Statistics of natural movements are reflected in motor errors.

Humans use their arms to engage in a wide variety of motor tasks during everyday life. However, little is known about the statistics of these natural arm movements. Studies of the sensory system have shown that the statistics of sensory inputs are key to determining sensory processing. We hypothesized that the statistics of natural everyday movements may, in a similar way, influence motor performance as measured in laboratory-based tasks. We developed a portable motion-tracking system that could be worn by subjects as they went about their daily routine outside of a laboratory setting. We found that the well-documented symmetry bias is reflected in the relative incidence of movements made during everyday tasks. Specifically, symmetric and antisymmetric movements are predominant at low frequencies, whereas only symmetric movements are predominant at high frequencies. Moreover, the statistics of natural movements, that is, their relative incidence, correlated with subjects' performance on a laboratory-based phase-tracking task. These results provide a link between natural movement statistics and motor performance and confirm that the symmetry bias documented in laboratory studies is a natural feature of human movement.

The ensemble statistics of the energy of a random system subjected to harmonic excitation

This paper is concerned with the ensemble statistics of the response to harmonic excitation of a single dynamic system such as a plate or an acoustic volume. Random point process theory is employed, and various statistical assumptions regarding the system natural frequencies are compared, namely: (i) Poisson natural frequency spacings, (ii) statistically independent Rayleigh natural frequency spacings, and (iii) natural frequency spacings conforming to the Gaussian orthogonal ensemble (GOE). The GOE is found to be the most realistic assumption, and simple formulae are derived for the variance of the energy of the system under either point loading or rain-on-the-roof excitation. The theoretical results are compared favourably with numerical simulations and experimental data for the case of a mass loaded plate. © 2003 Elsevier Ltd. All rights reserved.

Image-based localization and pose recovery using scale invariant features

In this paper, we propose a vision based mobile robot localization strategy. Local scale-invariant features are used as natural landmarks in unstructured and unmodified environment. The local characteristics of the features we use prove to be robust to occlusion and outliers. In addition, the invariance of the features to viewpoint change makes them suitable landmarks for mobile robot localization. Scale-invariant features detected in the first exploration are indexed into a location database. Indexing and voting allow efficient recognition of global localization. The localization result is verified by epipolar geometry between the representative view in database and the view to be localized, thus the probability of false localization will be decreased. The localization system can recover the pose of the camera mounted on the robot by essential matrix decomposition. Then the position of the robot can be computed easily. Both calibrated and un-calibrated cases are discussed and relative position estimation based on calibrated camera turns out to be the better choice. Experimental results show that our approach is effective and reliable in the case of illumination changes, similarity transformations and extraneous features. © 2004 IEEE.

Statistical image modelling using interscale phase relationships of complex wavelet coefficients

A novel method for modelling the statistics of 2D photographic images useful in image restoration is defined. The new method is based on the Dual Tree Complex Wavelet Transform (DT-CWT) but a phase rotation is applied to the coefficients to create complex coefficients whose phase is shift-invariant at multiscale edge and ridge features. This is in addition to the magnitude shift invariance achieved by the DT-CWT. The increased correlation between coefficients adjacent in space and scale provides an improved mechanism for signal estimation. © 2006 IEEE.

Statistics and dynamics of turbulence-flame alignment in premixed combustion

The geometric alignment of turbulent strain-rate structures with premixed flames greatly influences the results of the turbulence-flame interaction. Here, the statistics and dynamics of this alignment are experimentally investigated in turbulent premixed Bunsen flames using high-repetition-rate stereoscopic particle image velocimetry. In all cases, the statistics showed that the most extensive principal strain-rate associated with the turbulence preferentially aligned such that it was more perpendicular than parallel to the flame surface normal direction. The mean turbulence-flame alignment differed between the flames, with the stronger flames (higher laminar flame speed) exhibiting stronger preferential alignment. Furthermore, the preferential alignment was greatest on the reactant side of the mean flame brush. To understand these differences, individual structures of fluid-dynamic strain-rate were tracked through time in a Lagrangian manner (i.e., by following the fluid elements). It was found that the flame surface affected the orientation of the turbulence structures, with the majority of structures rotating as they approached the flame such that their most extensive principal strain-rate was perpendicular to the flame normal. The maximum change in turbulent structure orientation was found to decrease with the strength of the structure, increase with the strength of the flame, and exhibit similar trends when the structure strength and flame strength were represented by a Karlovitz number. The mean change in orientation decreased from the unburnt to burnt side of the flame brush and appears to be influenced by the overall flame shape. © 2011 The Combustion Institute.

Boundary effects on the vibration statistics of a random plate

This paper considers the estimation of statistics of displacement of a vibrating rectangular plate with random wave scatterers. The influence of uncertainty is investigated using point impedance theory. Coherent boundary effects are seen, which decrease when the number of scatterers increases. The boundary effect is investigated using images and the first side and corner reflections are found to be a minimum requirement to estimate the spatial correlation. Statistics for point driven response are investigated under the assumption that the statistics of the natural frequencies follow those of the Gaussian Orthogonal Ensemble (GOE). The estimates are compared with Monte Carlo simulation results, and they show good agreement. © 2012 Elsevier Ltd. All rights reserved.

On sparsity and overcompleteness in image models

Computational models of visual cortex, and in particular those based on sparse coding, have enjoyed much recent attention. Despite this currency, the question of how sparse or how over-complete a sparse representation should be, has gone without principled answer. Here, we use Bayesian model-selection methods to address these questions for a sparse-coding model based on a Student-t prior. Having validated our methods on toy data, we find that natural images are indeed best modelled by extremely sparse distributions; although for the Student-t prior, the associated optimal basis size is only modestly over-complete.