Adaptive Algorithms for Automated Processing of Document Images

Large scale document digitization projects continue to motivate interesting document understanding technologies such as script and language identification, page classification, segmentation and enhancement. Typically, however, solutions are still limited to narrow domains or regular formats such as books, forms, articles or letters and operate best on clean documents scanned in a controlled environment. More general collections of heterogeneous documents challenge the basic assumptions of state-of-the-art technology regarding quality, script, content and layout. Our work explores the use of adaptive algorithms for the automated analysis of noisy and complex document collections. We first propose, implement and evaluate an adaptive clutter detection and removal technique for complex binary documents. Our distance transform based technique aims to remove irregular and independent unwanted foreground content while leaving text content untouched. The novelty of this approach is in its determination of best approximation to clutter-content boundary with text like structures. Second, we describe a page segmentation technique called Voronoi++ for complex layouts which builds upon the state-of-the-art method proposed by Kise [Kise1999]. Our approach does not assume structured text zones and is designed to handle multi-lingual text in both handwritten and printed form. Voronoi++ is a dynamically adaptive and contextually aware approach that considers components' separation features combined with Docstrum [O'Gorman1993] based angular and neighborhood features to form provisional zone hypotheses. These provisional zones are then verified based on the context built from local separation and high-level content features. Finally, our research proposes a generic model to segment and to recognize characters for any complex syllabic or non-syllabic script, using font-models. This concept is based on the fact that font files contain all the information necessary to render text and thus a model for how to decompose them. Instead of script-specific routines, this work is a step towards a generic character and recognition scheme for both Latin and non-Latin scripts

Comparative analysis of extracted heights from topographic maps and measured reduced levels in Kumasi, Ghana

No other mapping product has had widespread applications in developmental planning than the topographic map. Topographic maps represent the three-dimensional landscape by providing relief information in the form of contours in addition to plan information on which natural and man-made landmarks are quite accurately represented. Height information, extractible from topographic maps, comes in handy for most land use planning. However, generalizations during contouring and the need to interpolate between successive contours for specific grid nodes introduce errors in extracted heights. There is therefore, the necessity to use some mathematical modeling to remove discrepancies in the interpolation process to improve elevation data extracted from topographic maps. In this study, the accuracy of spot heights derived from interpolated and extracted heights from topographical maps is assessed. Two different mathematical models - a third degree polynomial regression model and the Thompson’s Multiple Variable Polynomial regression models, were respectively used to model the relationship between extracted heights and ground reduced levels. Results from the two models indicate that, the latter presents better refinements to converting extracted heights into reduced levels with a coefficient of determination value of 95.9%, although further research is recommended to investigate numerical techniques that could improve the solution to the Thompson’s polynomial. The Thompson’s model was implemented as a crude height refiner program that receives extracted heights to return corrected heights. The implication of these results for the mapping community is that, it is possible to model a correction function that can help obtain reasonably accurate heights from topographic maps. This will reduce the necessity of always going back to the field for field surveys in spite of the fact that topographic maps covering an area already exists.Keywords: Topographic maps, Interpolation, Thompson’s polynomial, Levelling, Terrain model

