Four results on randomized incremental constructions

We prove four results on randomized incremental constructions (RICs): \begin{itemize} \item an analysis of the expected behavior under insertion and deletions, \item a fully dynamic data structure for convex hull maintenance in arbitrary dimensions, \item a tail estimate for the space complexity of RICs, \item a lower bound on the complexity of a game related to RICs. \end{itemize

How to build a 2d and 3d aerial multispectral map?—all steps deeply explained

UIDB/04111/2020 PCIF/SSI/0102/2017 IF/00325/2015 UIDB/00066/2020The increased development of camera resolution, processing power, and aerial platforms helped to create more cost-efficient approaches to capture and generate point clouds to assist in scientific fields. The continuous development of methods to produce three-dimensional models based on two-dimensional images such as Structure from Motion (SfM) and Multi-View Stereopsis (MVS) allowed to improve the resolution of the produced models by a significant amount. By taking inspiration from the free and accessible workflow made available by OpenDroneMap, a detailed analysis of the processes is displayed in this paper. As of the writing of this paper, no literature was found that described in detail the necessary steps and processes that would allow the creation of digital models in two or three dimensions based on aerial images. With this, and based on the workflow of OpenDroneMap, a detailed study was performed. The digital model reconstruction process takes the initial aerial images obtained from the field survey and passes them through a series of stages. From each stage, a product is acquired and used for the following stage, for example, at the end of the initial stage a sparse reconstruction is produced, obtained by extracting features of the images and matching them, which is used in the following step, to increase its resolution. Additionally, from the analysis of the workflow, adaptations were made to the standard workflow in order to increase the compatibility of the developed system to different types of image sets. Particularly, adaptations focused on thermal imagery were made. Due to the low presence of strong features and therefore difficulty to match features across thermal images, a modification was implemented, so thermal models could be produced alongside the already implemented processes for multispectral and RGB image sets.publishersversionpublishe

Digital Multispectral Map Reconstruction Using Aerial Imagery

Advances made in the computer vision field allowed for the establishment of faster and more accurate photogrammetry techniques. Structure from Motion(SfM) is a photogrammetric technique focused on the digital spatial reconstruction of objects based on a sequence of images. The benefit of Unmanned Aerial Vehicle (UAV) platforms allowed the ability to acquire high fidelity imagery intended for environmental mapping. This way, UAV platforms became a heavily adopted method of survey. The combination of SfM and the recent improvements of Unmanned Aerial Vehicle (UAV) platforms granted greater flexibility and applicability, opening a new path for a new remote sensing technique aimed to replace more traditional and laborious approaches often associated with high monetary costs. The continued development of digital reconstruction software and advances in the field of computer processing allowed for a more affordable and higher resolution solution when compared to the traditional methods. The present work proposed a digital reconstruction algorithm based on images taken by a UAV platform inspired by the work made available by the open-source project OpenDroneMap. The aerial images are inserted in the computer vision program and several operations are applied to them, including detection and matching of features, point cloud reconstruction, meshing, and texturing, which results in a final product that represents the surveyed site. Additionally, from the study, it was concluded that an implementation which addresses the processing of thermal images was not integrated in the works of OpenDroneMap. By this point, their work was altered to allow for the reconstruction of thermal maps without sacrificing the resolution of the final model. Standard methods to process thermal images required a larger image footprint (or area of ground capture in a frame), the reason for this is that these types of images lack the presence of invariable features and by increasing the image’s footprint, the number of features present in each frame also rises. However, this method of image capture results in a lower resolution of the final product. The algorithm was developed using open-source libraries. In order to validate the obtained results, this model was compared to data obtained from commercial products, like Pix4D. Furthermore, due to circumstances brought about by the current pandemic, it was not possible to conduct a field study for the comparison and assessment of our results, as such the validation of the models was performed by verifying if the geographic location of the model was performed correctly and by visually assessing the generated maps.Avanços no campo da visão computacional permitiu o desenvolvimento de algoritmos mais eficientes de fotogrametria. Structure from Motion (SfM) é uma técnica de fotogrametria que tem como objetivo a reconstrução digital de objectos no espaço derivados de uma sequência de imagens. A característica importante que os Veículos Aérios não-tripulados (UAV) conseguem fornecer, a nível de mapeamento, é a sua capacidade de obter um conjunto de imagens de alta resolução. Devido a isto, UAV tornaram-se num dos métodos adotados no estudo de topografia. A combinação entre SfM e recentes avanços nos UAV permitiram uma melhor flexibilidade e aplicabilidade, permitindo deste modo desenvolver um novo método de Remote Sensing. Este método pretende substituir técnicas tradicionais, as quais estão associadas a mão-de-obra intensiva e a custos monetários elevados. Avanços contínuos feitos em softwares de reconstrução digital e no poder de processamento resultou em modelos de maior resolução e menos dispendiosos comparando a métodos tradicionais. O presente estudo propõe um algoritmo de reconstrução digital baseado em imagens obtidas através de UAV inspiradas no estudo disponibilizado pela OpenDroneMap. Estas imagens são inseridas no programa de visão computacional, onde várias operações são realizadas, incluindo: deteção e correspondência de caracteristicas, geração da point cloud, meshing e texturação dos quais resulta o produto final que representa o local em estudo. De forma complementar, concluiu-se que o trabalho da OpenDroneMap não incluia um processo de tratamento de imagens térmicas. Desta forma, alterações foram efetuadas que permitissem a criação de mapas térmicos sem sacrificar resolução do produto final, pois métodos típicos para processamento de imagens térmicas requerem uma área de captura maior, devido à falta de características invariantes neste tipo de imagens, o que leva a uma redução de resolução. Desta forma, o programa proposto foi desenvolvido através de bibliotecas open-source e os resultados foram comparados com modelos gerados através de software comerciais. Além do mais, devido à situação pandémica atual, não foi possível efetuar um estudo de campo para validar os modelos obtidos, como tal esta verificação foi feita através da correta localização geográfica do modelo, bem como avaliação visual dos modelos criados

