Bayesian filtering over compressed appearance states

This paper presents a framework for performing real-time recursive estimation of landmarks’ visual appearance. Imaging data in its original high dimensional space is probabilistically mapped to a compressed low dimensional space through the definition of likelihood functions. The likelihoods are subsequently fused with prior information using a Bayesian update. This process produces a probabilistic estimate of the low dimensional representation of the landmark visual appearance. The overall filtering provides information complementary to the conventional position estimates which is used to enhance data association. In addition to robotics observations, the filter integrates human observations in the appearance estimates. The appearance tracks as computed by the filter allow landmark classification. The set of labels involved in the classification task is thought of as an observation space where human observations are made by selecting a label. The low dimensional appearance estimates returned by the filter allow for low cost communication in low bandwidth sensor networks. Deployment of the filter in such a network is demonstrated in an outdoor mapping application involving a human operator, a ground and an air vehicle.

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.

Robust filtering and smoothing with gaussian processes

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning, robotics, and control for representing unknown system functions by posterior probability distributions. This modern way of system identification is more robust than finding point estimates of a parametric function representation. Our principled filtering/smoothing approach for GP dynamic systems is based on analytic moment matching in the context of the forward-backward algorithm. Our numerical evaluations demonstrate the robustness of the proposed approach in situations where other state-of-the-art Gaussian filters and smoothers can fail. © 2011 IEEE.

Particle filtering in geophysical systems

The application of particle filters in geophysical systems is reviewed. Some background on Bayesian filtering is provided, and the existing methods are discussed. The emphasis is on the methodology, and not so much on the applications themselves. It is shown that direct application of the basic particle filter (i.e., importance sampling using the prior as the importance density) does not work in high-dimensional systems, but several variants are shown to have potential. Approximations to the full problem that try to keep some aspects of the particle filter beyond the Gaussian approximation are also presented and discussed.

Rich probabilistic representations for bearing only decentralised data fusion

The aim of this paper is to demonstrate the validity of using Gaussian mixture models (GMM) for representing probabilistic distributions in a decentralised data fusion (DDF) framework. GMMs are a powerful and compact stochastic representation allowing efficient communication of feature properties in large scale decentralised sensor networks. It will be shown that GMMs provide a basis for analytical solutions to the update and prediction operations for general Bayesian filtering. Furthermore, a variant on the Covariance Intersect algorithm for Gaussian mixtures will be presented ensuring a conservative update for the fusion of correlated information between two nodes in the network. In addition, purely visual sensory data will be used to show that decentralised data fusion and tracking of non-Gaussian states observed by multiple autonomous vehicles is feasible.

Fast re-parameterisation of Gaussian mixture models for robotics applications

Autonomous navigation and picture compilation tasks require robust feature descriptions or models. Given the non Gaussian nature of sensor observations, it will be shown that Gaussian mixture models provide a general probabilistic representation allowing analytical solutions to the update and prediction operations in the general Bayesian filtering problem. Each operation in the Bayesian filter for Gaussian mixture models multiplicatively increases the number of parameters in the representation leading to the need for a re-parameterisation step. A computationally efficient re-parameterisation step will be demonstrated resulting in a compact and accurate estimate of the true distribution.

Target Tracking in UWB Multistatic Radars

Detection, localization and tracking of non-collaborative objects moving inside an area is of great interest to many surveillance applications. An ultra- wideband (UWB) multistatic radar is considered as a good infrastructure for such anti-intruder systems, due to the high range resolution provided by the UWB impulse-radio and the spatial diversity achieved with a multistatic configuration. Detection of targets, which are typically human beings, is a challenging task due to reflections from unwanted objects in the area, shadowing, antenna cross-talks, low transmit power, and the blind zones arised from intrinsic peculiarities of UWB multistatic radars. Hence, we propose more effective detection, localization, as well as clutter removal techniques for these systems. However, the majority of the thesis effort is devoted to the tracking phase, which is an essential part for improving the localization accuracy, predicting the target position and filling out the missed detections. Since UWB radars are not linear Gaussian systems, the widely used tracking filters, such as the Kalman filter, are not expected to provide a satisfactory performance. Thus, we propose the Bayesian filter as an appropriate candidate for UWB radars. In particular, we develop tracking algorithms based on particle filtering, which is the most common approximation of Bayesian filtering, for both single and multiple target scenarios. Also, we propose some effective detection and tracking algorithms based on image processing tools. We evaluate the performance of our proposed approaches by numerical simulations. Moreover, we provide experimental results by channel measurements for tracking a person walking in an indoor area, with the presence of a significant clutter. We discuss the existing practical issues and address them by proposing more robust algorithms.

Unified detection and tracking of instruments during retinal microsurgery

Methods for tracking an object have generally fallen into two groups: tracking by detection and tracking through local optimization. The advantage of detection-based tracking is its ability to deal with target appearance and disappearance, but it does not naturally take advantage of target motion continuity during detection. The advantage of local optimization is efficiency and accuracy, but it requires additional algorithms to initialize tracking when the target is lost. To bridge these two approaches, we propose a framework for unified detection and tracking as a time-series Bayesian estimation problem. The basis of our approach is to treat both detection and tracking as a sequential entropy minimization problem, where the goal is to determine the parameters describing a target in each frame. To do this we integrate the Active Testing (AT) paradigm with Bayesian filtering, and this results in a framework capable of both detecting and tracking robustly in situations where the target object enters and leaves the field of view regularly. We demonstrate our approach on a retinal tool tracking problem and show through extensive experiments that our method provides an efficient and robust tracking solution.

Filtering via approximate Bayesian computation

Approximate Bayesian computation (ABC) has become a popular technique to facilitate Bayesian inference from complex models. In this article we present an ABC approximation designed to perform biased filtering for a Hidden Markov Model when the likelihood function is intractable. We use a sequential Monte Carlo (SMC) algorithm to both fit and sample from our ABC approximation of the target probability density. This approach is shown to, empirically, be more accurate w.r.t.~the original filter than competing methods. The theoretical bias of our method is investigated; it is shown that the bias goes to zero at the expense of increased computational effort. Our approach is illustrated on a constrained sequential lasso for portfolio allocation to 15 constituents of the FTSE 100 share index.