Contours in Visualization

This thesis studies the visualization of set collections either via or defines as the relations among contours. In the first part, dynamic Euler diagrams are used to communicate and improve semimanually the result of clustering methods which allow clusters to overlap arbitrarily. The contours of the Euler diagram are rendered as implicit surfaces called blobs in computer graphics. The interaction metaphor is the moving of items into or out of these blobs. The utility of the method is demonstrated on data arising from the analysis of gene expressions. The method works well for small datasets of up to one hundred items and few clusters. In the second part, these limitations are mitigated employing a GPU-based rendering of Euler diagrams and mixing textures and colors to resolve overlapping regions better. The GPU-based approach subdivides the screen into triangles on which it performs a contour interpolation, i.e. a fragment shader determines for each pixel which zones of an Euler diagram it belongs to. The rendering speed is thus increased to allow multiple hundred items. The method is applied to an example comparing different document clustering results. The contour tree compactly describes scalar field topology. From the viewpoint of graph drawing, it is a tree with attributes at vertices and optionally on edges. Standard tree drawing algorithms emphasize structural properties of the tree and neglect the attributes. Adapting popular graph drawing approaches to the problem of contour tree drawing it is found that they are unable to convey this information. Five aesthetic criteria for drawing contour trees are proposed and a novel algorithm for drawing contour trees in the plane that satisfies four of these criteria is presented. The implementation is fast and effective for contour tree sizes usually used in interactive systems and also produces readable pictures for larger trees. Dynamical models that explain the formation of spatial structures of RNA molecules have reached a complexity that requires novel visualization methods to analyze these model\''s validity. The fourth part of the thesis focuses on the visualization of so-called folding landscapes of a growing RNA molecule. Folding landscapes describe the energy of a molecule as a function of its spatial configuration; they are huge and high dimensional. Their most salient features are described by their so-called barrier tree -- a contour tree for discrete observation spaces. The changing folding landscapes of a growing RNA chain are visualized as an animation of the corresponding barrier tree sequence. The animation is created as an adaption of the foresight layout with tolerance algorithm for dynamic graph layout. The adaptation requires changes to the concept of supergraph and it layout. The thesis finishes with some thoughts on how these approaches can be combined and how the task the application should support can help inform the choice of visualization modality

Extracting Perceptual Structure in Dot Patterns: An Integrated Approach

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryAir Force Office of Scientific Research / AFOSR 86-000

Higher-order Voronoi diagrams of polygonal objects

Higher-order Voronoi diagrams are fundamental geometric structures which encode the k-nearest neighbor information. Thus, they aid in computations that require proximity information beyond the nearest neighbor. They are related to various favorite structures in computational geometry and are a fascinating combinatorial problem to study. While higher-order Voronoi diagrams of points have been studied a lot, they have not been considered for other types of sites. Points lack dimensionality which makes them unable to represent various real-life instances. Points are the simplest kind of geometric object and therefore higher- order Voronoi diagrams of points can be considered as the corner case of all higher-order Voronoi diagrams. The goal of this dissertation is to move away from the corner and bring the higher-order Voronoi diagram to more general geometric instances. We focus on certain polygonal objects as they provide flexibility and are able to represent real-life instances. Before this dissertation, higher-order Voronoi diagrams of polygonal objects had been studied only for the nearest neighbor and farthest Voronoi diagrams. In this dissertation we investigate structural and combinatorial properties and discover that the dimensionality of geometric objects manifests itself in numerous ways which do not exist in the case of points. We prove that the structural complexity of the order-k Voronoi diagram of non-crossing line segments is O(k(n-k)), as in the case of points. We study disjoint line segments, intersecting line segments, line segments forming a planar straight-line graph and extend the results to the Lp metric, 1<=p<=infty. We also establish the connection between two mathematical abstractions: abstract Voronoi diagrams and the Clarkson-Shor framework. We design several construction algorithms that cover the case of non-point sites. While computational geometry provides several approaches to study the structural complexity that give tight realizable bounds, developing an effective construction algorithm is still a challenging problem even for points. Most of the construction algorithms are designed to work with points as they utilize their simplicity and relations with data-structures that work specifically for points. We extend the iterative and the sweepline approaches that are quite efficient in constructing all order-i Voronoi diagrams, for i<=k and we also give three randomized construction algorithms for abstract higher-order Voronoi diagrams that deal specifically with the construction of the order-k Voronoi diagrams

