Gauge field theory for Poincar\'{e}-Weyl group

On the basis of the general principles of a gauge field theory the gauge theory for the Poincar\'{e}-Weyl group is constructed. It is shown that tetrads are not true gauge fields, but represent functions from true gauge fields: Lorentzian, translational and dilatational ones. The equations of gauge fields which sources are an energy-momentum tensor, orbital and spin momemta, and also a dilatational current of an external field are obtained. A new direct interaction of the Lorentzian gauge field with the orbital momentum of an external field appears, which describes some new effects. Geometrical interpretation of the theory is developed and it is shown that as a result of localization of the Poincar\'{e}-Weyl group spacetime becomes a Weyl-Cartan space. Also the geometrical interpretation of a dilaton field as a component of the metric tensor of a tangent space in Weyl-Cartan geometry is proposed.Comment: LaTex, 27 pages, no figure

Vessel tractography using an intensity based tensor model with branch detection

In this paper, we present a tubular structure seg- mentation method that utilizes a second order tensor constructed from directional intensity measurements, which is inspired from diffusion tensor image (DTI) modeling. The constructed anisotropic tensor which is fit inside a vessel drives the segmen- tation analogously to a tractography approach in DTI. Our model is initialized at a single seed point and is capable of capturing whole vessel trees by an automatic branch detection algorithm developed in the same framework. The centerline of the vessel as well as its thickness is extracted. Performance results within the Rotterdam Coronary Artery Algorithm Evaluation framework are provided for comparison with existing techniques. 96.4% average overlap with ground truth delineated by experts is obtained in addition to other measures reported in the paper. Moreover, we demonstrate further quantitative results over synthetic vascular datasets, and we provide quantitative experiments for branch detection on patient Computed Tomography Angiography (CTA) volumes, as well as qualitative evaluations on the same CTA datasets, from visual scores by a cardiologist expert

Topological Optimization of the Evaluation of Finite Element Matrices

We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on phrasing the computation on each element as the contraction of each collection of reference element tensors with an element-specific geometric tensor. We then present a new concept of complexity-reducing relations that serve as distance relations between these reference element tensors. This notion sets up a graph-theoretic context in which we may find an optimized algorithm by computing a minimum spanning tree. We present experimental results for some common multilinear forms showing significant reductions in operation count and also discuss some efficient algorithms for building the graph we use for the optimization

An orientation field approach to modelling fibre-generated spatial point processes

This thesis introduces a new approach to analysing spatial point data clustered along or around a system of curves or fibres with additional background noise. Such data arise in catalogues of galaxy locations, recorded locations of earthquakes, aerial images of minefields, and pore patterns on fingerprints. Finding the underlying curvilinear structure of these point-pattern data sets may not only facilitate a better understanding of how they arise but also aid reconstruction of missing data. We base the space of fibres on the set of integral lines of an orientation field. Using an empirical Bayes approach, we estimate the field of orientations from anisotropic features of the data. The orientation field estimation draws on ideas from tensor field theory (an area recently motivated by the study of magnetic resonance imaging scans), using symmetric positive-definite matrices to estimate local anisotropies in the point pattern through the tensor method. We also propose a new measure of anisotropy, the modified square Fractional Anisotropy, whose statistical properties are estimated for tensors calculated via the tensor method. A continuous-time Markov chain Monte Carlo algorithm is used to draw samples from the posterior distribution of fibres, exploring models with different numbers of clusters, and fitting fibres to the clusters as it proceeds. The Bayesian approach permits inference on various properties of the clusters and associated fibres, and the resulting algorithm performs well on a number of very different curvilinear structures

Automated Extraction of Road Information from Mobile Laser Scanning Data

Effective planning and management of transportation infrastructure requires adequate geospatial data. Existing geospatial data acquisition techniques based on conventional route surveys are very time consuming, labor intensive, and costly. Mobile laser scanning (MLS) technology enables a rapid collection of enormous volumes of highly dense, irregularly distributed, accurate geo-referenced point cloud data in the format of three-dimensional (3D) point clouds. Today, more and more commercial MLS systems are available for transportation applications. However, many transportation engineers have neither interest in the 3D point cloud data nor know how to transform such data into their computer-aided model (CAD) formatted geometric road information. Therefore, automated methods and software tools for rapid and accurate extraction of 2D/3D road information from the MLS data are urgently needed. This doctoral dissertation deals with the development and implementation aspects of a novel strategy for the automated extraction of road information from the MLS data. The main features of this strategy include: (1) the extraction of road surfaces from large volumes of MLS point clouds, (2) the generation of 2D geo-referenced feature (GRF) images from the road-surface data, (3) the exploration of point density and intensity of MLS data for road-marking extraction, and (4) the extension of tensor voting (TV) for curvilinear pavement crack extraction. In accordance with this strategy, a RoadModeler prototype with three computerized algorithms was developed. They are: (1) road-surface extraction, (2) road-marking extraction, and (3) pavement-crack extraction. Four main contributions of this development can be summarized as follows. Firstly, a curb-based approach to road surface extraction with assistance of the vehicle’s trajectory is proposed and implemented. The vehicle’s trajectory and the function of curbs that separate road surfaces from sidewalks are used to efficiently separate road-surface points from large volume of MLS data. The accuracy of extracted road surfaces is validated with manually selected reference points. Secondly, the extracted road enables accurate detection of road markings and cracks for transportation-related applications in road traffic safety. To further improve computational efficiency, the extracted 3D road data are converted into 2D image data, termed as a GRF image. The GRF image of the extracted road enables an automated road-marking extraction algorithm and an automated crack detection algorithm, respectively. Thirdly, the automated road-marking extraction algorithm applies a point-density-dependent, multi-thresholding segmentation to the GRF image to overcome unevenly distributed intensity caused by the scanning range, the incidence angle, and the surface characteristics of an illuminated object. The morphological operation is then implemented to deal with the presence of noise and incompleteness of the extracted road markings. Fourthly, the automated crack extraction algorithm applies an iterative tensor voting (ITV) algorithm to the GRF image for crack enhancement. The tensor voting, a perceptual organization method that is capable of extracting curvilinear structures from the noisy and corrupted background, is explored and extended into the field of crack detection. The successful development of three algorithms suggests that the RoadModeler strategy offers a solution to the automated extraction of road information from the MLS data. Recommendations are given for future research and development to be conducted to ensure that this progress goes beyond the prototype stage and towards everyday use

