100 research outputs found

    Recursive subdivision algorithms for curve and surface design

    Get PDF
    This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.In this thesis, the author studies recursIve subdivision algorithms for curves and surfaces. Several subdivision algorithms are constructed and investigated. Some graphic examples are also presented. Inspired by the Chaikin's algorithm and the Catmull-Clark's algorithm, some non-uniform schemes, the non-uniform corner cutting scheme and the recursive subdivision algorithm for non-uniform B-spline curves, are constructed and analysed. The adapted parametrization is introduced to analyse these non-uniform algorithms. In order to solve the surface interpolation problem, the Dyn-Gregory-Levin's 4-point interpolatory scheme is generalized to surfaces and the 10-point interpolatory subdivision scheme for surfaces is formulated. The so-called Butterfly Scheme, which was firstly introduced by Dyn, Gregory Levin in 1988, is just a special case of the scheme. By studying the Cross-Differences of Directional Divided Differences, a matrix approach for analysing uniform subdivision algorithms for surfaces is established and the convergence of the 10-point scheme over both uniform and non-uniform triangular networks is studied. Another algorithm, the subdivision algorithm for uniform bi-quartic B-spline surfaces over arbitrary topology is introduced and investigated. This algorithm is a generalization of Doo-Sabin's and Catmull-Clark's algorithms. It produces uniform Bi-quartic B-spline patches over uniform data. By studying the local subdivision matrix, which is a circulant, the tangent plane and curvature properties of the limit surfaces at the so-called Extraordinary Points are studied in detail.The Chinese Educational Commission and The British Council (SBFSS/1987

    Bench Measurements and Simulations of Beam Coupling Impedance

    Full text link
    After a general introduction, the basic principles of wake-field and beamcoupling- impedance computations are explained. This includes time domain, frequency domain, and methods that do not include excitations by means of a particle beam. The second part of this paper deals with radio frequency bench measurements of beam coupling impedances. The general procedure of the wire measurement is explained, and its features and limitations are discussed.Comment: presented at the Proceedings of the CAS-CERN Accelerator School on Intensity Limitation in Particle Beams, Geneva, Switzerland -2-11 November 201

    Processing Elastic Surfaces and Related Gradient Flows

    Get PDF
    Surface processing tools and techniques have a long history in the fields of computer graphics, computer aided geometric design and engineering. In this thesis we consider variational methods and geometric evolution problems for various surface processing applications including surface fairing, surface restoration and surface matching. Geometric evolution problems are often based on the gradient flow of geometric energies. The Willmore functional, defined as the integral of the squared mean curvature over the surface, is a geometric energy that measures the deviation of a surface from a sphere. Therefore, it is a suitable functional for surface restoration, where a destroyed surface patch is replaced by a smooth patch defined as the minimizer of the Willmore functional with boundary conditions for the position and the normal at the patch boundary. However, using the Willmore functional does not lead to satisfying results if an edge or a corner of the surface is destroyed. The anisotropic Willmore energy is a natural generalization of the Willmore energy which has crystal-shaped surfaces like cubes or octahedra as minimizers. The corresponding L2-gradient flow, the anisotropic Willmore flow, leads to a fourth-order partial differential equation that can be written as a system of two coupled second second order equations. Using linear Finite Elements, we develop a semi-implicit scheme for the anisotropic Willmore flow with boundary conditions. This approach suffer from significant restrictions on the time step size. Effectively, one usually has to enforce time steps smaller than the squared spatial grid size. Based on a natural approach for the time discretization of gradient flows we present a new scheme for the time and space discretization of the isotropic and anisotropic Willmore flow. The approach is variational and takes into account an approximation of the L2-distance between the surface at the current time step and the unknown surface at the new time step as well as a fully implicity approximation of the anisotropic Willmore functional at the new time step. To evaluate the anisotropic Willmore energy on the unknown surface of the next time step, we first ask for the solution of an inner, secondary variational problem describing a time step of anisotropic mean curvature motion. The time discrete velocity deduced from the solution of the latter problem is regarded as an approximation of the anisotropic mean curvature vector and enters the approximation of the actual anisotropic Willmore functional. The resulting two step time discretization of the Willmore flow is applied to polygonal curves and triangular surfaces and is independent of the co-dimension. Various numerical examples underline the stability of the new scheme, which enables time steps of the order of the spatial grid size. The Willmore functional of a surface is referred to as the elastic surface energy. Another interesting application of modeling elastic surfaces as minimizers of elastic energies is surface matching, where a correspondence between two surfaces is subject of investigation. There, we seek a mapping between two surfaces respecting certain properties of the surfaces. The approach is variational and based on well-established matching methods from image processing in the parameter domains of the surfaces instead of finding a correspondence between the two surfaces directly in 3D. Besides the appropriate modeling we analyze the derived model theoretically. The resulting deformations are globally smooth, one-to-one mappings. A physically proper morphing of characters in computer graphic is capable with the resulting computational approach