Shape analysis and description based on the isometric invariances of topological skeletonization

ilustracionesIn this dissertation, we explore the problem of how to describe the shape of an object in 2D and 3D with a set of features that are invariant to isometric transformations. We focus to based our approach on the well-known Medial Axis Transform and its topological properties. We aim to study two problems. The first is how to find a shape representation of a segmented object that exhibits rotation, translation, and reflection invariance. The second problem is how to build a machine learning pipeline that uses the isometric invariance of the shape representation to do both classification and retrieval. Our proposed solution demonstrates competitive results compared to state-of-the-art approaches. We based our shape representation on the medial axis transform (MAT), sometimes called the topological skeleton. Accepted and well-studied properties of the medial axis include: homotopy preservation, rotation invariance, mediality, one pixel thickness, and the ability to fully reconstruct the object. These properties make the MAT a suitable input to create shape features; however, several problems arise because not all skeletonization methods satisfy all the above-mentioned properties at the same time. In general, skeletons based on thinning approaches preserve topology but are noise sensitive and do not allow a proper reconstruction. They are also not invariant to rotations. Voronoi skeletons also preserve topology and are rotation invariant, but do not have information about the thickness of the object, making reconstruction impossible. The Voronoi skeleton is an approximation of the real skeleton. The denser the sampling of the boundary, the better the approximation; however, a denser sampling makes the Voronoi diagram more computationally expensive. In contrast, distance transform methods allow the reconstruction of the original object by providing the distance from every pixel in the skeleton to the boundary. Moreover, they exhibit an acceptable degree of the properties listed above, but noise sensitivity remains an issue. Therefore, we selected distance transform medial axis methods as our skeletonization strategy, and focused on creating a new noise-free approach to solve the contour noise problem. To effectively classify an object, or perform any other task with features based on its shape, the descriptor needs to be a normalized, compact form: $\Phi$ should map every shape $\Omega$ to the same vector space $\mathrm{R}^{n}$. This is not possible with skeletonization methods because the skeletons of different objects have different numbers of branches and different numbers of points, even when they belong to the same category. Consequently, we developed a strategy to extract features from the skeleton through the map $\Phi$, which we used as an input to a machine learning approach. After developing our method for robust skeletonization, the next step is to use such skeleton into the machine learning pipeline to classify object into previously defined categories. We developed a set of skeletal features that were used as input data to the machine learning architectures. We ran experiments on MPEG7 and ModelNet40 dataset to test our approach in both 2D and 3D. Our experiments show results comparable with the state-of-the-art in shape classification and retrieval. Our experiments also show that our pipeline and our skeletal features exhibit some degree of invariance to isometric transformations. In this study, we sought to design an isometric invariant shape descriptor through robust skeletonization enforced by a feature extraction pipeline that exploits such invariance through a machine learning methodology. We conducted a set of classification and retrieval experiments over well-known benchmarks to validate our proposed method. (Tomado de la fuente)En esta disertación se explora el problema de cómo describir la forma de un objeto en 2D y 3D con un conjunto de características que sean invariantes a transformaciones isométricas. La metodología propuesta en este documento se enfoca en la Transformada del Eje Medio (Medial Axis Transform) y sus propiedades topológicas. Nuestro objetivo es estudiar dos problemas. El primero es encontrar una representación matemática de la forma de un objeto que exhiba invarianza a las operaciones de rotación, translación y reflexión. El segundo problema es como construir un modelo de machine learning que use esas invarianzas para las tareas de clasificación y consulta de objetos a través de su forma. El método propuesto en esta tesis muestra resultados competitivos en comparación con otros métodos del estado del arte. En este trabajo basamos nuestra representación de forma en la transformada del eje medio, a veces llamada esqueleto topológico. Algunas propiedades conocidas y bien estudiadas de la transformada del eje medio son: conservación de la homotopía, invarianza a la rotación, su grosor consiste en un solo pixel (1D), y la habilidad para reconstruir el objeto original a través de ella. Estas propiedades hacen de la transformada del eje medio un punto de partida adecuado para crear características de forma. Sin embargo, en este punto surgen varios problemas dado que no todos los métodos de esqueletización satisfacen, al mismo tiempo, todas las propiedades mencionadas anteriormente. En general, los esqueletos basados en enfoques de erosión morfológica conservan la topología del objeto, pero son sensibles al ruido y no permiten una reconstrucción adecuada. Además, no son invariantes a las rotaciones. Otro método de esqueletización son los esqueletos de Voronoi. Los esqueletos de Voronoi también conservan la topología y son invariantes a la rotación, pero no tienen información sobre el grosor del objeto, lo que hace imposible su reconstrucción. Cuanto más denso sea el muestreo del contorno del objeto, mejor será la aproximación. Sin embargo, un muestreo más denso hace que el diagrama de Voronoi sea más costoso computacionalmente. Por el contrario, los métodos basados en la transformada de la distancia permiten la reconstrucción del objeto original, ya que proporcionan la distancia desde cada píxel del esqueleto hasta su punto más cercano en el contorno. Además, exhiben un grado aceptable de las propiedades enumeradas anteriormente, aunque la sensibilidad al ruido sigue siendo un problema. Por lo tanto, en este documento seleccionamos los métodos basados en la transformada de la distancia como nuestra estrategia de esqueletización, y nos enfocamos en crear un nuevo enfoque que resuelva el problema del ruido en el contorno. Para clasificar eficazmente un objeto o realizar cualquier otra tarea con características basadas en su forma, el descriptor debe ser compacto y estar normalizado: $\Phi$ debe relacionar cada forma $\Omega$ al mismo espacio vectorial $\mathrm{R}^{n}$. Esto no es posible con los métodos de esqueletización en el estado del arte, porque los esqueletos de diferentes objetos tienen diferentes números de ramas y diferentes números de puntos incluso cuando pertenecen a la misma categoría. Consecuentemente, en nuestra propuesta desarrollamos una estrategia para extraer características del esqueleto a través de la función $\Phi$, que usamos como entrada para un enfoque de aprendizaje automático. % TODO completar con resultados. Después de desarrollar nuestro método de esqueletización robusta, el siguiente paso es usar dicho esqueleto en un modelo de aprendizaje de máquina para clasificar el objeto en categorías previamente definidas. Para ello se desarrolló un conjunto de características basadas en el eje medio que se utilizaron como datos de entrada para la arquitectura de aprendizaje automático. Realizamos experimentos en los conjuntos de datos: MPEG7 y ModelNet40 para probar nuestro enfoque tanto en 2D como en 3D. Nuestros experimentos muestran resultados comparables con el estado del arte en clasificación y consulta de formas (retrieval). Nuestros experimentos también muestran que el modelo desarrollado junto con nuestras características basadas en el eje medio son invariantes a las transformaciones isométricas. (Tomado de la fuente)Beca para Doctorados Nacionales de Colciencias, convocatoria 725 de 2015DoctoradoDoctor en IngenieríaVisión por computadora y aprendizaje automátic

