Single camera pose estimation using Bayesian filtering and Kinect motion priors

Traditional approaches to upper body pose estimation using monocular vision rely on complex body models and a large variety of geometric constraints. We argue that this is not ideal and somewhat inelegant as it results in large processing burdens, and instead attempt to incorporate these constraints through priors obtained directly from training data. A prior distribution covering the probability of a human pose occurring is used to incorporate likely human poses. This distribution is obtained offline, by fitting a Gaussian mixture model to a large dataset of recorded human body poses, tracked using a Kinect sensor. We combine this prior information with a random walk transition model to obtain an upper body model, suitable for use within a recursive Bayesian filtering framework. Our model can be viewed as a mixture of discrete Ornstein-Uhlenbeck processes, in that states behave as random walks, but drift towards a set of typically observed poses. This model is combined with measurements of the human head and hand positions, using recursive Bayesian estimation to incorporate temporal information. Measurements are obtained using face detection and a simple skin colour hand detector, trained using the detected face. The suggested model is designed with analytical tractability in mind and we show that the pose tracking can be Rao-Blackwellised using the mixture Kalman filter, allowing for computational efficiency while still incorporating bio-mechanical properties of the upper body. In addition, the use of the proposed upper body model allows reliable three-dimensional pose estimates to be obtained indirectly for a number of joints that are often difficult to detect using traditional object recognition strategies. Comparisons with Kinect sensor results and the state of the art in 2D pose estimation highlight the efficacy of the proposed approach.Comment: 25 pages, Technical report, related to Burke and Lasenby, AMDO 2014 conference paper. Code sample: https://github.com/mgb45/SignerBodyPose Video: https://www.youtube.com/watch?v=dJMTSo7-uF

Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a comparatively small number of parameters, intrinsic errors from sampling fluctuations may outweigh the differences in the log marginal likelihood estimates. In the present article, we propose a thermodynamic integration scheme that directly targets the log Bayes factor. The method is based on a modified annealing path between the posterior distributions of the two models compared, which systematically avoids the high variance prior regime. We combine this scheme with the concept of non-equilibrium TI to minimise discretisation errors from numerical integration. Results obtained on Bayesian regression models applied to standard benchmark data, and a complex hierarchical model applied to biopathway inference, demonstrate a significant reduction in estimator variance over state-of-the-art TI methods

Likelihood Non-Gaussianity in Large-Scale Structure Analyses

Standard present day large-scale structure (LSS) analyses make a major assumption in their Bayesian parameter inference --- that the likelihood has a Gaussian form. For summary statistics currently used in LSS, this assumption, even if the underlying density field is Gaussian, cannot be correct in detail. We investigate the impact of this assumption on two recent LSS analyses: the Beutler et al. (2017) power spectrum multipole ($P_\ell$) analysis and the Sinha et al. (2017) group multiplicity function ($\zeta$) analysis. Using non-parametric divergence estimators on mock catalogs originally constructed for covariance matrix estimation, we identify significant non-Gaussianity in both the $P_\ell$ and $\zeta$ likelihoods. We then use Gaussian mixture density estimation and Independent Component Analysis on the same mocks to construct likelihood estimates that approximate the true likelihood better than the Gaussian $pseudo$-likelihood. Using these likelihood estimates, we accurately estimate the true posterior probability distribution of the Beutler et al. (2017) and Sinha et al. (2017) parameters. Likelihood non-Gaussianity shifts the $f\sigma_8$ constraint by $-0.44\sigma$, but otherwise, does not significantly impact the overall parameter constraints of Beutler et al. (2017). For the $\zeta$ analysis, using the pseudo-likelihood significantly underestimates the uncertainties and biases the constraints of Sinha et al. (2017) halo occupation parameters. For $\log M_1$ and $\alpha$, the posteriors are shifted by $+0.43\sigma$ and $-0.51\sigma$ and broadened by $42\%$ and $66\%$, respectively. The divergence and likelihood estimation methods we present provide a straightforward framework for quantifying the impact of likelihood non-Gaussianity and deriving more accurate parameter constraints.Comment: 33 pages, 7 figure