Real time feature-based facial tracking using Lie algebras

We have developed a novel human facial tracking system that operates in real time at a video frame rate without needing any special hardware. The approach is based on the use of Lie algebra, and uses three-dimensional feature points on the targeted human face. It is assumed that the roughly estimated facial model (relative coordinates of the three-dimensional feature points) is known. First, the initial feature positions of the face are determined using a model fitting technique. Then, the tracking is operated by the following sequence: (1) capture the new video frame and render feature points to the image plane; (2) search for new positions of the feature points on the image plane; (3) get the Euclidean matrix from the moving vector and the three-dimensional information for the points; and (4) rotate and translate the feature points by using the Euclidean matrix, and render the new points on the image plane. The key algorithm of this tracker is to estimate the Euclidean matrix by using a least square technique based on Lie algebra. The resulting tracker performed very well on the task of tracking a human face.

Polarisation diversity of conformal arrays based on geometric algebra via convex optimisation

A simple and general design procedure is presented for the polarisation diversity of arbitrary conformal arrays; this procedure is based on the mathematical framework of geometric algebra and can be solved optimally using convex optimisation. Aside from being simpler and more direct than other derivations in the literature, this derivation is also entirely general in that it expresses the transformations in terms of rotors in geometric algebra which can easily be formulated for any arbitrary conformal array geometry. Convex optimisation has a number of advantages; solvers are widespread and freely available, the process generally requires a small number of iterations and a wide variety of constraints can be readily incorporated. The study outlines a two-step approach for addressing polarisation diversity in arbitrary conformal arrays: first, the authors obtain the array polarisation patterns using geometric algebra and secondly use a convex optimisation approach to find the optimal weights for the polarisation diversity problem. The versatility of this approach is illustrated via simulations of a 7×10 cylindrical conformal array. © 2012 The Institution of Engineering and Technology.

Anchors, scales and the relative coding of value in the brain.

People are alarmingly susceptible to manipulations that change both their expectations and experience of the value of goods. Recent studies in behavioral economics suggest such variability reflects more than mere caprice. People commonly judge options and prices in relative terms, rather than absolutely, and display strong sensitivity to exemplar and price anchors. We propose that these findings elucidate important principles about reward processing in the brain. In particular, relative valuation may be a natural consequence of adaptive coding of neuronal firing to optimise sensitivity across large ranges of value. Furthermore, the initial apparent arbitrariness of value may reflect the brains' attempts to optimally integrate diverse sources of value-relevant information in the face of perceived uncertainty. Recent findings in neuroscience support both accounts, and implicate regions in the orbitofrontal cortex, striatum, and ventromedial prefrontal cortex in the construction of value.

Coordination on Lie groups

This paper studies the coordinated motion of a group of agents evolving on a Lie group. Left-or rightinvariance with respect to the absolute position on the group lead to two different characterizations of relative positions and two associated definitions of coordination (fixed relative positions). Conditions for each type of coordination are derived in the associated Lie algebra. This allows to formulate the coordination problem on Lie groups as consensus in a vector space. Total coordination occurs when both types of coordination hold simultaneously. The discussion in this paper provides a common geometric framework for previously published coordination control laws on SO(3), SE(2) and SE(3). The theory is illustrated on the group of planar rigid motion SE(2). © 2008 IEEE.

Negative Effects of Relative Proximity and Absolute Geography on Open Innovation Practices in High-tech SMEs in the UK

© 2014 IEEE. This exploratory study addresses a gap in management literature by addressing the role of location in the continuously expanding field of open innovation research. In this context, we analyze potential negative effects of absolute geography and relative proximity on open innovation practices in high-tech small and medium-sized enterprises (SMEs) in the United Kingdom. Drawing upon cluster theory and business ecosystem literature, the analysis from three SME case studies in the East of England suggests that presumed 'favorable' location variables, such as close relative proximity between partners and the presence of economic clusters, can have certain negative effects on open innovation practices.