Surface Reconstruction from Unorganized Point Cloud Data via Progressive Local Mesh Matching

This thesis presents an integrated triangle mesh processing framework for surface reconstruction based on Delaunay triangulation. It features an innovative multi-level inheritance priority queuing mechanism for seeking and updating the optimum local manifold mesh at each data point. The proposed algorithms aim at generating a watertight triangle mesh interpolating all the input points data when all the fully matched local manifold meshes (umbrellas) are found. Compared to existing reconstruction algorithms, the proposed algorithms can automatically reconstruct watertight interpolation triangle mesh without additional hole-filling or manifold post-processing. The resulting surface can effectively recover the sharp features in the scanned physical object and capture their correct topology and geometric shapes reliably. The main Umbrella Facet Matching (UFM) algorithm and its two extended algorithms are documented in detail in the thesis. The UFM algorithm accomplishes and implements the core surface reconstruction framework based on a multi-level inheritance priority queuing mechanism according to the progressive matching results of local meshes. The first extended algorithm presents a new normal vector combinatorial estimation method for point cloud data depending on local mesh matching results, which is benefit to sharp features reconstruction. The second extended algorithm addresses the sharp-feature preservation issue in surface reconstruction by the proposed normal vector cone (NVC) filtering. The effectiveness of these algorithms has been demonstrated using both simulated and real-world point cloud data sets. For each algorithm, multiple case studies are performed and analyzed to validate its performance

