Variational methods and its applications to computer vision

Many computer vision applications such as image segmentation can be formulated in a ''variational'' way as energy minimization problems. Unfortunately, the computational task of minimizing these energies is usually difficult as it generally involves non convex functions in a space with thousands of dimensions and often the associated combinatorial problems are NP-hard to solve. Furthermore, they are ill-posed inverse problems and therefore are extremely sensitive to perturbations (e.g. noise). For this reason in order to compute a physically reliable approximation from given noisy data, it is necessary to incorporate into the mathematical model appropriate regularizations that require complex computations. The main aim of this work is to describe variational segmentation methods that are particularly effective for curvilinear structures. Due to their complex geometry, classical regularization techniques cannot be adopted because they lead to the loss of most of low contrasted details. In contrast, the proposed method not only better preserves curvilinear structures, but also reconnects some parts that may have been disconnected by noise. Moreover, it can be easily extensible to graphs and successfully applied to different types of data such as medical imagery (i.e. vessels, hearth coronaries etc), material samples (i.e. concrete) and satellite signals (i.e. streets, rivers etc.). In particular, we will show results and performances about an implementation targeting new generation of High Performance Computing (HPC) architectures where different types of coprocessors cooperate. The involved dataset consists of approximately 200 images of cracks, captured in three different tunnels by a robotic machine designed for the European ROBO-SPECT project.Open Acces

Syntax inside the grammar

This volume collects novel contributions to comparative generative linguistics that “rethink” existing approaches to an extensive range of phenomena, domains, and architectural questions in linguistic theory. At the heart of the contributions is the tension between descriptive and explanatory adequacy which has long animated generative linguistics and which continues to grow thanks to the increasing amount and diversity of data available to us. The chapters address research questions on the relation of syntax to other aspects of grammar and linguistics more generally, including studies on language acquisition, variation and change, and syntactic interfaces. Many of these contributions show the influence of research by Ian Roberts and collaborators and give the reader a sense of the lively nature of current discussion of topics in synchronic and diachronic comparative syntax ranging from the core verbal domain to higher, propositional domains

Adaptive Methods for Robust Document Image Understanding

A vast amount of digital document material is continuously being produced as part of major digitization efforts around the world. In this context, generic and efficient automatic solutions for document image understanding represent a stringent necessity. We propose a generic framework for document image understanding systems, usable for practically any document types available in digital form. Following the introduced workflow, we shift our attention to each of the following processing stages in turn: quality assurance, image enhancement, color reduction and binarization, skew and orientation detection, page segmentation and logical layout analysis. We review the state of the art in each area, identify current defficiencies, point out promising directions and give specific guidelines for future investigation. We address some of the identified issues by means of novel algorithmic solutions putting special focus on generality, computational efficiency and the exploitation of all available sources of information. More specifically, we introduce the following original methods: a fully automatic detection of color reference targets in digitized material, accurate foreground extraction from color historical documents, font enhancement for hot metal typesetted prints, a theoretically optimal solution for the document binarization problem from both computational complexity- and threshold selection point of view, a layout-independent skew and orientation detection, a robust and versatile page segmentation method, a semi-automatic front page detection algorithm and a complete framework for article segmentation in periodical publications. The proposed methods are experimentally evaluated on large datasets consisting of real-life heterogeneous document scans. The obtained results show that a document understanding system combining these modules is able to robustly process a wide variety of documents with good overall accuracy

LULU operators on multidimensional arrays and applications

The LULU operators, Ln and Un, are smoothers, that is they smooth data received as a signal. They are nonlinear and this nonlinearity makes them more robust but also more complicated to study since the projection theorem does not hold. Their smoothing action is aimed at removing the impulsive noise present in any received signal. A signal can be of one or two dimensions, or of any higher dimension. In one dimension a signal is represented as a sequence and in two dimensions as an image. Higher dimensions include video feed and other more complex data streams. Carl Rohwer developed the LULU smoothers for sequences over the last three decades and the need for an extension to higher dimensions became more and more obvious as the applications of these smoothers were investigated. Perhaps the most important application is that of the Discrete Pulse Transform which is obtained via recursive application of the smoothers. In this dissertation the extension to dimensions higher than one is presented. All the essential properties developed for the one dimensional smoothers are replicated in this work. In addition, the Discrete Pulse Transform is used to illustrate some simple applications to image smoothing and feature detection. CopyrightDissertation (MSc)--University of Pretoria, 2010.Mathematics and Applied Mathematicsunrestricte