Operator Gauge Symmetry in QED

In this paper, operator gauge transformation, first introduced by Kobe, is applied to Maxwell's equations and continuity equation in QED. The gauge invariance is satisfied after quantization of electromagnetic fields. Inherent nonlinearity in Maxwell's equations is obtained as a direct result due to the nonlinearity of the operator gauge transformations. The operator gauge invariant Maxwell's equations and corresponding charge conservation are obtained by defining the generalized derivatives of the first and second kinds. Conservation laws for the real and virtual charges are obtained too. The additional terms in the field strength tensor are interpreted as electric and magnetic polarization of the vacuum.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Relative Facial Action Unit Detection

This paper presents a subject-independent facial action unit (AU) detection method by introducing the concept of relative AU detection, for scenarios where the neutral face is not provided. We propose a new classification objective function which analyzes the temporal neighborhood of the current frame to decide if the expression recently increased, decreased or showed no change. This approach is a significant change from the conventional absolute method which decides about AU classification using the current frame, without an explicit comparison with its neighboring frames. Our proposed method improves robustness to individual differences such as face scale and shape, age-related wrinkles, and transitions among expressions (e.g., lower intensity of expressions). Our experiments on three publicly available datasets (Extended Cohn-Kanade (CK+), Bosphorus, and DISFA databases) show significant improvement of our approach over conventional absolute techniques. Keywords: facial action coding system (FACS); relative facial action unit detection; temporal information;Comment: Accepted at IEEE Winter Conference on Applications of Computer Vision, Steamboat Springs Colorado, USA, 201