In a large number of applications, the processing relies on objects or area of interests, and the pixel-based image representation is notwell adapted. These applications would benefit from a region-based processing. Early examples of region-based processing can be found in the area of image segmentation, such as the quad tree. Recently, in mathematical morphology, the connected operators have received much attention. They are region-based filtering tools that act by merging flat zones. They have good contour preservation properties in the sense that they do not create any new boundaries, neither do they shift the existing ones. One popular implementation for connected operators relies on tree-based image representations, notably threshold decomposition representations and hierarchical representations. Those tree-based image representations are widely used in many image processing and computer vision applications. Tree-based connected operators consist in constructing a set of nested or disjoint connected components, followed by a filtering of these connected components based on an attribute function characterizing each connected component. Finally, the filtered image is reconstructed from the simplified tree composed of the remaining connected components. In the work presented in this thesis, we propose to expand the ideas of tree-based connected operators. We introduce the notion of tree-based shape spaces, built from tree-based image representations. Many state-of-the-art methods relying on tree-based image representations consist of analyzing this shape space. A first consequence of this change of point of view is our proposition of a local feature detector, called the tree-based Morse regions (TBMR). It can be seen as a variant of the MSER method. The selection of TBMRs is based on topological information, and hence it extracts the regions independently of the contrast, which makes it truly contrast invariant and quasi parameters free. The accuracy and robustness of the TBMR approach are demonstrated by the repeatability test and by applications to image registration and 3D reconstruction, as compared to some state-of-the-art methods. The basic idea of the main proposition in this thesis is to apply connected filters on the shape space. Such a processing is called the framework of shape-based morphology. It is a versatile framework that deals with region-based image representations. It has three main consequences. 1) For filtering purpose, it is a generalization of the existing tree-based connected operators. Indeed, the framework encompasses classical existing connected operators by attributes. Besides, It also allows us to propose two classes of novel connected operators: shape-based lower/upper levelings and shapings. 2) This framework can be used to object detection/segmentation by selecting relevant points in the shape space. 3) We can also use this framework to transform the hierarchies using the extinction values, so that a hierarchical simplification or segmentation is obtained. Some applications are developed using the framework of shape-based morphology to demonstrate its usefulness. The applications of the shape-based filtering to retinal image analysis show that a mere filtering step that we compare to more evolved processings, achieves state-of-the-art results. An efficient shaping used for image simplification is proposed by minimizing Mumford-Shah functional subordinated to the topographic map. For object detection/segmentation, we proposed a context-based energy estimator that is suitable to characterize object meaningfulness. Last, we extend the hierarchy of constrained connectivity using the aspect of hierarchy transformation of constrained connectivity using the aspect ofhierarchy transformation.

Dans le travail présenté dans cette thèse, nous proposons d'élargir les idées des opérateurs connexes à base d'arbres. Nous introduisons la notion d'espaces de formes à base d'arbres, construit à partir des représentations d'image à base d'arbres. De nombreuses méthodes de l'état de l'art, s'appuyant sur ces représentations d'images à base d'arbres, consistent à analyser cet espace de forme. Une première conséquence de ce changement de point de vue est notre proposition d'un détecteur de caractéristiques locales, appelé les « tree-based Morse regions » (TBMR). Cette approche peut être considérée comme une variante de la méthode des MSER. La sélection des TBMRs est basée sur des informations topologiques, et donc extrait les régions indépendamment du contraste, ce qui la rend vraiment invariante aux changements de contraste; de plus, la méthode peut être considérée sans paramètres. La précision et la robustesse de l'approche TBMR sont démontrées par le test de reproductibilité et par des applications au recalage d'image et à la reconstruction 3D, en comparaison des méthodes de l'état de l'art. L'idée de base de la proposition principale dans cette thèse est d'appliquer les opérateurs connexes à l'espace des formes. Un tel traitement est appelé la morphologie basée sur la forme. Ce cadre polyvalent traite des représentations d'images à base de région. Il a trois conséquences principales. 