An autonomous robot able to navigate inside an unknown environment and reconstruct full 3D scene models using monocular video has been a long term goal in the field of Machine Vision. A key component of such a system is the reconstruction of surface models from estimated scene structure. Sparse 3D measurements of real scenes are readily estimated from N-view image sequences using structure-from-motion techniques. In this thesis we present a geometric theory for reconstruction of surface models from sparse 3D data captured from N camera views. Based on this theory we introduce a general N-view algorithm for reconstruction of 3D models of arbitrary scenes from sparse data. Using a hypothesise and verify strategy this algorithm reconstructs a surface model which interpolates the sparse data and is guaranteed to be consistent with the feature visibility in the N-views. To achieve efficient reconstruction independent of the number of views a simplified incremental algorithm is developed which integrates the feature visibility independently for each view. This approach is shown to converge to an approximation of the real scene structure and have a computational cost which is linear in the number of views. Surface hypothesis are generated based on a new incremental planar constrained Delaunay triangulation algorithm. We present a statistical geometric framework to explicitly consider noise inherent in estimates of 3D scene structure from any real vision system. This approach ensures that the reconstruction is reliable in the presence of noise and missing data. Results are presented for reconstruction of both real and synthetic scenes together with an evaluation of the reconstruction performance in the presence of noise.

Triangle meshes can provide an effective geometric representation of images. Although many mesh generation methods have been proposed to date, many of them do not explicitly take image discontinuities into consideration. In this thesis, a new mesh model for images, which explicitly represents discontinuities (i.e., image edges), is proposed along with two corresponding mesh-generation methods that determine the mesh-model parameters for a given input image. The mesh model is based on constrained Delaunay triangulations (DTs), where the constrained edges correspond to image edges. One of the proposed methods is named explicitly-represented discontinuities-with error diffusion (ERDED), and is fast and easy to implement. In the ERDED method, the error diffusion (ED) scheme is employed to select a subset of sample points that are not on the constrained edges. The other proposed method is called ERDGPI. In the ERDGPI method, a constrained DT is first constructed with a set of prespecified constrained edges. Then, the greedy point insertion (GPI) scheme is employed to insert one point into the constrained DT in each iteration until a certain number of points is reached. The ERDED and ERDGPI methods involve several parameters which must be provided as input. These parameters can affect the quality of the resulting image approximations, and are discussed in detail. We also evaluate the performance of our proposed ERDED and ERDGPI methods by comparing them with the highly effective ED and GPI schemes. Our proposed methods are demonstrated to be capable of producing image approximations of higher quality both in terms of PSNR and subjective quality than those generated by other schemes. For example, the reconstructed images produced by the proposed ERDED method are often about 3.77 dB higher in PSNR than those produced by the ED scheme, and our proposed ERDGPI scheme produces image approximations of about 1.08 dB higher PSNR than those generated by the GPI approach. / Graduate

A novel progressive lossy-to-lossless coding method is proposed for mesh models of images whose underlying triangulations have arbitrary connectivity. For a triangulation T of a set P of points, our proposed method represents the connectivity of T as a sequence of edge flips that maps a uniquely-determined Delaunay triangulation (i.e., preferred-directions Delaunay triangulation) of P to T. The coding efficiency of our method is highest when the underlying triangulation connectivity is close to Delaunay, and slowly degrades as connectivity moves away from being Delaunay. Through experimental results, we show that our proposed coding method is able to significantly outperform a simple baseline coding scheme. Furthermore, our proposed method can outperform traditional connectivity coding methods for meshes that do not deviate too far from Delaunay connectivity. This result is of practical significance since, in many applications, mesh connectivity is often not so far from being Delaunay, due to the good approximation properties of Delaunay triangulations. / Graduate

Subject of this paper is triangulation of given domain also called as mesh generation. Overview of main mesh types (structured, unstructured and hybrid) is given. Groups of triangulation methods are defined and include collective triangulation, incremental triangulation, pliant mesh generation with post-triangulation and plaint mesh generation with retriangulation. Delaunay triangulation is described in greater detail and variuos Delaunay triangulation algorithms are presented including use of Delaunay triangulation for anisotropic mesh generation and method to generate Constrained Delaunay triangulation. Greedy insertion Delaunay and data dependent allgorithms are developed for hight fields surface aproximation. Significant improvements are made to these algorithms including faster recalculation, node selection and use of supplementary data sets in order to maximise efficiency of calculations. Main criteria to evaluate developed algorithms is overall error of approximation and speed of calculation. Data dependent algorithm generates better quality mesh (less approximation error), however Delaunay triangulation algorithm is significantly faster. Results and conclusions are presented at the end of paper.

