Implicit scene modelling from imprecise point clouds

In applying optical methods for automated 3D indoor modelling, the 3D reconstruction of objects and surfaces is very sensitive to both lighting conditions and the observed surface properties, which ultimately compromise the utility of the acquired 3D point clouds. This paper presents a robust scene reconstruction method which is predicated upon the observation that most objects contain only a small set of primitives. The approach combines sparse approximation techniques from the compressive sensing domain with surface rendering approaches from computer graphics. The amalgamation of these techniques allows a scene to be represented by a small set of geometric primitives and to generate perceptually appealing results. The resulting scene surface models are defined as implicit functions and may be processed using conventional rendering algorithms such as marching cubes, to deliver polygonal models of arbitrary resolution. It will also be shown that 3D point clouds with outliers, strong noise and varying sampling density can be reliably processed without manual intervention

A Knowledge Integration Framework for 3D Shape Reconstruction

The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points in sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment in which the robots operate with. This means unstructured 3D samples must be processed by application-specific models to enable a robot, for instance, to detect and identify objects and infer the scene geometry for path-planning more efficiently than by using raw 3D data. This thesis specifically focuses on the fundamental task of 3D shape reconstruction and modelling by presenting a new knowledge integration framework for unstructured 3D samples. The novelty lies in the representation of surfaces by algebraic functions with limited support, which enables the extraction of smooth consistent shapes from noisy samples with a heterogeneous density. Moreover, many surfaces in urban environments can reasonably be assumed to be planar, and the framework exploits this knowledge to enable effective noise suppression without loss of detail. This is achieved by using a convex optimization technique which has linear computational complexity. Thus is much more efficient than existing solutions. The new framework has been validated by critical experimental analysis and evaluation and has been shown to increase the accuracy of the reconstructed shape significantly compared to state-of-the-art methods. Applying this new knowledge integration framework means that less accurate, low-cost 3D sensors can be employed without sacrificing the high demands that 3D perception must achieve. This links well into the area of robotic inspection, as for example regarding small drones that use inaccurate and lightweight image sensors

Precursor problem and holographic mutual information

The recent proposal of Almheiri et al.http://arxiv.org/abs/1411.7041, together with the Ryu-Takayanagi formula, implies the entanglement wedge hypothesis for certain choices of boundary subregions. This fact is derived in the pure AdS space. A similar conclusion holds in the presence of quantum corrections, but in a more restricted domain of applicability. We also comment on http://arxiv.org/abs/1601.05416 and some similarities and differences with this workComment: 13 pages, 1 figur