1) Dans un but de filtrage, il s'agit d'une généralisation des opérateurs connexes à base d'arbres. En effet, le cadre englobe les opérateurs connexes classiques par attributs. En outre, il permet également de proposer deux nouvelles classes d'opérateurs connexes: nivellements inférieurs/supérieurs à base de forme et shapings. 2) Ce cadre peut être utilisé pour la détection/segmentation d'objets en sélectionnant les points pertinents dans l'espace des formes. 3) Nous pouvons également utiliser ce cadre pour transformer les hiérarchies en utilisant les valeurs d'extinction, obtenant ainsi une simplification/segmentation hiérarchique. Afin de montrer l'utilité de l'approche proposée, plusieurs applications sont développées. Les applications à l'analyse d'images rétinenne de filtrage basé sur la forme montrent qu'une simple étape de filtrage, comparée à des traitements plus évolués, réalise des résultats au niveau de l'état de l'art. Une application de shaping pour la simplification d'image est proposée, fondée sur une minimisation de la fonctionnelle de Mumford-Shah subordonnée à l'arbre de formes. Pour la détection/segmentation d'objets, nous proposons un estimateur de l'énergie basée sur le contexte. Cet estimateur est approprié pour caractériser la signification d'objet. Enfin, nous étendons le cadre de la connectivité contrainte en utilisant l'aspect de transformation de hiérarchie / In a large number of applications, the processing relies on objects or area of interests, and the pixel-based image representation is notwell adapted. These applications would benefit from a region-based processing. Early examples of region-based processing can be found in the area of image segmentation, such as the quad tree. Recently, in mathematical morphology, the connected operators have received much attention. They are region-based filtering tools that act by merging flat zones. They have good contour preservation properties in the sense that they do not create any new boundaries, neither do they shift the existing ones. One popular implementation for connected operators relies on tree-based image representations, notably threshold decomposition representations and hierarchical representations. Those tree-based image representations are widely used in many image processing and computer vision applications. Tree-based connected operators consist in constructing a set of nested or disjoint connected components, followed by a filtering of these connected components based on an attribute function characterizing each connected component. Finally, the filtered image is reconstructed from the simplified tree composed of the remaining connected components. In the work presented in this thesis, we propose to expand the ideas of tree-based connected operators. We introduce the notion of tree-based shape spaces, built from tree-based image representations. Many state-of-the-art methods relying on tree-based image representations consist of analyzing this shape space. A first consequence of this change of point of view is our proposition of a local feature detector, called the tree-based Morse regions (TBMR). It can be seen as a variant of the MSER method. The selection of TBMRs is based on topological information, and hence it extracts the regions independently of the contrast, which makes it truly contrast invariant and quasi parameters free. The accuracy and robustness of the TBMR approach are demonstrated by the repeatability test and by applications to image registration and 3D reconstruction, as compared to some state-of-the-art methods. The basic idea of the main proposition in this thesis is to apply connected filters on the shape space. Such a processing is called the framework of shape-based morphology. It is a versatile framework that deals with region-based image representations. It has three main consequences. 1) For filtering purpose, it is a generalization of the existing tree-based connected operators. Indeed, the framework encompasses classical existing connected operators by attributes. Besides, It also allows us to propose two classes of novel connected operators: shape-based lower/upper levelings and shapings. 2) This framework can be used to object detection/segmentation by selecting relevant points in the shape space. 3) We can also use this framework to transform the hierarchies using the extinction values, so that a hierarchical simplification or segmentation is obtained. Some applications are developed using the framework of shape-based morphology to demonstrate its usefulness. The applications of the shape-based filtering to retinal image analysis show that a mere filtering step that we compare to more evolved processings, achieves state-of-the-art results. An efficient shaping used for image simplification is proposed by minimizing Mumford-Shah functional subordinated to the topographic map. For object detection/segmentation, we proposed a context-based energy estimator that is suitable to characterize object meaningfulness. Last, we extend the hierarchy of constrained connectivity using the aspect of hierarchy transformation of constrained connectivity using the aspect ofhierarchy transformation.