The main aim of this thesis is to generate 3D models of human heads from uncalibrated images. In order to extract geometric values of a human head, we find camera parameters using camera auto calibration. However, some image sequences generate non-unique (degenerate) solutions. An algorithm for removing degeneracy from the most common form of camera movement in face image acquisition is described. The geometric values of main facial features are computed initially. The model is then generated by gradual deformation of a generic polygonal model of a head. The accuracy of the models is evaluated using ground truth data from a range scanner. 3D models are covered with cylindrical texture values obtained from images. The models are appropriate for animation or identification applications.

The main goal of this work is to present a discrete analogous of the laplacian operator, that is, a linear operator on the set of piecewise linear functions over a triangular mesh that has similar properties to the continuous laplacian over a surface. Particularly, we will show that if the mesh satisfies a Delaunay criterion, the laplacian obeys a discrete version of the maximum principle, which importance in the discrete setting is similar to the importance of the maximum principle in the theory of harmonic functions. We also present three applications of the discrete laplacian: the first one has as objective to get parametrizations of meshes for texture mapping; the second one consists of mesh smoothing by a diffusion process; the third and last application aims to identify forms and symmetries of objects by means of the contour curves associated to the eigenfunctions of the laplacian operator. / Fundação de Amparo a Pesquisa do Estado de Alagoas / O objetivo desta disserta¸c ao ´e apresentar um an´alogo discreto do operador laplaciano, ou seja, um operador linear definido no conjunto das fun¸c oes lineares por partes em uma malha de tri angulos que possua o m´aximo de propriedades an´alogas ao operador laplaciano cont´ınuo sobre uma superf´ıcie. Em particular, mostraremos que se a malha satisfaz ao crit´erio de Delaunay, o laplaciano obedece a uma vers ao discreta do princ´ıpio do m´aximo, que possui import ancia semelhante ao princ´ıpio do m´aximo na teoria das fun¸c oes harm onicas. Apresentamos ainda tr es aplica¸c oes do laplaciano discretizado: a primeira tem como objetivo obter parametriza¸c oes de malhas para efeito de mapeamento de textura; a segunda consiste na suaviza¸c ao de malhas por meio do processo de difus ao; a terceira e ´ultima aplica¸c ao visa identificar formas e simetrias de objetos por meio das curvas de contorno associadas `as autofun¸c oes do laplaciano.

Mobile robotics has been very discussed and wide spread topic recently.   This due to the development in the computer technology that allows us to create   better and more sophisticated robots. The goal of this effort is to create robots   that will be able to autonomously move in the chosen environment. To achieve this goal,   it is necessary for the robot to create the map of its environment, where   the motion planning will occur. Nowadays, the probabilistic algorithms based   on the SLAM algorithm are considered standard in the mapping in these times.   This Phd. thesis deals with the proposal of the motion planning of the robot with   stereocamera placed on the pan-and-tilt unit. The motion planning is designed with   regard to the use of algorithms, which will look for the significant features   in the pair of the images. With the use of the triangulation the map, or a model will be created.     The benefits of this work can be divided into three parts. In the first one the way   of marking the free area, where the robot will plan its motion, is described. The second part   describes the motion planning of the robot in this free area. It takes into account   the properties of the SLAM algorithm and it tries to plan the exploration in order to create   the most precise map. The motion of the pan-and-tilt unit is described in the third part.   It takes advantage of the fact that the robot can observe places that are in the different   directions than the robot moves. This allows us to observe much bigger space without   losing the information about the precision of the movements.

