Advanced traffic video analytics for robust traffic accident detection

Automatic traffic accident detection is an important task in traffic video analysis due to its key applications in developing intelligent transportation systems. Reducing the time delay between the occurrence of an accident and the dispatch of the first responders to the scene may help lower the mortality rate and save lives. Since 1980, many approaches have been presented for the automatic detection of incidents in traffic videos. In this dissertation, some challenging problems for accident detection in traffic videos are discussed and a new framework is presented in order to automatically detect single-vehicle and intersection traffic accidents in real-time. First, a new foreground detection method is applied in order to detect the moving vehicles and subtract the ever-changing background in the traffic video frames captured by static or non-stationary cameras. For the traffic videos captured during day-time, the cast shadows degrade the performance of the foreground detection and road segmentation. A novel cast shadow detection method is therefore presented to detect and remove the shadows cast by moving vehicles and also the shadows cast by static objects on the road. Second, a new method is presented to detect the region of interest (ROI), which applies the location of the moving vehicles and the initial road samples and extracts the discriminating features to segment the road region. After detecting the ROI, the moving direction of the traffic is estimated based on the rationale that the crashed vehicles often make rapid change of direction. Lastly, single-vehicle traffic accidents and trajectory conflicts are detected using the first-order logic decision-making system. The experimental results using publicly available videos and a dataset provided by the New Jersey Department of Transportation (NJDOT) demonstrate the feasibility of the proposed methods. Additionally, the main challenges and future directions are discussed regarding (i) improving the performance of the foreground segmentation, (ii) reducing the computational complexity, and (iii) detecting other types of traffic accidents

Hardware acceleration of the trace transform for vision applications

Computer Vision is a rapidly developing field in which machines process visual data to extract meaningful information. Digitised images in their pixels and bits serve no purpose of their own. It is only by interpreting the data, and extracting higher level information that a scene can be understood. The algorithms that enable this process are often complex, and data-intensive, limiting the processing rate when implemented in software. Hardware-accelerated implementations provide a significant performance boost that can enable real- time processing. The Trace Transform is a newly proposed algorithm that has been proven effective in image categorisation and recognition tasks. It is flexibly defined allowing the mathematical details to be tailored to the target application. However, it is highly computationally intensive, which limits its applications. Modern heterogeneous FPGAs provide an ideal platform for accelerating the Trace transform for real-time performance, while also allowing an element of flexibility, which highly suits the generality of the Trace transform. This thesis details the implementation of an extensible Trace transform architecture for vision applications, before extending this architecture to a full flexible platform suited to the exploration of Trace transform applications. As part of the work presented, a general set of architectures for large-windowed median and weighted median filters are presented as required for a number of Trace transform implementations. Finally an acceleration of Pseudo 2-Dimensional Hidden Markov Model decoding, usable in a person detection system, is presented. Such a system can be used to extract frames of interest from a video sequence, to be subsequently processed by the Trace transform. All these architectures emphasise the need for considered, platform-driven design in achieving maximum performance through hardware acceleration

Matlab

This book is a collection of 19 excellent works presenting different applications of several MATLAB tools that can be used for educational, scientific and engineering purposes. Chapters include tips and tricks for programming and developing Graphical User Interfaces (GUIs), power system analysis, control systems design, system modelling and simulations, parallel processing, optimization, signal and image processing, finite different solutions, geosciences and portfolio insurance. Thus, readers from a range of professional fields will benefit from its content

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the successful rst edition of this workshop in 20061 and second edition in New-York in 20082, the third edition was held in Toronto on September 22 20113. Contributions were solicited in Riemannian and group theoretical methods, geometric measurements of the anatomy, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, modeling of growth and longitudinal shape changes. 22 submissions were reviewed by three members of the program committee. To guaranty a high level program, 11 papers only were selected for oral presentation in 4 sessions. Two of these sessions regroups classical themes of the workshop: statistics on manifolds and diff eomorphisms for surface or longitudinal registration. One session gathers papers exploring new mathematical structures beyond Riemannian geometry while the last oral session deals with the emerging theme of statistics on graphs and trees. Finally, a poster session of 5 papers addresses more application oriented works on computational anatomy

Left-invariant Stochastic Evolution Equations on SE(2) and its Applications to Contour Enhancement and Contour Completion via Invertible Orientation Scores

We provide the explicit solutions of linear, left-invariant, (convection)-diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2). These diffusion equations are forward Kolmogorov equations for stochastic processes for contour enhancement and completion. The solutions are group-convolutions with the corresponding Green's function, which we derive in explicit form. We mainly focus on the Kolmogorov equations for contour enhancement processes which, in contrast to the Kolmogorov equations for contour completion, do not include convection. The Green's functions of these left-invariant partial differential equations coincide with the heat-kernels on SE(2), which we explicitly derive. Then we compute completion distributions on SE(2) which are the product of a forward and a backward resolvent evolved from resp. source and sink distribution on SE(2). On the one hand, the modes of Mumford's direction process for contour completion coincide with elastica curves minimizing $\int \kappa^{2} + \epsilon ds$, related to zero-crossings of 2 left-invariant derivatives of the completion distribution. On the other hand, the completion measure for the contour enhancement concentrates on geodesics minimizing $\int \sqrt{\kappa^{2} + \epsilon} ds$. This motivates a comparison between geodesics and elastica, which are quite similar. However, we derive more practical analytic solutions for the geodesics. The theory is motivated by medical image analysis applications where enhancement of elongated structures in noisy images is required. We use left-invariant (non)-linear evolution processes for automated contour enhancement on invertible orientation scores, obtained from an image by means of a special type of unitary wavelet transform

Making Presentation Math Computable

This Open-Access-book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats. To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries. This is an open access book

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described