Schistosoma mansoni é o parasita causador da esquistossomose mansônica que, de acordo com o Ministério da Saúde do Brasil, afeta atualmente vários milhões de pessoas no país. Uma das formas de diagnóstico da esquistossomose é a detecção de ovos do parasita através da análise de lâminas microscópicas com material fecal. Esta tarefa é extremamente cansativa, principalmente nos casos de baixa endemicidade, pois a quantidade de ovos é muito pequena. Nesses casos, uma abordagem computacional para auxílio na detecção de ovos facilitaria o trabalho de diagnóstico. Os ovos têm formato ovalado, possuem uma membrana translúcida, apresentam uma espícula e sua cor é ligeiramente amarelada. Porém nem todas essas características são observadas em todos os ovos e algumas delas são visíveis apenas com uma ampliação adequada. Além disso, o aspecto visual do material fecal varia muito de indivíduo para indivíduo em termos de cor e presença de diversos artefatos (tais como partículas que não são desintegradas pelo sistema digestivo), tornando difícil a tarefa de detecção dos ovos. Neste trabalho investigamos, em particular, o problema de detecção das linhas que contornam a borda de vários dos ovos. Propomos um método composto por duas fases. A primeira fase consiste na detecção de estruturas do tipo linha usando operadores morfológicos. A detecção de linhas é dividida em três etapas principais: (i) realce de linhas, (ii) detecção de linhas, e (iii) refinamento do resultado para eliminar segmentos de linhas que não são de interesse. O resultado dessa fase é um conjunto de segmentos de linhas. A segunda fase consiste na detecção de subconjuntos de segmentos de linha dispostos em formato elíptico, usando um algoritmo baseado na transformada Hough. As elipses detectadas são fortes candidatas a contorno de ovos de S. mansoni. Resultados experimentais mostram que a abordagem proposta pode ser útil para compor um sistema de auxílio à detecção dos ovos. / Schistosoma mansoni is one of the parasites which causes schistosomiasis. According to the Brazilian Ministry of Health, several million people in the country are currently affected by schistosomiasis. One way of diagnosing it is by egg identification in stool. This task is extremely time-consuming and tiring, especially in cases of low endemicity, when only few eggs are present. In such cases, a computational approach to help the detection of eggs would greatly facilitate the diagnostic task. Schistosome eggs present oval shape, have a translucent membrane and a spike, and their color is slightly yellowish. However, not all these features are observed in every egg and some of them are visible only with an adequate microscopic magnification. Furthermore, the visual aspect of the fecal material varies widely from person to person in terms of color and presence of different artifacts (such as particles which are not disintegrated by the digestive system), making it difficult to detect the eggs. In this work we investigate the problem of detecting lines which delimit the contour of the eggs. We propose a method comprising two steps. The first phase consists in detecting line-like structures using morphological operators. This line detection phase is divided into three steps: (i) line enhancement, (ii) line detection, and (iii) result refinement in order to eliminate line segments that are not of interest. The output of this phase is a set of line segments. The second phase consists in detecting subsets of line segments arranged in an elliptical shape, using an algorithm based on the Hough transform. Detected ellipses are strong candidates to contour of S. mansoni eggs. Experimental results show that the proposed approach has potential to be effectively used as a component in a computer system to help egg detection.

