Dimension and bases for geometrically continuous splines on surfaces of arbitrary topology

We analyze the space of geometrically continuous piecewise polynomial functions, or splines, for rectangular and triangular patches with arbitrary topology and general rational transition maps. To define these spaces of G 1 spline functions, we introduce the concept of topological surface with gluing data attached to the edges shared by faces. The framework does not require manifold constructions and is general enough to allow non-orientable surfaces. We describe compatibility conditions on the transition maps so that the space of differentiable functions is ample and show that these conditions are necessary and sufficient to construct ample spline spaces. We determine the dimension of the space of G1 spline functions which are of degree less than or equal to k on triangular pieces and of bi-degree less than or equal to (k, k) on rectangular pieces, for k big enough. A separability property on the edges is involved to obtain the dimension formula. An explicit construction of basis functions attached resspectively to vertices, edges and faces is proposed; examples of bases of G1 splines of small degree for topological surfaces with boundary and without boundary are detailed

Segmentation of candidate bacillus objects in images of Ziehl-Neelsen-stained sputum smears using deformable models

Includes abstract.Includes bibliographical references (leaves 83-88).Automated microscopy for the detection of tuberculosis (TB) in sputum smears seeks to address the strain on technicians and to achieve faster diagnosis in order to cope with the rising number of TB cases. Image processing techniques provide a useful alternative to the conventional, manual analysis of sputum smears for diagnosis. In the project described here, the use of parametric and geometric deformable models was explored for segmentation of TB bacilli in images of Ziehl-Neelsen-stained sputum smears for automated TB diagnosis. The goal of segmentation is to produce candidate bacillus objects for input into a classifier

Design paramétrico a partir da digitalização 3D de geometrias da natureza com padrão de crescimento espiral

A modelagem de geometrias da natureza pode ser um processo complexo devido ás características orgânicas dos elementos. Propõe-se com essa dissertação identificar geometrias espaciais que sigam o padrão de crescimento espiral observado na natureza, utilizando as Tecnologias 3D como ferramentas para o processo de projeto. Para a execução do trabalho foram investigadas os Métodos de Biônica, Crescimento Espiral e a Sequência de Fibonacci, Engenharia Reversa e Design Paramétrico. O processo de representação dos elementos foi realizado em conformidade com a Metodologia para o Desenvolvimento de Produtos Baseados no Estudo da Biônica com o acréscimo das tecnologias de digitalização tridimensional e de processamento de nuvem de pontos, complementado pela parametrização de superfícies à base de curvas. Foram utilizados três processos para modelagem de curvas paramétricas representadas (i) pelo desenho de linhas sobre a malha digitalizada em 3D, (ii) por programação visual no software Grasshopper e (iii) por programação com scripts Python. Foi avaliada como melhor alternativa para o Design Paramétrico a utilização da programação visual otimizada com a programação por scripts, a qual apresentou melhor aproximação entre as curvas analisadas. Estudos de casos realizados com elementos da natureza (abacaxi e pinha) demonstraram a viabilização do método. Desta maneira a sistematização do conhecimento permitirá a proposição de um modelo paramétrico baseado na Biônica para fase inicial de inspiração e concepção de alternativas do projeto de produto.Modeling the geometries of nature can be a complex process due to the organic characteristics of the elements. It is proposed with this dissertation to identify spatial geometries that follow the pattern of spiral growth observed in nature, using 3D Technologies as tools for the design process. For the execution of the work were investigated the Bionics, Spiral Growth and Fibonacci Sequence, Reverse Engineering and Parametric Design. The process of representation of the elements was carried out in accordance with the Methodology for the Development of Products Based on the Study of the Bionics with the addition of the technologies of three-dimensional digitization and processing of cloud of points, complemented by the parameterization of surfaces based on curves. Three methods were used for modeling parametric curves represented by (i) the drawing of lines on the 3D scanned mesh, (ii) by visual programming in the Grasshopper software and (iii) by programming with Python scripts. It was evaluated as the best alternative for Parametric Design the use of optimized visual programming with programming by scripts, which presented better approximation between the analyzed curves. Case studies carried out with nature elements (pineapple and pine cone) demonstrated the viability of the method. In this way the systematization of the knowledge will allow the proposition of a parametric model based on the Bionics for the initial phase of inspiration and design of alternatives of the product design

Using contour information and segmentation for object registration, modeling and retrieval

This thesis considers different aspects of the utilization of contour information and syntactic and semantic image segmentation for object registration, modeling and retrieval in the context of content-based indexing and retrieval in large collections of images. Target applications include retrieval in collections of closed silhouettes, holistic w ord recognition in handwritten historical manuscripts and shape registration. Also, the thesis explores the feasibility of contour-based syntactic features for improving the correspondence of the output of bottom-up segmentation to semantic objects present in the scene and discusses the feasibility of different strategies for image analysis utilizing contour information, e.g. segmentation driven by visual features versus segmentation driven by shape models or semi-automatic in selected application scenarios. There are three contributions in this thesis. The first contribution considers structure analysis based on the shape and spatial configuration of image regions (socalled syntactic visual features) and their utilization for automatic image segmentation. The second contribution is the study of novel shape features, matching algorithms and similarity measures. Various applications of the proposed solutions are presented throughout the thesis providing the basis for the third contribution which is a discussion of the feasibility of different recognition strategies utilizing contour information. In each case, the performance and generality of the proposed approach has been analyzed based on extensive rigorous experimentation using as large as possible test collections

Combinatorial optimisation for arterial image segmentation.

Cardiovascular disease is one of the leading causes of the mortality in the western world. Many imaging modalities have been used to diagnose cardiovascular diseases. However, each has different forms of noise and artifacts that make the medical image analysis field important and challenging. This thesis is concerned with developing fully automatic segmentation methods for cross-sectional coronary arterial imaging in particular, intra-vascular ultrasound and optical coherence tomography, by incorporating prior and tracking information without any user intervention, to effectively overcome various image artifacts and occlusions. Combinatorial optimisation methods are proposed to solve the segmentation problem in polynomial time. A node-weighted directed graph is constructed so that the vessel border delineation is considered as computing a minimum closed set. A set of complementary edge and texture features is extracted. Single and double interface segmentation methods are introduced. Novel optimisation of the boundary energy function is proposed based on a supervised classification method. Shape prior model is incorporated into the segmentation framework based on global and local information through the energy function design and graph construction. A combination of cross-sectional segmentation and longitudinal tracking is proposed using the Kalman filter and the hidden Markov model. The border is parameterised using the radial basis functions. The Kalman filter is used to adapt the inter-frame constraints between every two consecutive frames to obtain coherent temporal segmentation. An HMM-based border tracking method is also proposed in which the emission probability is derived from both the classification-based cost function and the shape prior model. The optimal sequence of the hidden states is computed using the Viterbi algorithm. Both qualitative and quantitative results on thousands of images show superior performance of the proposed methods compared to a number of state-of-the-art segmentation methods

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity