New concepts for beam angle selection in IMRT treatment planning : From heuristics to combinatorial optimization

This thesis investigates beam ensemble selection strategies in intensity-modulated radiation therapy treatment planning. Beam ensemble selection strategies are applied to find the very beam ensembles that meet the treatments' objectives at the best possible rate. (1) A formal description of the beam ensemble selection problem is presented and the characteristics of the search space is discussed with a focus on its non-convexity and exponential complexity. (2) We review existing approaches to beam ensemble selection and provide a comprehensive overview of the field. (3) Conceptual advancements of beam ensemble selection strategies relying on score functions and geometric considerations are introduced. For photons, we demonstrate a clear benefit regarding organ at risk sparing for asymmetric patient geometries as regularly observed within the abdomen or skull. For protons, phantom studies yield plausible beam configurations. The measures taken to guarantee robustness regarding potential uncertainties are promising but require refinements. (4) The simultaneous optimization of beamlet weights and beam orientations is investigated at a very high precision. We apply different metaheuristics for the combinatorial optimization of beam ensembles and confirm the beneficial performance of genetic algorithms in this context. Both heuristic selection and combinatorial optimization of beam ensembles may yield extensive benefits for complicated planning cases. In the future it will be critical to transfer automated beam ensemble selection to the clinic for the benefit of the patient

Infinite von Mises-Fisher Mixture Modeling of Whole Brain fMRI Data

Cluster analysis of functional magnetic resonance imaging (fMRI) data is often performed using gaussian mixture models, but when the time series are standardized such that the data reside on a hypersphere, this modeling assumption is questionable. The consequences of ignoring the underlying spherical manifold are rarely analyzed, in part due to the computational challenges imposed by directional statistics. In this letter, we discuss a Bayesian von Mises–Fisher (vMF) mixture model for data on the unit hypersphere and present an efficient inference procedure based on collapsed Markov chain Monte Carlo sampling. Comparing the vMF and gaussian mixture models on synthetic data, we demonstrate that the vMF model has a slight advantage inferring the true underlying clustering when compared to gaussian-based models on data generated from both a mixture of vMFs and a mixture of gaussians subsequently normalized. Thus, when performing model selection, the two models are not in agreement. Analyzing multisubject whole brain resting-state fMRI data from healthy adult subjects, we find that the vMF mixture model is considerably more reliable than the gaussian mixture model when comparing solutions across models trained on different groups of subjects, and again we find that the two models disagree on the optimal number of components. The analysis indicates that the fMRI data support more than a thousand clusters, and we confirm this is not a result of overfitting by demonstrating better prediction on data from held-out subjects. Our results highlight the utility of using directional statistics to model standardized fMRI data and demonstrate that whole brain segmentation of fMRI data requires a very large number of functional units in order to adequately account for the discernible statistical patterns in the data. </jats:p

Isotropic Multiple Scattering Processes on Hyperspheres

This paper presents several results about isotropic random walks and multiple scattering processes on hyperspheres ${\mathbb S}^{p-1}$. It allows one to derive the Fourier expansions on ${\mathbb S}^{p-1}$ of these processes. A result of unimodality for the multiconvolution of symmetrical probability density functions (pdf) on ${\mathbb S}^{p-1}$ is also introduced. Such processes are then studied in the case where the scattering distribution is von Mises Fisher (vMF). Asymptotic distributions for the multiconvolution of vMFs on ${\mathbb S}^{p-1}$ are obtained. Both Fourier expansion and asymptotic approximation allows us to compute estimation bounds for the parameters of Compound Cox Processes (CCP) on ${\mathbb S}^{p-1}$.Comment: 16 pages, 4 figure

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions

Finite mixtures of von Mises-Fisher distributions allow to apply model-based clustering methods to data which is of standardized length, i.e., all data points lie on the unit sphere. The R package movMF contains functionality to draw samples from finite mixtures of von Mises-Fisher distributions and to fit these models using the expectation-maximization algorithm for maximum likelihood estimation. Special features are the possibility to use sparse matrix representations for the input data, different variants of the expectation-maximization algorithm, different methods for determining the concentration parameters in the M-step and to impose constraints on the concentration parameters over the components. In this paper we describe the main fitting function of the package and illustrate its application. In addition we compare the clustering performance of finite mixtures of von Mises-Fisher distributions to spherical k-means. We also discuss the resolution of several numerical issues which occur for estimating the concentration parameters and for determining the normalizing constant of the von Mises-Fisher distribution

Sensor-based human activity mining using Dirichlet process mixtures of directional statistical models

Funding: UK EPSRC under grant number EP/N007565/1, “Science of Sensor Systems Software”.We have witnessed an increasing number of activity-aware applications being deployed in real-world environments, including smart home and mobile healthcare. The key enabler to these applications is sensor-based human activity recognition; that is, recognising and analysing human daily activities from wearable and ambient sensors. With the power of machine learning we can recognise complex correlations between various types of sensor data and the activities being observed. However the challenges still remain: (1) they often rely on a large amount of labelled training data to build the model, and (2) they cannot dynamically adapt the model with emerging or changing activity patterns over time. To directly address these challenges, we propose a Bayesian nonparametric model, i.e. Dirichlet process mixture of conditionally independent von Mises Fisher models, to enable both unsupervised and semi-supervised dynamic learning of human activities. The Bayesian nonparametric model can dynamically adapt itself to the evolving activity patterns without human intervention and the learning results can be used to alleviate the annotation effort. We evaluate our approach against real-world, third-party smart home datasets, and demonstrate significant improvements over the state-of-the-art techniques in both unsupervised and supervised settings.Postprin

Real-time manhattan world rotation estimation in 3D

Drift of the rotation estimate is a well known problem in visual odometry systems as it is the main source of positioning inaccuracy. We propose three novel algorithms to estimate the full 3D rotation to the surrounding Manhattan World (MW) in as short as 20 ms using surface-normals derived from the depth channel of a RGB-D camera. Importantly, this rotation estimate acts as a structure compass which can be used to estimate the bias of an odometry system, such as an inertial measurement unit (IMU), and thus remove its angular drift. We evaluate the run-time as well as the accuracy of the proposed algorithms on groundtruth data. They achieve zerodrift rotation estimation with RMSEs below 3.4° by themselves and below 2.8° when integrated with an IMU in a standard extended Kalman filter (EKF). Additional qualitative results show the accuracy in a large scale indoor environment as well as the ability to handle fast motion. Selected segmentations of scenes from the NYU depth dataset demonstrate the robustness of the inference algorithms to clutter and hint at the usefulness of the segmentation for further processing.United States. Office of Naval Research. Multidisciplinary University Research Initiative6 (Awards N00014-11-1-0688 and N00014-10-1-0936)National Science Foundation (U.S.) (Award IIS-1318392