Inferring Geodesic Cerebrovascular Graphs: Image Processing, Topological Alignment and Biomarkers Extraction

A vectorial representation of the vascular network that embodies quantitative features - location, direction, scale, and bifurcations - has many potential neuro-vascular applications. Patient-specific models support computer-assisted surgical procedures in neurovascular interventions, while analyses on multiple subjects are essential for group-level studies on which clinical prediction and therapeutic inference ultimately depend. This first motivated the development of a variety of methods to segment the cerebrovascular system. Nonetheless, a number of limitations, ranging from data-driven inhomogeneities, the anatomical intra- and inter-subject variability, the lack of exhaustive ground-truth, the need for operator-dependent processing pipelines, and the highly non-linear vascular domain, still make the automatic inference of the cerebrovascular topology an open problem. In this thesis, brain vessels’ topology is inferred by focusing on their connectedness. With a novel framework, the brain vasculature is recovered from 3D angiographies by solving a connectivity-optimised anisotropic level-set over a voxel-wise tensor field representing the orientation of the underlying vasculature. Assuming vessels joining by minimal paths, a connectivity paradigm is formulated to automatically determine the vascular topology as an over-connected geodesic graph. Ultimately, deep-brain vascular structures are extracted with geodesic minimum spanning trees. The inferred topologies are then aligned with similar ones for labelling and propagating information over a non-linear vectorial domain, where the branching pattern of a set of vessels transcends a subject-specific quantized grid. Using a multi-source embedding of a vascular graph, the pairwise registration of topologies is performed with the state-of-the-art graph matching techniques employed in computer vision. Functional biomarkers are determined over the neurovascular graphs with two complementary approaches. Efficient approximations of blood flow and pressure drop account for autoregulation and compensation mechanisms in the whole network in presence of perturbations, using lumped-parameters analog-equivalents from clinical angiographies. Also, a localised NURBS-based parametrisation of bifurcations is introduced to model fluid-solid interactions by means of hemodynamic simulations using an isogeometric analysis framework, where both geometry and solution profile at the interface share the same homogeneous domain. Experimental results on synthetic and clinical angiographies validated the proposed formulations. Perspectives and future works are discussed for the group-wise alignment of cerebrovascular topologies over a population, towards defining cerebrovascular atlases, and for further topological optimisation strategies and risk prediction models for therapeutic inference. Most of the algorithms presented in this work are available as part of the open-source package VTrails

Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects

Numerical modeling of nematic liquid crystals using the tensorial Landau-de Gennes (LdG) theory provides detailed insights into the structure and energetics of the enormous variety of possible topological defect configurations that may arise when the liquid crystal is in contact with colloidal inclusions or structured boundaries. However, these methods can be computationally expensive, making it challenging to predict (meta)stable configurations involving several colloidal particles, and they are often restricted to system sizes well below the experimental scale. Here we present an open-source software package that exploits the embarrassingly parallel structure of the lattice discretization of the LdG approach. Our implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate simulations using both CPU and GPU resources in either single- or multiple-core configurations. We make use of an efficient minimization algorithm, the Fast Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale parallelization, requiring little additional memory or computational cost while offering performance competitive with other commonly used methods. In multi-core operation we are able to scale simulations up to supra-micron length scales of experimental relevance, and in single-core operation the simulation package includes a user-friendly GUI environment for rapid prototyping of interfacial features and the multifarious defect states they can promote. To demonstrate this software package, we examine in detail the competition between curvilinear disclinations and point-like hedgehog defects as size scale, material properties, and geometric features are varied. We also study the effects of an interface patterned with an array of topological point-defects.Comment: 16 pages, 6 figures, 1 youtube link. The full catastroph