    An arbitrary curvilinear coordinate particle in cell method

    Get PDF
    A new approach to the kinetic simulation of plasmas in complex geometries, based on the Particle-in-Cell (PIC) simulation method, is explored. In this method, called the Arbitrary Curvilinear Coordinate PIC (ACC-PIC) method, all essential PIC operations are carried out on a uniform, unitary square logical domain and mapped to a nonuniform, boundary fitted physical domain. We utilize an elliptic grid generation technique known as Winslow\u27s method to generate boundary-fitted physical domains. We have derived the logical grid macroparticle equations of motion based on a canonical transformation of Hamilton\u27s equations from the physical domain to the logical. These equations of motion are not seperable, and therefore unable to be integrated using the standard Leapfrog method. We have developed an extension of the semi-implicit Modified Leapfrog (ML) integration technique to preserve the symplectic nature of the logical grid particle mover. We constructed a proof to show that the ML integrator is symplectic for systems of arbitrary dimension. We have constructed a generalized, curvilinear coordinate formulation of Poisson\u27s equations to solve for the electrostatic fields on the uniform logical grid. By our formulation, we supply the plasma charge density on the logical grid as a source term. By the formulations of the logical grid particle mover and the field equations, the plasma particles are weighted to the uniform logical grid and the self-consistent mean fields obtained from the solution of the Poisson equation are interpolated to the particle position on the logical grid. This process coordinates the complexity associated with the weighting and interpolation processes on the nonuniform physical grid. In this work, we explore the feasibility of the ACC-PIC method as a first step towards building a production level, time-adaptive-grid, 3D electromagnetic ACC-PIC code. We begin by combining the individual components to construct a 1D, electrostatic ACC-PIC code on a stationary nonuniform grid. Several standard physics tests were used to validate the accuracy of our method in comparison with a standard uniform grid PIC code. We then extend the code to two spatial dimensions and repeat the physics tests on a rectangular domain with both orthogonal and nonorthogonal meshing in comparison with a standard 2D uniform grid PIC code. As a proof of principle, we then show the time evolution of an electrostatic plasma oscillation on an annular domain obtained using Winslow\u27s method

    Balanced-force two-phase flow modelling on unstructured and adaptive meshes

    Get PDF
    Two-phase flows occur regularly in nature and industrial processes and their understanding is of significant interest in engineering research and development. Various numerical methods to predict two-phase phase flows have been developed as a result of extensive research efforts in past decades, however, most methods are limited to Cartesian meshes. A fully-coupled implicit numerical framework for two-phase flows on unstructured meshes is presented, solving the momentum equations and a specifically constructed continuity constraint in a single equation system. The continuity constraint, derived using a momentum interpolation method, satisfies continuity, provides a strong pressure-velocity coupling and ensures a discrete balance between pressure gradient and body forces. The numerical framework is not limited to specific density ratios or a particular interface topology and includes several novelties. A further step towards a more accurate prediction of two-phase flows on unstructured meshes is taken by proposing a new method to evaluate the interface curvature. The curvature estimates obtained with this new method are shown to be as good as or better than methods reported in literature, which are mostly limited to Cartesian meshes, and the accuracy on structured and unstructured meshes is shown to be comparable. Furthermore, lasting contributions are made towards the understanding of convolution methods for two-phase flow modelling and the underlying mechanisms of parasitic currents are studied in detailed. The mesh resolution is of particular importance for two-phase flows due to the inherent first-order accuracy of the interface position using interface capturing methods. A mesh adaption algorithm for tetrahedral meshes with application to two-phase flows and its implementation are presented. The algorithm is applied to study mesh resolution requirements at interfaces and force-balancing for surface-tension-dominated two-phase flows on adaptive meshes.Open Acces

    Robust surface modelling of visual hull from multiple silhouettes

    Get PDF
    Reconstructing depth information from images is one of the actively researched themes in computer vision and its application involves most vision research areas from object recognition to realistic visualisation. Amongst other useful vision-based reconstruction techniques, this thesis extensively investigates the visual hull (VH) concept for volume approximation and its robust surface modelling when various views of an object are available. Assuming that multiple images are captured from a circular motion, projection matrices are generally parameterised in terms of a rotation angle from a reference position in order to facilitate the multi-camera calibration. However, this assumption is often violated in practice, i.e., a pure rotation in a planar motion with accurate rotation angle is hardly realisable. To address this problem, at first, this thesis proposes a calibration method associated with the approximate circular motion. With these modified projection matrices, a resulting VH is represented by a hierarchical tree structure of voxels from which surfaces are extracted by the Marching cubes (MC) algorithm. However, the surfaces may have unexpected artefacts caused by a coarser volume reconstruction, the topological ambiguity of the MC algorithm, and imperfect image processing or calibration result. To avoid this sensitivity, this thesis proposes a robust surface construction algorithm which initially classifies local convex regions from imperfect MC vertices and then aggregates local surfaces constructed by the 3D convex hull algorithm. Furthermore, this thesis also explores the use of wide baseline images to refine a coarse VH using an affine invariant region descriptor. This improves the quality of VH when a small number of initial views is given. In conclusion, the proposed methods achieve a 3D model with enhanced accuracy. Also, robust surface modelling is retained when silhouette images are degraded by practical noise

    Geometric modeling of non-rigid 3D shapes : theory and application to object recognition.