G-CSC Report 2010

The present report gives a short summary of the research of the Goethe Center for Scientific Computing (G-CSC) of the Goethe University Frankfurt. G-CSC aims at developing and applying methods and tools for modelling and numerical simulation of problems from empirical science and technology. In particular, fast solvers for partial differential equations (i.e. pde) such as robust, parallel, and adaptive multigrid methods and numerical methods for stochastic differential equations are developed. These methods are highly adanvced and allow to solve complex problems.. The G-CSC is organised in departments and interdisciplinary research groups. Departments are localised directly at the G-CSC, while the task of interdisciplinary research groups is to bridge disciplines and to bring scientists form different departments together. Currently, G-CSC consists of the department Simulation and Modelling and the interdisciplinary research group Computational Finance

Mapping three-dimensional geological features from remotely-sensed images and digital elevation models.

Accurate mapping of geological structures is important in numerous applications, ranging from mineral exploration through to hydrogeological modelling. Remotely sensed data can provide synoptic views of study areas enabling mapping of geological units within the area. Structural information may be derived from such data using standard manual photo-geologic interpretation techniques, although these are often inaccurate and incomplete. The aim of this thesis is, therefore, to compile a suite of automated and interactive computer-based analysis routines, designed to help a the user map geological structure. These are examined and integrated in the context of an expert system. The data used in this study include Digital Elevation Model (DEM) and Airborne Thematic Mapper images, both with a spatial resolution of 5m, for a 5 x 5 km area surrounding Llyn Cow lyd, Snowdonia, North Wales. The geology of this area comprises folded and faulted Ordo vician sediments intruded throughout by dolerite sills, providing a stringent test for the automated and semi-automated procedures. The DEM is used to highlight geomorphological features which may represent surface expressions of the sub-surface geology. The DEM is created from digitized contours, for which kriging is found to provide the best interpolation routine, based on a number of quantitative measures. Lambertian shading and the creation of slope and change of slope datasets are shown to provide the most successful enhancement of DEMs, in terms of highlighting a range of key geomorphological features. The digital image data are used to identify rock outcrops as well as lithologically controlled features in the land cover. To this end, a series of standard spectral enhancements of the images is examined. In this respect, the least correlated 3 band composite and a principal component composite are shown to give the best visual discrimination of geological and vegetation cover types. Automatic edge detection (followed by line thinning and extraction) and manual interpretation techniques are used to identify a set of 'geological primitives' (linear or arc features representing lithological boundaries) within these data. Inclusion of the DEM data provides the three-dimensional co-ordinates of these primitives enabling a least-squares fit to be employed to calculate dip and strike values, based, initially, on the assumption of a simple, linearly dipping structural model. A very large number of scene 'primitives' is identified using these procedures, only some of which have geological significance. Knowledge-based rules are therefore used to identify the relevant. For example, rules are developed to identify lake edges, forest boundaries, forest tracks, rock-vegetation boundaries, and areas of geomorphological interest. Confidence in the geological significance of some of the geological primitives is increased where they are found independently in both the DEM and remotely sensed data. The dip and strike values derived in this way are compared to information taken from the published geological map for this area, as well as measurements taken in the field. Many results are shown to correspond closely to those taken from the map and in the field, with an error of < 1°. These data and rules are incorporated into an expert system which, initially, produces a simple model of the geological structure. The system also provides a graphical user interface for manual control and interpretation, where necessary. Although the system currently only allows a relatively simple structural model (linearly dipping with faulting), in the future it will be possible to extend the system to model more complex features, such as anticlines, synclines, thrusts, nappes, and igneous intrusions

