Inference and experimental design for percolation and random graph models.

The problem of optimal arrangement of nodes of a random weighted graph is studied in this thesis. The nodes of graphs under study are fixed, but their edges are random and established according to the so called edge-probability function. This function is assumed to depend on the weights attributed to the pairs of graph nodes (or distances between them) and a statistical parameter. It is the purpose of experimentation to make inference on the statistical parameter and thus to extract as much information about it as possible. We also distinguish between two different experimentation scenarios: progressive and instructive designs. We adopt a utility-based Bayesian framework to tackle the optimal design problem for random graphs of this kind. Simulation based optimisation methods, mainly Monte Carlo and Markov Chain Monte Carlo, are used to obtain the solution. We study optimal design problem for the inference based on partial observations of random graphs by employing data augmentation technique. We prove that the infinitely growing or diminishing node configurations asymptotically represent the worst node arrangements. We also obtain the exact solution to the optimal design problem for proximity graphs (geometric graphs) and numerical solution for graphs with threshold edge-probability functions. We consider inference and optimal design problems for finite clusters from bond percolation on the integer lattice Zd and derive a range of both numerical and analytical results for these graphs. We introduce inner-outer plots by deleting some of the lattice nodes and show that the ‘mostly populated’ designs are not necessarily optimal in the case of incomplete observations under both progressive and instructive design scenarios. Finally, we formulate a problem of approximating finite point sets with lattice nodes and describe a solution to this problem

Digital Library Services for Three-Dimensional Models

With the growth in computing, storage and networking infrastructure, it is becoming increasingly feasible for multimedia professionals—such as graphic designers in commercial, manufacturing, scientific and entertainment areas—to work with 3D digital models of the objects with which they deal in their domain. Unfortunately most of these models exist in individual repositories, and are not accessible to geographically distributed professionals who are in need of them. Building an efficient digital library system presents a number of challenges. In particular, the following issues need to be addressed: (1) What is the best way of representing 3D models in a digital library, so that the searches can be done faster? (2) How to compress and deliver the 3D models to reduce the storage and bandwidth requirements? (3) How can we represent the user\u27s view on similarity between two objects? (4) What search types can be used to enhance the usability of the digital library and how can we implement these searches, what are the trade-offs? In this research, we have developed a digital library architecture for 3D models that addresses the above issues as well as other technical issues. We have developed a prototype for our 3D digital library (3DLIB) that supports compressed storage, along with retrieval of 3D models. The prototype also supports search and discovery services that are targeted for 3-D models. The key to 3DLIB is a representation of a 3D model that is based on “surface signatures”. This representation captures the shape information of any free-form surface and encodes it into a set of 2D images. We have developed a shape similarity search technique that uses the signature images to compare 3D models. One advantage of the proposed technique is that it works in the compressed domain, thus it eliminates the need for uncompressing in content-based search. Moreover, we have developed an efficient discovery service consisting of a multi-level hierarchical browsing service that enables users to navigate large sets of 3D models. To implement this targeted browsing (find an object that is similar to a given object in a large collection through browsing) we abstract a large set of 3D models to a small set of representative models (key models). The abstraction is based on shape similarity and uses specially tailored clustering techniques. The browsing service applies clustering recursively to limit the number of key models that a user views at any time. We have evaluated the performance of our digital library services using the Princeton Shape Benchmark (PSB) and it shows significantly better precision and recall, as compared to other approaches

Smart environment monitoring through micro unmanned aerial vehicles

In recent years, the improvements of small-scale Unmanned Aerial Vehicles (UAVs) in terms of flight time, automatic control, and remote transmission are promoting the development of a wide range of practical applications. In aerial video surveillance, the monitoring of broad areas still has many challenges due to the achievement of different tasks in real-time, including mosaicking, change detection, and object detection. In this thesis work, a small-scale UAV based vision system to maintain regular surveillance over target areas is proposed. The system works in two modes. The first mode allows to monitor an area of interest by performing several flights. During the first flight, it creates an incremental geo-referenced mosaic of an area of interest and classifies all the known elements (e.g., persons) found on the ground by an improved Faster R-CNN architecture previously trained. In subsequent reconnaissance flights, the system searches for any changes (e.g., disappearance of persons) that may occur in the mosaic by a histogram equalization and RGB-Local Binary Pattern (RGB-LBP) based algorithm. If present, the mosaic is updated. The second mode, allows to perform a real-time classification by using, again, our improved Faster R-CNN model, useful for time-critical operations. Thanks to different design features, the system works in real-time and performs mosaicking and change detection tasks at low-altitude, thus allowing the classification even of small objects. The proposed system was tested by using the whole set of challenging video sequences contained in the UAV Mosaicking and Change Detection (UMCD) dataset and other public datasets. The evaluation of the system by well-known performance metrics has shown remarkable results in terms of mosaic creation and updating, as well as in terms of change detection and object detection

