demonstrate that ANOVA methods can be used to normalize microarray data and provide estimates of changes in gene expression that are corrected for potential confounding effects. This approach establishes a framework for the general analysis and interpretation of microarray data.     

Evaluating how hunters see and react to telemetry collars on white-tailed deer

Fates of individuals outfitted with radiotransmitters commonly are used for estimating survival rates in populations of large animals that are hunted. Despite precautions, this practice may be subject to complex biases associated with hunter reaction to presence of radiotransmitters. To assess this potential bias we conducted an experiment using artificial deer (i.e., decoys) to measure hunters' abilities to see deer and determine if deer seen were wearing radiocollars. We used logistic regression to quantify probabilities that seeing deer and subsequently seeing radiocollars might be influenced by distance, percent visual obstruction, body orientation, hunter experience, and antler characteristics of deer. Additionally, we evaluated how experience and antler characteristics of deer might influence a hunter's decision to harvest a radiocollared deer. We found that 25.8% of the potentially observable collared deer (n = 663) were subsequently observed by hunters. Odds of observing deer and radiocollars increased 95% and 230%, respectively, for each additional log(yr) of hunting experience. Willingness to harvest radiocollared deer increased 89% for each additional log(yr) of hunting experience and 144% for large-antlered deer relative to antlerless deer. When hunting is an important source of mortality, analysts need to understand how potential biases associated with observing deer are associated with hunters' reactions to and subsequent decisions to harvest radiocollared animals. Our study suggested that presence of radiocollars may influence a deer's potential risk of being harvested and in turn bias telemetry-based estimates of survival, given that hunting mortality is the largest component of total mortality in hunted deer populations. Collar-based telemetry is used nearly universally by wildlife managers and researchers throughout North America and elsewhere to estimate and monitor the survival of big game populations that are managed through hunting. Our findings demonstrate that these estimates are likely subject to complex and systematic biases that managers should consider when evaluating future population-level effects of managed hunting. © 2011 The Wildlife Society     

Main component of soft tissue artifact of the upper-limbs with respect to different functional,daily life and sports movements

Soft tissue artifact (STA) is the main source of error in kinematic estimation of human movements based on skin markers. Our objective was to determine the components of marker displacements that best describe STA of the shoulder and arm (i.e. clavicle, scapula and humerus). Four participants performed arm flexion and rotation, a daily-life and a sports movement. Three pins with reflective markers were inserted into the clavicle, scapula and humerus. In addition, up to seven skin markers were stuck on each segment. STA was described with a modal approach: individual marker displacements or marker-cluster (i.e. translations, rotations, homotheties and stretches) relative to the local segment coordinate system defined by markers secured to the pins. The modes were then ranked according to the percentage of total STA energy that they explained. Both individual skin marker displacements and marker-cluster geometrical transformations were task-, location-, segment- and subject-specific. However, 85% of the total STA energy was systematically explained by the rigid transformations (i.e. translations and rotations of the marker-cluster). In conclusion, large joint dislocations and limited efficiency of least squares bone pose estimators are expected for the computation of upper limb joint kinematics from skin markers. Future developments shall consider the rigid transformations of marker-clusters in the implementation of an STA model to reduce its effects on kinematics estimation.     

Orientation variance as a quantifier of structure in texture

I consider how structure is derived from texture containing changes in orientation over space, and propose that multi-local orientation variance (the average orientation variance across a series of discrete images locales) is an estimate of the degree of organization that is useful both for spatial scale selection and for discriminating structure from noise. The oriented textures used in this paper are Glass patterns, which contain structure at a narrow range of scales. The effect of adding noise to Glass patterns, on a structure versus noise task (Maloney et al., 1987), is compared to discrimination based on orientation variance and template matching (i.e. having prior knowledge of the target's orientation structure). At all but very low densities, the variance model accounts well for human data. Next, both models' estimates of tolerable orientation variance are shown to be broadly consistent with human discrimination of texture from noise. However, neither model can account for subjects' lower tolerance to noise for translational patterns than other (e.g. rotational) patterns. Finally, to investigate how well these structural measures preserve local orientation discontinuities, I show that the presence of a patch of unstructured dots embedded in a Glass pattern produces a change in multi-local orientation variance that is sufficient to account for human detection (Hel Or and Zucker, 1989). Together, these data suggest that simple orientation statistics could drive a range of 'texture tasks', although the dependency of noise resistance on the pattern type (rotation, translation, etc.) remains to be accounted for.     

Anthropogenic noise affects risk assessment and attention: the distracted prey hypothesis

Many studies have focused on the effects of anthropogenic noise on animal communication, but only a few have looked at its effect on other behavioural systems. We designed a playback experiment to test the effect of noise on predation risk assessment. We found that in response to boat motor playback, Caribbean hermit crabs (Coenobita clypeatus) allowed a simulated predator to approach closer before they hid. Two hypotheses may explain how boat noise affected risk assessment: it masked an approaching predator''s sound; and/or it reallocated some of the crabs'' finite attention, effectively distracting them, and thus preventing them from responding to an approaching threat. We found no support for the first hypothesis: a silent looming object still got closer during boat motor playbacks than during silence. However, we found support for the attentional hypothesis: when we added flashing lights to the boat motor noise to further distract the hermit crabs, we were able to approach the crabs more closely than with the noise alone. Anthropogenic sounds may thus distract prey and make them more vulnerable to predation.     

Which data should be tracked in forward-dynamic optimisation to best predict muscle forces in a pathological co-contraction case?

The choice of the cost-function for predicting muscle forces during a movement remains a challenge, especially in patients with neuromuscular disorders. Forward dynamics-based optimisations mainly track joint kinematics or torques, combined with a least-excitation criterion. Tracking marker trajectories and/or electromyography (EMG) has rarely been proposed. Our objective was to determine the best tracking objective-function to accurately predict the upper-limb muscle forces. A musculoskeletal model was created and EMG was simulated to obtain a reference movement – a shoulder abduction. A Gaussian noise (mean = 0; standard deviation = 15%) was added to the simulated EMG. Another noise – corresponding to the actual soft tissue artefacts (STA) of experimental shoulder abduction movements – was added to the trajectories of the markers placed on the model. Muscle forces were estimated from these noisy data, using forward dynamics assisted by six non-linear least-squared objective-functions. These functions involved the tracking of marker trajectories, joint angles or torques, with and without EMG-tracking. All six approaches used the same musculoskeletal model and were solved using a direct multiple shooting algorithm. Finally, the predicted joint angles, muscle forces and activations were compared to the reference values, using root-mean-square errors (RMSe) and biases. The force RMSe of the approach tracking both marker trajectories and EMG (18.45 ± 12.60 N) was almost five times lower than the one of the approach tracking only joint angles (82.37 ± 66.26 N) or torques (85.10 ± 116.40 N). Therefore, using EMG as a complementary tracking-data in forward dynamics seems to be promising for the estimation of muscle forces.