A New Spatio-Temporal Model Exploiting Hamiltonian Equations

The solutions of Hamiltonian equations are known to describe the underlying phase space of the mechanical system. In Bayesian Statistics, the only place, where the properties of solutions to the Hamiltonian equations are successfully applied, is Hamiltonian Monte Carlo. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations, incorporating appropriate stochasticity via Gaussian processes. The resultant sptaio-temporal process, continuously varying with time, turns out to be nonparametric, nonstationary, nonseparable and no-Gaussian. Besides, the lagged correlations tend to zero as the spatio-temporal lag tends to infinity. We investigate the theoretical properties of the new spatio-temporal process, along with its continuity and smoothness properties. Considering the Bayesian paradigm, we derive methods for complete Bayesian inference using MCMC techniques. Applications of our new model and methods to two simulation experiments and two real data sets revealed encouraging performance

Review of constraints on vision-based gesture recognition for human–computer interaction

The ability of computers to recognise hand gestures visually is essential for progress in human-computer interaction. Gesture recognition has applications ranging from sign language to medical assistance to virtual reality. However, gesture recognition is extremely challenging not only because of its diverse contexts, multiple interpretations, and spatio-temporal variations but also because of the complex non-rigid properties of the hand. This study surveys major constraints on vision-based gesture recognition occurring in detection and pre-processing, representation and feature extraction, and recognition. Current challenges are explored in detail

Long-Term Memory Motion-Compensated Prediction

Long-term memory motion-compensated prediction extends the spatial displacement vector utilized in block-based hybrid video coding by a variable time delay permitting the use of more frames than the previously decoded one for motion compensated prediction. The long-term memory covers several seconds of decoded frames at the encoder and decoder. The use of multiple frames for motion compensation in most cases provides significantly improved prediction gain. The variable time delay has to be transmitted as side information requiring an additional bit rate which may be prohibitive when the size of the long-term memory becomes too large. Therefore, we control the bit rate of the motion information by employing rate-constrained motion estimation. Simulation results are obtained by integrating long-term memory prediction into an H.263 codec. Reconstruction PSNR improvements up to 2 dB for the Foreman sequence and 1.5 dB for the Mother–Daughter sequence are demonstrated in comparison to the TMN-2.0 H.263 coder. The PSNR improvements correspond to bit-rate savings up to 34 and 30%, respectively. Mathematical inequalities are used to speed up motion estimation while achieving full prediction gain

Loop Quantum Gravity

The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a mathematically well-defined, non-perturbative and background independent quantization of general relativity, with its conventional matter couplings. The research in loop quantum gravity forms today a vast area, ranging from mathematical foundations to physical applications. Among the most significative results obtained are: (i) The computation of the physical spectra of geometrical quantities such as area and volume; which yields quantitative predictions on Planck-scale physics. (ii) A derivation of the Bekenstein-Hawking black hole entropy formula. (iii) An intriguing physical picture of the microstructure of quantum physical space, characterized by a polymer-like Planck scale discreteness. This discreteness emerges naturally from the quantum theory and provides a mathematically well-defined realization of Wheeler's intuition of a spacetime ``foam''. Long standing open problems within the approach (lack of a scalar product, overcompleteness of the loop basis, implementation of reality conditions) have been fully solved. The weak part of the approach is the treatment of the dynamics: at present there exist several proposals, which are intensely debated. Here, I provide a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.Comment: Review paper written for the electronic journal `Living Reviews'. 34 page