Submitted by Sandro Camargo (sandro.camargo@unipampa.edu.br) on 2015-05-09T18:40:27Z No. of bitstreams: 1 117110023.pdf: 2523085 bytes, checksum: 76eb3f9960e2b4f9df14435d3092b156 (MD5) / Made available in DSpace on 2015-05-09T18:40:27Z (GMT). No. of bitstreams: 1 117110023.pdf: 2523085 bytes, checksum: 76eb3f9960e2b4f9df14435d3092b156 (MD5) Previous issue date: 2013-12-13 / Este trabalho tem como objetivo a proposição de um novo método para a detecção automática de microaneurismas e hemorragias em imagens de fundo do olho. Essas lesões são consideradas o primeiro sinal de retinopatia diabética. A retinopatia diabética é uma doença originada pelo diabetes e é apontada com a principal causa de cegueira na população com idade ativa de trabalho. O método proposto é fundamentado em conceitos de morfologia matemática e consiste em eliminar os componentes da anatomia da retina até atingir o conjunto de lesões. Este método é formado por cinco etapas: a) pré-processamento; b) destaque das estruturas escuras; c) detecção dos vasos sanguíneos; d) eliminação dos vasos sanguíneos; e) eliminação da fóvea. A precisão do método foi testada num banco de dados público de imagens de fundo do olho, onde o mesmo obteve resultados satisfatórios e comparáveis aos demais métodos da literatura, reportando médias de sensitividade e especificidade de 87.69% e 92.44%, respectivamente. / This contribution presents an approach for automatic detection of microaneurysms and hemorrhages in fundus images. These lesions are considered the earliest signs of diabetic retinopathy. The diabetic retinopathy is a disease caused by diabetes and is considered as the major cause of blindness in working age population. The proposed method is based on mathematical morphology and consists in removing components of retinal anatomy to reach the lesions. This method consists of five steps: a) pre-processing; b) enhancement of low intensity structures; c) detection of blood vessels; d) elimination of blood vessels; e) elimination of the fovea. The accuracy of the method was tested on a public database of fundus images, where it achieved satisfactory results, comparable to other methods from the literature, reporting 87.69% and 92.44% of mean sensitivity and specificity, respectively.

O mapeamento de ambientes é um dos maiores desafios para pesquisadores na área de navegação autônoma. As técnicas existentes estão divididas em dois importantes paradigmas, o mapeamento métrico e o topológico. Diversos métodos de mapeamento que combinam as vantagens de cada um desses paradigmas têm sido propostos. Este projeto consiste na adaptação e extensão de um sistema integrado para navegação autônoma de robôs móveis através do aperfeiçoamento da interface e também da incorporação de uma técnica de mapeamento topológico. Para isso, a técnica conhecida como Grade de Ocupação, utilizada em geral para mapeamento métrico é combinada com um método de esqueletização de imagens para a realização do mapeamento topológico. Além disso, transformações morfológicas de erosão e abertura, adequadas a ambientes reais, foram utilizadas, visando reduzir a influência de ruídos na abordagem proposta, uma vez que devido a ruídos inerentes as leituras sensoriais obtidas pelo robô, o mapa topológico gerado apresenta diversas linhas topológicas desnecessárias, dificultando consequentemente a tarefa de navegação autônoma. Vários experimentos foram executados para verificar a eficiência da combinação de técnicas proposta, tanto em nível de simulação quanto em um robô real. Os resultados obtidos demonstraram que a técnica de esqueletização de imagens combinada ao mapeamento métrico do ambiente é uma forma simples e viável de se obter as linhas topológicas do espaço livre do ambiente. A aplicação das transformações morfológicas demonstrou ser eficiente para a criação de mapas topológicos livres de ruído, uma vez que elimina grande parte das linhas topológicas geradas em conseqüência dos ruídos dos sensores do robô / Environment mapping has been a great challenge for many researchers in the autonomous navigation area. There are two important paradigms for mapping, metric and topological mapping. Several mapping methods that combine the advantages of each paradigm have been proposed. This project consists to the adaptation and extension of a mobile robots autonomous navigation integrated system by improving the interface and incorporation of a topological mapping technique. For this, the technique known as Occupation Grid for metric mapping is combined with an image skeletonization method used for topological mapping. This work also aims to propose a set of morphology transformations to generation of topological maps suitable for real environments, seeking to reduce influence of noise in performed mapping. The topological map generated through this combination presents several unnecessary topological lines, due noise inherent to the own robot ability of capturing sensor signals, hindering consequently the task of autonomous navigation. Several experiments have been performed to verify the efficiency of the proposed approach. The results obtained demonstrate that image skeletonization technique combined with the metric mapping is a simple and feasible method for obtaining the topological lines corresponding to free space of the environment. The application of the morphology transformations demonstrated to be a useful method to the creation of topological maps considerably less noise, since it eliminates most of the topological lines generated in consequence of noise in the sensors

Esta dissertação apresenta um novo método de segmentação de movimento baseado na obtenção dos contornos e em filtros morfológicos. A nova técnica apresenta vantagens em relação ao número de falsos positivos e falsos negativos em situações específicas quando comparada às técnicas tradicionais. / This work presents a novel motion segmentation technique based in contours and in morphological filters. It presents advantages in the number of false positives and false negatives in some situations when compared to the classic techniques.

