74 research outputs found

    Elastic shape analysis of geometric objects with complex structures and partial correspondences

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    In this dissertation, we address the development of elastic shape analysis frameworks for the registration, comparison and statistical shape analysis of geometric objects with complex topological structures and partial correspondences. In particular, we introduce a variational framework and several numerical algorithms for the estimation of geodesics and distances induced by higher-order elastic Sobolev metrics on the space of parametrized and unparametrized curves and surfaces. We extend our framework to the setting of shape graphs (i.e., geometric objects with branching structures where each branch is a curve) and surfaces with complex topological structures and partial correspondences. To do so, we leverage the flexibility of varifold fidelity metrics in order to augment our geometric objects with a spatially-varying weight function, which in turn enables us to indirectly model topological changes and handle partial matching constraints via the estimation of vanishing weights within the registration process. In the setting of shape graphs, we prove the existence of solutions to the relaxed registration problem with weights, which is the main theoretical contribution of this thesis. In the setting of surfaces, we leverage our surface matching algorithms to develop a comprehensive collection of numerical routines for the statistical shape analysis of sets of 3D surfaces, which includes algorithms to compute Karcher means, perform dimensionality reduction via multidimensional scaling and tangent principal component analysis, and estimate parallel transport across surfaces (possibly with partial matching constraints). Moreover, we also address the development of numerical shape analysis pipelines for large-scale data-driven applications with geometric objects. Towards this end, we introduce a supervised deep learning framework to compute the square-root velocity (SRV) distance for curves. Our trained network provides fast and accurate estimates of the SRV distance between pairs of geometric curves, without the need to find optimal reparametrizations. As a proof of concept for the suitability of such approaches in practical contexts, we use it to perform optical character recognition (OCR), achieving comparable performance in terms of computational speed and accuracy to other existing OCR methods. Lastly, we address the difficulty of extracting high quality shape structures from imaging data in the field of astronomy. To do so, we present a state-of-the-art expectation-maximization approach for the challenging task of multi-frame astronomical image deconvolution and super-resolution. We leverage our approach to obtain a high-fidelity reconstruction of the night sky, from which high quality shape data can be extracted using appropriate segmentation and photometric techniques

    Verification and Validation of Numerical Modelling Approaches Pertinent to Stomach Modelling

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    The digestive system is vital to the human body. Over many decades, scientists have been investigating the food breakdown mechanisms inside the stomach through in vivo human and animal studies and in vitro experiments. Due to recent improvements in computing speed and algorithm development, computational modelling has become a viable option to investigate in-body processes. Such in silico models are more easily controlled to investigate individual variables, do not require invasive physical experiments, and can provide valuable insights into the local physics of gastric flow. There is a huge potential for numerical approaches in stomach modelling as they can provide a comprehensive understanding of the complex flow and chemistry in the stomach. However, to make sure the numerical methods are accurate and reliable, rigorous verification and validation are essential as part of model development. A significant focus of this thesis was on verifying and validating the numerical modelling approaches pertinent to stomach modellin

    Review of Particle Physics

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    The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,143 new measurements from 709 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 120 reviews are many that are new or heavily revised, including a new review on Machine Learning, and one on Spectroscopy of Light Meson Resonances. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume 2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app.United States Department of Energy (DOE) DE-AC02-05CH11231government of Japan (Ministry of Education, Culture, Sports, Science and Technology)Istituto Nazionale di Fisica Nucleare (INFN)Physical Society of Japan (JPS)European Laboratory for Particle Physics (CERN)United States Department of Energy (DOE

    Adaptive image vectorisation and brushing using mesh colours

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    We propose the use of curved triangles and mesh colours as a vector primitive for image vectorisation. We show that our representation has clear benefits for rendering performance, texture detail, as well as further editing of the resulting vector images. The proposed method focuses on efficiency, but it still leads to results that compare favourably with those from previous work. We show results over a variety of input images ranging from photos, drawings, paintings, all the way to designs and cartoons. We implemented several editing workflows facilitated by our representation: interactive user-guided vectorisation, and novel raster-style feature-aware brushing capabilities

    The Construction of Optimized High-Order Surface Meshes by Energy-Minimization

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    Despite the increasing popularity of high-order methods in computational fluid dynamics, their application to practical problems still remains challenging. In order to exploit the advantages of high-order methods with geometrically complex computational domains, coarse curved meshes are necessary, i.e. high-order representations of the geometry. This dissertation presents a strategy for the generation of curved high-order surface meshes. The mesh generation method combines least-squares fitting with energy functionals, which approximate physical bending and stretching energies, in an incremental energy-minimizing fitting strategy. Since the energy weighting is reduced in each increment, the resulting surface representation features high accuracy. Nevertheless, the beneficial influence of the energy-minimization is retained. The presented method aims at enabling the utilization of the superior convergence properties of high-order methods by facilitating the construction of coarser meshes, while ensuring accuracy by allowing an arbitrary choice of geometric approximation order. Results show surface meshes of remarkable quality, even for very coarse meshes representing complex domains, e.g. blood vessels

    Blending techniques in Curve and Surface constructions

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    Source at https://www.geofo.no/geofoN.html. <p

    Semi-Sharp Subdivision Shading

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    Subdivision is a method for generating a limit surface from a coarse mesh by recursively dividing its faces into several smaller faces. This process leads to smooth surfaces, but often suffers from shading artifacts near extraordinary points due to the lower quality of the normal field there. The idea of subdivision shading is to apply the same subdivision rules that are used to subdivide geometry to also subdivide the normals associated with mesh vertices. This leads to smoother normal fields, which in turn removes the shading artifacts. However, the original subdivision shading method does not support sharp and semi-sharp creases, which are important ingredients in subdivision surface modelling. We present two approaches to extending subdivision shading to work also on models with (semi-)sharp creases

    Accurate, Fast and Controllable Image and Point Cloud Registration

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    Registration is the process of establishing spatial correspondences between two objects. Many downstream tasks, e.g, in image analysis, shape animation, can make use of these spatial correspondences. A variety of registration approaches have been developed over the last decades, but only recently registration approaches have been developed that make use of and can easily process the large data samples of the big data era. On the one hand, traditional optimization-based approaches are too slow and cannot take advantage of very large data sets. On the other hand, registration users expect more controllable and accurate solutions since most downstream tasks, e.g., facial animation and 3D reconstruction, increasingly rely on highly precise spatial correspondences. In recent years, deep network registration approaches have become popular as learning-based approaches are fast and can benefit from large-scale data during network training. However, how to make such deep-learning-based approached accurate and controllable is still a challenging problem that is far from being completely solved. This thesis explores fast, accurate and controllable solutions for image and point cloud registration. Specifically, for image registration, we first improve the accuracy of deep-learning-based approaches by introducing a general framework that consists of affine and non-parametric registration for both global and local deformation. We then design a more controllable image registration approach that image regions could be regularized differently according to their local attributes. For point cloud registration, existing works either are limited to small-scale problems, hardly handle complicated transformations or are slow to solve. We thus develop fast, accurate and controllable solutions for large-scale real-world registration problems via integrating optimal transport with deep geometric learning.Doctor of Philosoph

    Review of Particle Physics

    Get PDF
    The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,143 new measurements from 709 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 120 reviews are many that are new or heavily revised, including a new review on Machine Learning, and one on Spectroscopy of Light Meson Resonances. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume 2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app
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