Over time RF fitting for Jitter Free 3D Vertebra Reconstruction from Video Fluoroscopy

Over the past decades, there has been an increasing interest in spine kinematics. Various approaches have been proposed on how to observe and analyse spine kinematics from a computer vision perspective. Amongst all, emphasis has been given to both the shape of the individual vertebrae as well as the overall spine curvature as a means of providing accurate and valid spinal condition diagnosis. Traditional invasive methods cannot accurately delineate the intersegmental motion of the spine vertebrae. On the contrary, capturing and measuring spinal motion via the non-invasive fluoroscopy has been a popular technique choice because of its low incurred patient radiation exposure nature. In general, image-based and other reconstruction methods target individual frames and focus on static spine instances. However, even the ones analysing sequences yield in unstable and jittery animations of the reconstructed spine. In this report, we address this issue using a novel approach to robustly reconstruct and rigidly derive a shape with no inter-frame variations. This is to produce animations that are jitter free across our sequence based on fluoroscopy video. Our main contributions are 1) retaining the shape of the solid vertebrae across the frame range, 2) helping towards a more accurate image segmentation even when there's a limited training set. We show our pipeline's success by reconstructing and comparing 3D animations of the lumbar spine from a corresponding fluoroscopic video

Iterative State Estimation in Non-linear Dynamical Systems Using Approximate Expectation Propagation

Bayesian inference in non-linear dynamical systems seeks to find good posterior approximations of a latent state given a sequence of observations. Gaussian filters and smoothers, including the (extended/unscented) Kalman filter/smoother, which are commonly used in engineering applications, yield Gaussian posteriors on the latent state. While they are computationally efficient, they are often criticised for their crude approximation of the posterior state distribution. In this paper, we address this criticism by proposing a message passing scheme for iterative state estimation in non-linear dynamical systems, which yields more informative (Gaussian) posteriors on the latent states. Our message passing scheme is based on expectation propagation (EP). We prove that classical Rauch--Tung--Striebel (RTS) smoothers, such as the extended Kalman smoother (EKS) or the unscented Kalman smoother (UKS), are special cases of our message passing scheme. Running the message passing scheme more than once can lead to significant improvements of the classical RTS smoothers, so that more informative state estimates can be obtained. We address potential convergence issues of EP by generalising our state estimation framework to damped updates and the consideration of general alpha-divergences

Model-Predictive Control with New NUV Priors

Normals with unknown variance (NUV) can represent many useful priors including $L_p$ norms and other sparsifying priors, and they blend well with linear-Gaussian models and Gaussian message passing algorithms. In this paper, we elaborate on recently proposed discretizing NUV priors, and we propose new NUV representations of half-space constraints and box constraints. We then demonstrate the use of such NUV representations with exemplary applications in model predictive control, with a variety of constraints on the input, the output, or the internal stateof the controlled system. In such applications, the computations boil down to iterations of Kalman-type forward-backward recursions, with a complexity (per iteration) that is linear in the planning horizon. In consequence, this approach can handle long planning horizons, which distinguishes it from the prior art. For nonconvex constraints, this approach has no claim to optimality, but it is empirically very effective

Nonparametric Message Passing Methods for Cooperative Localization and Tracking

The objective of this thesis is the development of cooperative localization and tracking algorithms using nonparametric message passing techniques. In contrast to the most well-known techniques, the goal is to estimate the posterior probability density function (PDF) of the position of each sensor. This problem can be solved using Bayesian approach, but it is intractable in general case. Nevertheless, the particle-based approximation (via nonparametric representation), and an appropriate factorization of the joint PDFs (using message passing methods), make Bayesian approach acceptable for inference in sensor networks. The well-known method for this problem, nonparametric belief propagation (NBP), can lead to inaccurate beliefs and possible non-convergence in loopy networks. Therefore, we propose four novel algorithms which alleviate these problems: nonparametric generalized belief propagation (NGBP) based on junction tree (NGBP-JT), NGBP based on pseudo-junction tree (NGBP-PJT), NBP based on spanning trees (NBP-ST), and uniformly-reweighted NBP (URW-NBP). We also extend NBP for cooperative localization in mobile networks. In contrast to the previous methods, we use an optional smoothing, provide a novel communication protocol, and increase the efficiency of the sampling techniques. Moreover, we propose novel algorithms for distributed tracking, in which the goal is to track the passive object which cannot locate itself. In particular, we develop distributed particle filtering (DPF) based on three asynchronous belief consensus (BC) algorithms: standard belief consensus (SBC), broadcast gossip (BG), and belief propagation (BP). Finally, the last part of this thesis includes the experimental analysis of some of the proposed algorithms, in which we found that the results based on real measurements are very similar with the results based on theoretical models