This thesis primarily addresses the problem of automatic measurement of ore textures by image analysis in a way that is relevant to mineral processing. Specifically, it addresses the following major hypotheses: • Automatic logging of drill core by image analysis provides a feasible alternative to manual logging by geologists. • Image analysis can quantify process mineralogy by physically meaningful parameters. • Multi-scale image analysis, over a wide range of size scales, provides potential benefits to process mineralogy that are additional to those available from small-scale analysis alone, and also better retains the information content of manual logging. • Image analysis can provide physically meaningful, ore-texture-related, additive regionalised variables that can be input to geostatistical models and the definition of domains. The central focus of the thesis is the development of an automatic, multi-scale method to identify and measure objects in an image, using a specially-developed skeleton termed the morphological CWT skeleton. This skeleton is a multi-scale extension of the morphological skeleton commonly used in image analysis, and is derived from the continuous wavelet transform (CWT). Objects take the form of hierarchical segments from image segmentation based on the CWT. Only the Mexican hat, also known as the Laplacian-of-Gaussian, wavelet is used, although other wavelet shapes are possible. The natural scale of each object is defined to be the size scale at which its CWT signal (the contrast between the interior and exterior of the object) is strongest. In addition to the natural scale, the analysis automatically records the mineral composition of both the interior and exterior of each object, and shape descriptors of the object. The measurements of natural scale, mineral composition and shape are designed to relate to: • The size to which ore must be broken in order to liberate objects. • Minerals that need to be separated by physical or chemical means once objects have been liberated. • Capability to distinguish qualitatively different ore-texture types that may have different geological origins and for which different processing regimes may provide an economic benefit. Measurements are taken over size scales from three pixels to hundreds of pixels. For the major case study the pixel size is about 50 µm, but the methodology is equally applicable to photomicrographs in which the pixel size is about 4 µm. The methodology for identifying objects in images contributes to the field of scale-space image segmentation, and has advantages in performing the following actions automatically: • Finding optimal size scales in hierarchical image segmentation (natural scale). • Merging segments that are similar and spatially close together (although not necessarily touching), using the structure of the morphological CWT skeleton, thus aiding recognition of complex structures in an image. • Defining the contrast between each segment and its surrounding segments appropriately for the size scale of the segment, in a way that extends well beyond the segment boundary. For process mineralogy this contrast quantifies mineral associations at different size scales. The notion of natural scale defined in this thesis may have applications to other fields of image processing, such as mammography and cell measurements in biological microscopy. The objects identified in images are input to cluster analysis, using a finite mixture model to group the objects into object populations according to their size, composition and shape descriptors. Each image is then characterised by the abundances of different object populations that occur in it. These abundances form additive, regionalised variables that can be input into geostatistical block models. The images are themselves input to higher-level cluster analysis based on a hidden Markov model. A collection of images is divided into different ore texture types, based on differences in the abundances of the textural object populations. The ore texture types help to define geostatistical domains in an ore body. Input images for the methodology take the form of mineral maps, in which a particular mineral has been assigned to each pixel in the image prior to analysis. A method of analysing unmapped, raw colour images of ore is also outlined, as is a new model for fracture of ore. The major case study in the thesis is an analysis of approximately 1000 metres of continuously-imaged drill core from four drill holes in the Ernest Henry iron-oxide-copper-gold ore deposit (Queensland, Australia). Thirty-one texture-related variables are used to summarise the individual half-metres of drill core, and ten major ore texture types are identified. Good agreement is obtained between locations of major changes in ore type found by automatic image analysis, and those identified from manual core logging carried out by geologists. The texture-related variables are found to explain a significant amount of the variation in comminution hardness of ore within the deposit, over and above that explained by changes in abundances of the component minerals. The thesis also contributes new algorithms with wide applicability in image processing: • A fast algorithm for computing the continuous wavelet transform of a signal or image: The new algorithm is simpler in form and several times faster than the best previously-published algorithms. It consists of a single finite impulse response (FIR) filter. • A fast algorithm for computing Euclidean geodesic distance. This algorithm runs in O(1) arithmetic operations per pixel processed, which has not been achieved by any previously published algorithm. Geodesic distance is widely used in image processing, for segmentation and shape characterisation.