A combinatorial approach to orthogonal placement problems

liegt nicht vor!Wir betrachten zwei Familien von NP-schwierigen orthogonalen Platzierungsproblemen aus dem Bereich der Informationsvisualisierung von einem theoretischen und praktischen Standpunkt aus. Diese Arbeit enthält ein gemeinsames kombinatorisches Gerüst für Kompaktierungsprobleme aus dem Bereich des orthogonalen Graphenzeichnens und Beschriftungsprobleme von Punktmengen aus dem Gebiet der Computer-Kartografie. Bei den Kompaktierungsproblemen geht es darum, eine gegebene dimensionslose Beschreibung der orthogonalen Form eines Graphen in eine orthogonale Gitterzeichnung mit kurzen Kanten und geringem Flächenverbrauch zu transformieren. Die Beschriftungsprobleme haben zur Aufgabe, eine gegebene Menge von rechteckigen Labels so zu platzieren, dass eine lesbare Karte entsteht. In einer klassischen Anwendung repräsentieren die Punkte beispielsweise Städte einer Landkarte, und die Labels enthalten die Namen der Städte. Wir präsentieren neue kombinatorische Formulierungen für diese Probleme und verwenden dabei eine pfad- und kreisbasierte graphentheoretische Eigenschaft in einem zugehörigen problemspezifschen Paar von Constraint-Graphen. Die Umformulierung ermöglicht es uns, exakte Algorithmen für die Originalprobleme zu entwickeln. Umfassende experimentelle Studien mit Benchmark-Instanzen aus der Praxis zeigen, dass unsere Algorithmen, die auf linearer Programmierung beruhen, in der Lage sind, große Instanzen der Platzierungsprobleme beweisbar optimal und in kurzer Rechenzeit zu lösen. Ferner kombinieren wir die Formulierungen für Kompaktierungs- und Beschriftungsprobleme und präsentieren einen exakten algorithmischen Ansatz für ein Graphbeschriftungsproblem. Oftmals sind unsere neuen Algorithmen die ersten exakten Algorithmen für die jeweilige Problemvariante

A combinatorial approach to orthogonal placement problems

liegt nicht vor!Wir betrachten zwei Familien von NP-schwierigen orthogonalen Platzierungsproblemen aus dem Bereich der Informationsvisualisierung von einem theoretischen und praktischen Standpunkt aus. Diese Arbeit enthält ein gemeinsames kombinatorisches Gerüst für Kompaktierungsprobleme aus dem Bereich des orthogonalen Graphenzeichnens und Beschriftungsprobleme von Punktmengen aus dem Gebiet der Computer-Kartografie. Bei den Kompaktierungsproblemen geht es darum, eine gegebene dimensionslose Beschreibung der orthogonalen Form eines Graphen in eine orthogonale Gitterzeichnung mit kurzen Kanten und geringem Flächenverbrauch zu transformieren. Die Beschriftungsprobleme haben zur Aufgabe, eine gegebene Menge von rechteckigen Labels so zu platzieren, dass eine lesbare Karte entsteht. In einer klassischen Anwendung repräsentieren die Punkte beispielsweise Städte einer Landkarte, und die Labels enthalten die Namen der Städte. Wir präsentieren neue kombinatorische Formulierungen für diese Probleme und verwenden dabei eine pfad- und kreisbasierte graphentheoretische Eigenschaft in einem zugehörigen problemspezifschen Paar von Constraint-Graphen. Die Umformulierung ermöglicht es uns, exakte Algorithmen für die Originalprobleme zu entwickeln. Umfassende experimentelle Studien mit Benchmark-Instanzen aus der Praxis zeigen, dass unsere Algorithmen, die auf linearer Programmierung beruhen, in der Lage sind, große Instanzen der Platzierungsprobleme beweisbar optimal und in kurzer Rechenzeit zu lösen. Ferner kombinieren wir die Formulierungen für Kompaktierungs- und Beschriftungsprobleme und präsentieren einen exakten algorithmischen Ansatz für ein Graphbeschriftungsproblem. Oftmals sind unsere neuen Algorithmen die ersten exakten Algorithmen für die jeweilige Problemvariante

Diamond-based models for scientific visualization

Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds. In this thesis, we introduce several diamond-based approaches for scientific visualization. We first formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes. This enables us to enumerate the vertices, simplices, parents and children of a diamond. In particular, we identify the number of simplices involved in conforming updates to be factorial in the dimension and group these into a linear number of subclusters of simplices that are generated simultaneously. The latter form the basis for a compact pointerless representation for conforming meshes generated by regular simplex bisection and for efficiently navigating the topological connectivity of these meshes. Secondly, we introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We propose the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of such a representation for modeling multiresolution terrain and volumetric datasets. Next, we introduce Isodiamond Hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that exploits the implicit hierarchical and geometric relationships of the diamond model. We use an isodiamond hierarchy to encode irregular updates to a multiresolution isosurface or interval volume in terms of regular updates to diamonds. Finally, we consider nested hypercubic meshes, such as quadtrees, octrees and their higher dimensional analogues, through the lens of diamond hierarchies. This allows us to determine the relationships involved in generating balanced hypercubic meshes and to propose a compact pointerless representation of such meshes. We also provide a local diamond-based triangulation algorithm to generate high-quality conforming simplicial meshes