Automated Pattern Detection and Generalization of Building Groups

This dissertation focuses on the topic of building group generalization by considering the detection of building patterns. Generalization is an important research field in cartography, which is part of map production and the basis for the derivation of multiple representation. As one of the most important features on map, buildings occupy large amount of map space and normally have complex shape and spatial distribution, which leads to that the generalization of buildings has long been an important and challenging task. For social, architectural and geographical reasons, the buildings were built with some special rules which forms different building patterns. Building patterns are crucial structures which should be carefully considered during graphical representation and generalization. Although people can effortlessly perceive these patterns, however, building patterns are not explicitly described in building datasets. Therefore, to better support the subsequent generalization process, it is important to automatically recognize building patterns. The objective of this dissertation is to develop effective methods to detect building patterns from building groups. Based on the identified patterns, some generalization methods are proposed to fulfill the task of building generalization. The main contribution of the dissertation is described as the following five aspects: (1) The terminology and concept of building pattern has been clearly explained; a detailed and relative complete typology of building patterns has been proposed by summarizing the previous researches as well as extending by the author; (2) A stroke-mesh based method has been developed to group buildings and detect different patterns from the building groups; (3) Through the analogy between line simplification and linear building group typification, a stroke simplification based typification method has been developed aiming at solving the generalization of building groups with linear patterns; (4) A mesh-based typification method has been developed for the generalization of the building groups with grid patterns; (5) A method of extracting hierarchical skeleton structures from discrete buildings have been proposed. The extracted hierarchical skeleton structures are regarded as the representations of the global shape of the entire region, which is used to control the generalization process. With the above methods, the building patterns are detected from the building groups and the generalization of building groups are executed based on the patterns. In addition, the thesis has also discussed the drawbacks of the methods and gave the potential solutions.:Abstract I Kurzfassung III Contents V List of Figures IX List of Tables XIII List of Abbreviations XIV Chapter 1 Introduction 1 1.1 Background and motivation 1 1.1.1 Cartographic generalization 1 1.1.2 Urban building and building patterns 1 1.1.3 Building generalization 3 1.1.4 Hierarchical property in geographical objects 3 1.2 Research objectives 4 1.3 Study area 5 1.4 Thesis structure 6 Chapter 2 State of the Art 8 2.1 Operators for building generalization 8 2.1.1 Selection 9 2.1.2 Aggregation 9 2.1.3 Simplification 10 2.1.4 Displacement 10 2.2 Researches of building grouping and pattern detection 11 2.2.1 Building grouping 11 2.2.2 Pattern detection 12 2.2.3 Problem analysis . 14 2.3 Researches of building typification 14 2.3.1 Global typification 15 2.3.2 Local typification 15 2.3.3 Comparison analysis 16 2.3.4 Problem analysis 17 2.4 Summary 17 Chapter 3 Using stroke and mesh to recognize building group patterns 18 3.1 Abstract 19 3.2 Introduction 19 3.3 Literature review 20 3.4 Building pattern typology and study area 22 3.4.1 Building pattern typology 22 3.4.2 Study area 24 3.5 Methodology 25 3.5.1 Generating and refining proximity graph 25 3.5.2 Generating stroke and mesh 29 3.5.3 Building pattern recognition 31 3.6 Experiments 33 3.6.1 Data derivation and test framework 33 3.6.2 Pattern recognition results 35 3.6.3 Evaluation 39 3.7 Discussion 40 3.7.1 Adaptation of parameters 40 3.7.2 Ambiguity of building patterns 44 3.7.3 Advantage and Limitation 45 3.8 Conclusion 46 Chapter 4 A typification method for linear building groups based on stroke simplification 47 4.1 Abstract 48 4.2 Introduction 48 4.3 Detection of linear building groups 50 4.3.1 Stroke-based detection method 50 4.3.2 Distinguishing collinear and curvilinear patterns 53 4.4 Typification method 55 4.4.1 Analogy of building typification and line simplification 55 4.4.2 Stroke generation 56 4.4.3 Stroke simplification 57 4.5 Representation of newly typified buildings 60 4.6 Experiment 63 4.6.1 Linear building group detection 63 4.6.2 Typification results 65 4.7 Discussion 66 4.7.1 Comparison of reallocating remained nodes 66 4.7.2 Comparison with classic line simplification method 67 4.7.3 Advantage 69 4.7.4 Further improvement 71 4.8 Conclusion 71 Chapter 5 A mesh-based typification method for building groups with grid patterns 73 5.1 Abstract 74 5.2 Introduction 74 5.3 Related work 75 5.4 Methodology of mesh-based typification 78 5.4.1 Grid pattern classification 78 5.4.2 Mesh generation 79 5.4.3 Triangular mesh elimination 80 5.4.4 Number and positioning of typified buildings 82 5.4.5 Representation of typified buildings 83 5.4.6 Resizing Newly Typified Buildings 85 5.5 Experiments 86 5.5.1 Data derivation 86 5.5.2 Typification results and evaluation 87 5.5.3 Comparison with official map 91 5.6 Discussion 92 5.6.1 Advantages 92 5.6.2 Further improvements 93 5.7 Conclusion 94 Chapter 6 Hierarchical extraction of skeleton structures from discrete buildings 95 6.1 Abstract 96 6.2 Introduction 96 6.3 Related work 97 6.4 Study area 99 6.5 Hierarchical extraction of skeleton structures 100 6.5.1 Proximity Graph Network (PGN) of buildings 100 6.5.2 Centrality analysis of proximity graph network 103 6.5.3 Hierarchical skeleton structures of buildings 108 6.6 Generalization application 111 6.7 Experiment and discussion 114 6.7.1 Data statement 114 6.7.2 Experimental results 115 6.7.3 Discussion 118 6.8 Conclusions 120 Chapter 7 Discussion 121 7.1 Revisiting the research problems 121 7.2 Evaluation of the presented methodology 123 7.2.1 Strengths 123 7.2.2 Limitations 125 Chapter 8 Conclusions 127 8.1 Main contributions 127 8.2 Outlook 128 8.3 Final thoughts 131 Bibliography 132 Acknowledgements 142 Publications 14