Surface Reconstruction From 3D Point Clouds

The triangulation of a point cloud of a 3D object is a complex problem, since it depends on the complexity of the shape of such object, as well as on the density of points generated by a specific scanner. In the literature, there are essentially two approaches to the reconstruction of surfaces from point clouds: interpolation and approximation. In general, interpolation approaches are associated with simplicial methods; that is, methods that directly generate a triangle mesh from a point cloud. On the other hand, approximation approaches generate a global implicit function — that represents an implicit surface — from local shape functions, then generating a triangulation of such implicit surface. The simplicial methods are divided into two families: Delaunay and mesh growing. Bearing in mind that the first of the methods presented in this dissertation falls under the category of mesh growing methods, let us focus our attention for now on these methods. One of the biggest problems with these methods is that, in general, they are based on the establishment of dihedral angle bounds between adjacent triangles, as needed to make the decision on which triangle to add to the expansion mesh front. Typically, other bounds are also used for the internal angles of each triangle. In the course of this dissertation, we will see how this problem was solved. The second algorithm introduced in this dissertation is also a simplicial method but does not fit into any of the two families mentioned above, which makes us think that we are in the presence of a new family: triangulation based on the atlas of charts or triangle stars. This algorithm generates an atlas of the surface that consists of overlapping stars of triangles, that is, one produces a total surface coverage, thus solving one of the common problems of this family of direct triangulation methods, which is the appearance of holes or incomplete triangulation of the surface. The third algorithm refers to an implicit method, but, unlike other implicit methods, it uses an interpolation approach. That is, the local shape functions interpolate the points of the cloud. It is, perhaps, one of a few implicit methods that we can find in the literature that interpolates all points of the cloud. Therefore, one of the biggest problems of the implicit methods is solved, which has to do with the smoothing of the surface sharp features resulting from the blending of the local functions into the global function. What is common to the three methods is the interpolation approach, either in simple or implicit methods, that is, the linearization of the surface subject to reconstruction. As will be seen, the linearization of the neighborhood of each point allows us to solve several problems posed to the surface reconstruction algorithms, namely: point sub‐sampling, non‐uniform sampling, as well as sharp features.A triangulação de uma nuvem de pontos de um objeto 3D é um problema complexo, uma vez que depende da complexidade da forma desse objeto, assim como da densidade dos pontos extraídos desse objeto através de um scanner 3D particular. Na literatura, existem essencialmente duas abordagens na reconstrução de superfícies a partir de nuvens de pontos: interpolação e aproximação. Em geral, as abordagens de interpolação estão associadas aos métodos simpliciais, ou seja, a métodos que geram diretamente uma malha de triângulos a partir de uma nuvem de pontos. Por outro lado, as abordagens de aproximação estão habitualmente associadas à geração de uma função implícita global —que representa uma superfície implícita— a partir de funções locais de forma, para em seguida gerar uma triangulação da dita superfície implícita. Os métodos simpliciais dividem‐se em duas famílias: triangulação de Delaunay e triangulação baseada em crescimento progressivo da triangulação (i.e., mesh growing). Tendo em conta que o primeiro dos métodos apresentados nesta dissertação se enquadra na categoria de métodos de crescimento progressivo, foquemos a nossa atenção por ora nestes métodos. Um dos maiores problemas destes métodos é que, em geral, se baseiam no estabelecimento de limites de ângulos diédricos (i.e., dihedral angle bounds) entre triângulos adjacentes, para assim tomar a decisão sobre qual triângulo acrescentar à frente de expansão da malha. Tipicamente, também se usam limites para os ângulos internos de cada triângulo. No decorrer desta dissertação veremos como é que este problema foi resolvido. O segundo algoritmo introduzido nesta dissertação também é um método simplicial, mas não se enquadra em nenhuma das duas famílias acima referidas, o que nos faz pensar que estaremos na presença de uma nova família: triangulação baseada em atlas de vizinhanças sobrepostas (i.e., atlas of charts) ou estrelas de triângulos (i.e., triangle star). Este algoritmo gera um atlas da superfície que é constituído por estrelas sobrepostas de triângulos, ou seja, produz‐se a cobertura total da superfície, resolvendo assim um dos problemas comuns desta família de métodos de triangulação direta que é o do surgimento de furos ou de triangulação incompleta da superfície. O terceiro algoritmo refere‐se a um método implícito, mas, ao invés de grande parte dos métodos implícitos, utiliza uma abordagem de interpolação. Ou seja, as funções locais de forma interpolam os pontos da nuvem. É, talvez, um dos poucos métodos implícitos que podemos encontrar na literatura que interpola todos os pontos da nuvem. Desta forma resolve‐se um dos maiores problemas dos métodos implícitos que é o do arredondamento de forma resultante do blending das funções locais que geram a função global, em particular ao longo dos vincos da superfície (i.e., sharp features). O que é comum aos três métodos é a abordagem de interpolação, quer em métodos simpliciais quer em métodos implícitos, ou seja a linearização da superfície sujeita a reconstrução. Como se verá, a linearização da vizinhança de cada ponto permite‐nos resolver vários problemas colocados aos algoritmos de reconstrução de superfícies, nomeadamente: sub‐amostragem de pontos (point sub‐sampling), amostragem não uniforme (non‐uniform sampling), bem como formas vincadas (sharp features)

Holographic Entanglement Entropy

We review the developments in the past decade on holographic entanglement entropy, a subject that has garnered much attention owing to its potential to teach us about the emergence of spacetime in holography. We provide an introduction to the concept of entanglement entropy in quantum field theories, review the holographic proposals for computing the same, providing some justification for where these proposals arise from in the first two parts. The final part addresses recent developments linking entanglement and geometry. We provide an overview of the various arguments and technical developments that teach us how to use field theory entanglement to detect geometry. Our discussion is by design eclectic; we have chosen to focus on developments that appear to us most promising for further insights into the holographic map. This is a draft of a few chapters of a book which will appear sometime in the near future, to be published by Springer. The book in addition contains a discussion of application of holographic ideas to computation of entanglement entropy in strongly coupled field theories, and discussion of tensor networks and holography, which we have chosen to exclude from the current manuscript.Comment: 154 pages. many figures. preliminary version of book chapters. comments welcome. v2: typos fixed and references adde

A Unified Surface Geometric Framework for Feature-Aware Denoising, Hole Filling and Context-Aware Completion

Technologies for 3D data acquisition and 3D printing have enormously developed in the past few years, and, consequently, the demand for 3D virtual twins of the original scanned objects has increased. In this context, feature-aware denoising, hole filling and context-aware completion are three essential (but far from trivial) tasks. In this work, they are integrated within a geometric framework and realized through a unified variational model aiming at recovering triangulated surfaces from scanned, damaged and possibly incomplete noisy observations. The underlying non-convex optimization problem incorporates two regularisation terms: a discrete approximation of the Willmore energy forcing local sphericity and suited for the recovery of rounded features, and an approximation of the l(0) pseudo-norm penalty favouring sparsity in the normal variation. The proposed numerical method solving the model is parameterization-free, avoids expensive implicit volumebased computations and based on the efficient use of the Alternating Direction Method of Multipliers. Experiments show how the proposed framework can provide a robust and elegant solution suited for accurate restorations even in the presence of severe random noise and large damaged areas