Bayesian Methods in the Search for MH370

Probability theor

Dynamical models for neonatal intensive care monitoring

The vital signs monitoring data of an infant receiving intensive care are a rich source of information about its health condition. One major concern about the state of health of such patients is the onset of neonatal sepsis, a life-threatening bloodstream infection. As early signs are subtle and current diagnosis procedures involve slow laboratory testing, sepsis detection based on the monitored physiological dynamics is a clinically significant task. This challenging problem can be thoroughly modelled as real-time inference within a machine learning framework. In this thesis, we develop probabilistic dynamical models centred around the goal of providing useful predictions about the onset of neonatal sepsis. This research is characterised by the careful incorporation of domain knowledge for the purpose of extracting the infant’s true physiology from the monitoring data. We make two main contributions. The first one is the formulation of sepsis detection as learning and inference in an Auto-Regressive Hidden Markov Model (AR-HMM). The model investigates the extent to which physiological events observed in the patient’s monitoring traces could be used for the early detection of neonatal sepsis. In addition, the proposed approach involves exact marginalisation over missing data at inference time. When applying the ARHMM on a real-world dataset, we found that it can produce effective predictions about the onset of sepsis. Second, both sepsis and clinical event detection are formulated as learning and inference in a Hierarchical Switching Linear Dynamical System (HSLDS). The HSLDS models dynamical systems where complex interactions between modes of operation can be represented as a twolevel hidden discrete hierarchical structure. For neonatal condition monitoring, the lower layer models clinical events and is controlled by upper layer variables with semantics sepsis/nonsepsis. The model parameterisation and estimation procedures are adapted to the specifics of physiological monitoring data. We demonstrate that the performance of the HSLDS for the detection of sepsis is not statistically different from the AR-HMM, despite the fact that the latter model is given “ground truth” annotations of the patient’s physiology

Bayesian Methods in the Search for MH370

Probability theor

Kernel-based fault diagnosis of inertial sensors using analytical redundancy

Kernel methods are able to exploit high-dimensional spaces for representational advantage, while only operating implicitly in such spaces, thus incurring none of the computational cost of doing so. They appear to have the potential to advance the state of the art in control and signal processing applications and are increasingly seeing adoption across these domains. Applications of kernel methods to fault detection and isolation (FDI) have been reported, but few in aerospace research, though they offer a promising way to perform or enhance fault detection. It is mostly in process monitoring, in the chemical processing industry for example, that these techniques have found broader application. This research work explores the use of kernel-based solutions in model-based fault diagnosis for aerospace systems. Specifically, it investigates the application of these techniques to the detection and isolation of IMU/INS sensor faults – a canonical open problem in the aerospace field. Kernel PCA, a kernelised non-linear extension of the well-known principal component analysis (PCA) algorithm, is implemented to tackle IMU fault monitoring. An isolation scheme is extrapolated based on the strong duality known to exist between probably the most widely practiced method of FDI in the aerospace domain – the parity space technique – and linear principal component analysis. The algorithm, termed partial kernel PCA, benefits from the isolation properties of the parity space method as well as the non-linear approximation ability of kernel PCA. Further, a number of unscented non-linear filters for FDI are implemented, equipped with data-driven transition models based on Gaussian processes - a non-parametric Bayesian kernel method. A distributed estimation architecture is proposed, which besides fault diagnosis can contemporaneously perform sensor fusion. It also allows for decoupling faulty sensors from the navigation solution