In pursuit of linear complexity in discrete and computational geometry

Many computational problems arise naturally from geometric data. In this thesis, we consider three such problems: (i) distance optimization problems over point sets, (ii) computing contour trees over simplicial meshes, and (iii) bounding the expected complexity of weighted Voronoi diagrams. While these topics are broad, here the focus is on identifying structure which implies linear (or near linear) algorithmic and descriptive complexity. The first topic we consider is in geometric optimization. More specifically, we define a large class of distance problems, for which we provide linear time exact or approximate solutions. Roughly speaking, the class of problems facilitate either clustering together close points (i.e. netting) or throwing out outliers (i.e pruning), allowing for successively smaller summaries of the relevant information in the input. A surprising number of classical geometric optimization problems are unified under this framework, including finding the optimal k-center clustering, the kth ranked distance, the kth heaviest edge of the MST, the minimum radius ball enclosing k points, and many others. In several cases we get the first known linear time approximation algorithm for a given problem, where our approximation ratio matches that of previous work. The second topic we investigate is contour trees, a fundamental structure in computational topology. Contour trees give a compact summary of the evolution of level sets on a mesh, and are typically used on massive data sets. Previous algorithms for computing contour trees took Θ(n log n) time and were worst-case optimal. Here we provide an algorithm whose running time lies between Θ(nα(n)) and Θ(n log n), and varies depending on the shape of the tree, where α(n) is the inverse Ackermann function. In particular, this is the first algorithm with O(nα(n)) running time on instances with balanced contour trees. Our algorithmic results are complemented by lower bounds indicating that, up to a factor of α(n), on all instance types our algorithm performs optimally. For the final topic, we consider the descriptive complexity of weighted Voronoi diagrams. Such diagrams have quadratic (or higher) worst-case complexity, however, as was the case for contour trees, here we push beyond worst-case analysis. A new diagram, called the candidate diagram, is introduced, which allows us to bound the complexity of weighted Voronoi diagrams arising from a particular probabilistic input model. Specifically, we assume weights are randomly permuted among fixed Voronoi sites, an assumption which is weaker than the more typical sampled locations assumption. Under this assumption, the expected complexity is shown to be near linear