Ocular fundus image can provide information on pathological changes caused by local ocular diseases and early signs of certain systemic diseases. Automated analysis and interpretation of fundus images has become a necessary and important diagnostic procedure in ophthalmology. Among the features in ocular fundus image are the optic disc, fovea (central vision area), lesions, and retinal vessels. These features are useful in revealing the states of diseases in the form of measurable abnormalities such as length of diameter, change in color, and degree of tortuosity in the vessels. In addition, retinal vessels can also serve as landmarks for image-guided laser treatment of choroidal neovascularization. Thus, reliable methods for blood vessel detection that preserve various vessel measurements are needed. In this paper, we will examine the pathological issues in the analysis of retinal vessels in digital fundus images and give a survey of current image processing methods for extracting vessels in retinal images with a view to categorize them and highlight their differences and similarities. We have also implemented two major approaches using matched filter and mathematical morphology respectively and compared their performances. Some prospective research directions are identified. / Singapore-MIT Alliance (SMA)

The focus of this research is the extension of topological operators with the addition of a inclusion measure. This extension is carried out in both crisp and fuzzy topological spaces. The mathematical properties of the new operators are discussed and compared with traditional operators. Ignoring small errors due to imperfections and noise in digital images is the main motivation in introducing the proposed operators. To show the effectiveness of the new operators, we demonstrate their utility in image database classification and shape classification. Each image (shape) category is modeled with a topological space and the interior of the query image is obtained with respect to different topologies. This novel way of looking at the image categories and classifying a query image shows some promising results. Moreover, the proposed interior and closure operators with inclusion degree is utilized in mathematical morphology area. The morphological operators with inclusion degree outperform traditional morphology in noise removal and edge detection in a noisy environment

In this work we study the framework of mathematical morphology on simplicial complex spaces. Simplicial complexes are a versatile and widely used structure to represent multidimensional data, such as meshes, that are tridimensional complexes, or graphs, that can be interpreted as bidimensional complexes. Mathematical morphology is one of the most powerful frameworks for image processing, including the processing of digital structures, and is heavily used for many applications. However, mathematical morphology operators on simplicial complex spaces is not a concept fully developped in the literature. In this work, we review some classical operators from simplicial complexes under the light of mathematical morphology, to show that they are morphology operators. We define some basic lattices and operators acting on these lattices: dilations, erosions, openings, closings and alternating sequential filters, including their extension to weighted simplexes. However, the main contributions of this work are what we called dimensional operators, small, versatile operators that can be used to define new operators on simplicial complexes, while mantaining properties from mathematical morphology. These operators can also be used to express virtually any operator from the literature. We illustrate all the defined operators and compare the alternating sequential filters against filters defined in the literature, where our filters show better results for removal of small, intense, noise from binary images