Numerical modelling of local scour with computational methods

Evaluating bed morphological evolution (specifically the scoured bed level) accurately using computational modelling is critical for analyses of the stability of many marine and coastal structures, such as piers, groynes, breakwaters, submarine pipelines and even telecommunication cables. This thesis considers the coupled hydrodynamic and morphodynamic modelling of the local scour around hydraulic structures, such as near a vertical pile or near a horizontal pipe. The focus in this study is on applying a fluid-structure interaction (FSI) approach to simulate the morphodynamical behaviour of the bed deformation, replacing the structural (i.e. solid mechanics) equation by the sediment continuity equation or Exner equation. Specifically, this works presents a novel method of mesh movement with anisotropic mesh adaptivity based on optimization for simulating local scour near structures with discontinuous Garlerkin (DG) discretisation methods for solving the flow field. Amongst the other goals of this work is the validation of the proposed procedure with previously performed laboratory as well as two- and three-dimensional numerical experiments. Additionally, performance is considered using an implementation of the methodology within Fluidity (http://fluidityproject.github.io/), an open-source, multi-physics, computational fluid dynamics (CFD) code, capable of handling arbitrary multi-scale unstructured tetrahedral meshes and including algorithms to perform dynamic anisotropic mesh adaptivity and mesh movement. The flexibility over mesh structure and resolution that these optimisation capabilities provide makes it potentially highly suitable for accounting the extreme bed morphological evolution close to a fixed solid structure under the action of hydrodynamics. Galerkin-based finite element methods have been used for the hydrodynamics (including discontinuous Galerkin discretisations) and morphological calculations, and automatic mesh deformation has been utilised to account for bed evolution changes while preserving the validity and quality of the mesh. Finally, the work extends the scope in regards of computational methods and considers scour modelling with pure Lagrangian and meshless methods such as smoothed particle hydrodynamics (SPH), which have also become of interest in the analysis and modelling of coastal sediment transport, particularly in scour-related processes. The SPH modelling is considered in a two-phase, flow-sediment fully Lagrangian scour simulation where the discrete-particle interaction forces between phases are resolved at the interface and continuous changes in the bed profile are obtained naturally.Open Acces

Generation of 3D characters from existing cartoons and a unified pipeline for animation and video games.

Despite the remarkable growth of 3D animation in the last twenty years, 2D is still popular today and often employed for both films and video games. In fact, 2D offers important economic and artistic advantages to production. In this thesis has been introduced an innovative system to generate 3D character from 2D cartoons, while maintaining important 2D features in 3D as well. However, handling 2D characters and animation in a 3D environment is not a trivial task, as they do not possess any depth information. Three different solutions have been proposed in this thesis. A 2.5D modelling method, which exploits billboarding, parallax scrolling and 2D shape interpolation to simulate the depth between the different body parts of the characters. Two additional full 3D solution have been presented. One based on inflation and supported by a surface registration method, and one that produces more accurate approximations by using information from the side views to solve an optimization problem. These methods have been introduced into a new unified pipeline that involves a game engine, and that could be used for animation and video games production. A unified pipeline introduces several benefits to animation production for either 2D and 3D content. On one hand, assets can be shared for different productions and media. On the other hand, real-time rendering for animated films allows immediate previews of the scenes and offers artists a way to experiment more during the making of a scene