This thesis aims to seek interesting patterns from massive amounts of Flickr data in Sweden with pro- posed new clustering strategies. The aim can be further divided into three objectives. The first one is to acquire large amount of timestamped geolocation data from Flickr servers. The second objective is to develop effective and efficient methods to process the data. More specifically, the methods to be developed are bifold, namely, the preprocessing method to solve the “Big Data” issue encountered in the study and the new clustering method to extract spatio-temporal patterns from data. The third one is to analyze the extracted patterns with scaling analysis techniques in order to interpret human social activities underlying the Flickr Data within the urban envrionment of Sweden. During the study, the three objectives were achieved sequentially. The data employed for this study was vector points downloaded through Flickr Application Programming Interface (API). After data ac- quisition, preprocessing was performed on the raw data. The whole dataset was firstly separated by year based on the temporal information. Then data of each year was accumulated with its former year(s) so that the evovling process can be explored. After that, large datasets were splitted into small pieces and each piece was clipped, georeferenced, and rectified respectively. Then the pieces were merged together for clustering. With respect to clustering, the strategy was developed based on the Delaunay Triangula- tion (DT) and head/tail break rule. After that, the generated clusters were analyzed with scaling analysis techniques and spatio-temporal patterns were interpreted from the analysis results. It has been found that the spatial pattern of the human social activities in the urban environment of Sweden generally follows the power-law distribution and the cities defined by human social activities are evolving as time goes by. To conclude, the contributions of this research are threefold and fulfill the objectives of this study, respectively. Firstly, large amount of Flickr data is acquired and collated as a contribution to other aca- demic researches related to Flickr. Secondly, the clustering strategy based on the DT and head/tail break rule is proposed for spatio-temporal pattern seeking. Thirdly, the evolving of the cities in terms of human activities in Sweden is detected from the perspective of scaling. Future work is expected in major two aspects, namely, data and data processing. For the data aspect, the downloaded Flickr data is expected to be employed by other studies, especially those closely related to human social activities within urban environment. For the processing aspect, new algorithms are expected to either accelerate the processing process or better fit machines with super computing capacities.

In this thesis, an approach is presented for the generation of grids suitable for the simulation of high Reynolds number viscous flows in complex three-dimensional geometries. The automatic and reliable generation of such grids is today on the biggest bottlenecks in the industrial CFD simulation environment. In the proposed approach, unstructured tetrahedral grids are employed for the regions far from the viscous boundaries of the domain, while semi-structured layers of high aspect ratio prismatic and hexahedral elements are used to provide the necessary grid resolution inside the boundary layers and normal to the viscous walls. The definition of the domain model is based on the STEP ISO standard and the topological information contained in the model is used for applying the hierarchical grid generation parameters defined by the user. An efficient, high-quality and robust algorithm is presented for the generation of the unstructured simplicial (triangular of tetrahedral) part of the grid. The algorithm is based on the Delaunay triangulation and the internal grid points are created following a centroid or frontal approach. For the surface grid generation, a hybrid approach is also proposed similar to the volume. Semi-structured grids are generated on the surface grid (both on the edges and faces of the domain) to improve the grid resolution around convex and concave ridges and corners, by aligning the grid elements in the directions of high solution gradients along the surface. A method is also developed for automatically setting the grid generation parameters related to the surface grid generation based on the curvature of the surface in order to obtain an accurate and smooth surface grid. Finally, a semi-structured prismatic/hexahedral grid generation algorithm is presented for the generation of the part of grid close to the viscous walls of the domain. The algorithm is further extended with improvements meant to increase the grid quality around concave and convex ridges of the domain, where the semi-structured grids are known to be inadequate. The combined methodology is demonstrated on a variety of complex examples mainly from the automotive and aeronautical industry.

This work deals with the description and analysis of image data, which related to the initial stages of the thin film growth. The introductory retrieval section includes a description of thin films and methods of their deposition. The following part is an overview of the growth models of thin layers. The heart of my thesis is the analysis and modification of morphological methods and interpretation of their results. The emphasis is placed on the statistical aspect of methods and their optimal implementation due to the accuracy of the results. The work shows how to modify the radial distribution function and methods based on so-called Voronoi and Delaunay triangulation tessellation so that they can better affect the character of test data. New methods are tested both on the experimental and model data. Then we examine their robustness, sensitivity and their mutual independence. At the conclusion it is introduced and analyzed a new model of thin film growth.