    Get PDF
    One of the major goals of computer vision is the development of flexible and efficient methods for shape representation. This is true, especially for non-rigid 3D shapes where a great variety of shapes are produced as a result of deformations of a non-rigid object. Modeling these non-rigid shapes is a very challenging problem. Being able to analyze the properties of such shapes and describe their behavior is the key issue in research. Also, considering photometric features can play an important role in many shape analysis applications, such as shape matching and correspondence because it contains rich information about the visual appearance of real objects. This new information (contained in photometric features) and its important applications add another, new dimension to the problem\u27s difficulty. Two main approaches have been adopted in the literature for shape modeling for the matching and retrieval problem, local and global approaches. Local matching is performed between sparse points or regions of the shape, while the global shape approaches similarity is measured among entire models. These methods have an underlying assumption that shapes are rigidly transformed. And Most descriptors proposed so far are confined to shape, that is, they analyze only geometric and/or topological properties of 3D models. A shape descriptor or model should be isometry invariant, scale invariant, be able to capture the fine details of the shape, computationally efficient, and have many other good properties. A shape descriptor or model is needed. This shape descriptor should be: able to deal with the non-rigid shape deformation, able to handle the scale variation problem with less sensitivity to noise, able to match shapes related to the same class even if these shapes have missing parts, and able to encode both the photometric, and geometric information in one descriptor. This dissertation will address the problem of 3D non-rigid shape representation and textured 3D non-rigid shapes based on local features. Two approaches will be proposed for non-rigid shape matching and retrieval based on Heat Kernel (HK), and Scale-Invariant Heat Kernel (SI-HK) and one approach for modeling textured 3D non-rigid shapes based on scale-invariant Weighted Heat Kernel Signature (WHKS). For the first approach, the Laplace-Beltrami eigenfunctions is used to detect a small number of critical points on the shape surface. Then a shape descriptor is formed based on the heat kernels at the detected critical points for different scales. Sparse representation is used to reduce the dimensionality of the calculated descriptor. The proposed descriptor is used for classification via the Collaborative Representation-based Classification with a Regularized Least Square (CRC-RLS) algorithm. The experimental results have shown that the proposed descriptor can achieve state-of-the-art results on two benchmark data sets. For the second approach, an improved method to introduce scale-invariance has been also proposed to avoid noise-sensitive operations in the original transformation method. Then a new 3D shape descriptor is formed based on the histograms of the scale-invariant HK for a number of critical points on the shape at different time scales. A Collaborative Classification (CC) scheme is then employed for object classification. The experimental results have shown that the proposed descriptor can achieve high performance on the two benchmark data sets. An important observation from the experiments is that the proposed approach is more able to handle data under several distortion scenarios (noise, shot-noise, scale, and under missing parts) than the well-known approaches. For modeling textured 3D non-rigid shapes, this dissertation introduces, for the first time, a mathematical framework for the diffusion geometry on textured shapes. This dissertation presents an approach for shape matching and retrieval based on a weighted heat kernel signature. It shows how to include photometric information as a weight over the shape manifold, and it also propose a novel formulation for heat diffusion over weighted manifolds. Then this dissertation presents a new discretization method for the weighted heat kernel induced by the linear FEM weights. Finally, the weighted heat kernel signature is used as a shape descriptor. The proposed descriptor encodes both the photometric, and geometric information based on the solution of one equation. Finally, this dissertation proposes an approach for 3D face recognition based on the front contours of heat propagation over the face surface. The front contours are extracted automatically as heat is propagating starting from a detected set of landmarks. The propagation contours are used to successfully discriminate the various faces. The proposed approach is evaluated on the largest publicly available database of 3D facial images and successfully compared to the state-of-the-art approaches in the literature. This work can be extended to the problem of dense correspondence between non-rigid shapes. The proposed approaches with the properties of the Laplace-Beltrami eigenfunction can be utilized for 3D mesh segmentation. Another possible application of the proposed approach is the view point selection for 3D objects by selecting the most informative views that collectively provide the most descriptive presentation of the surface

    Synthesization and reconstruction of 3D faces by deep neural networks

    Get PDF
    The past few decades have witnessed substantial progress towards 3D facial modelling and reconstruction as it is high importance for many computer vision and graphics applications including Augmented/Virtual Reality (AR/VR), computer games, movie post-production, image/video editing, medical applications, etc. In the traditional approaches, facial texture and shape are represented as triangle mesh that can cover identity and expression variation with non-rigid deformation. A dataset of 3D face scans is then densely registered into a common topology in order to construct a linear statistical model. Such models are called 3D Morphable Models (3DMMs) and can be used for 3D face synthesization or reconstruction by a single or few 2D face images. The works presented in this thesis focus on the modernization of these traditional techniques in the light of recent advances of deep learning and thanks to the availability of large-scale datasets. Ever since the introduction of 3DMMs by over two decades, there has been a lot of progress on it and they are still considered as one of the best methodologies to model 3D faces. Nevertheless, there are still several aspects of it that need to be upgraded to the "deep era". Firstly, the conventional 3DMMs are built by linear statistical approaches such as Principal Component Analysis (PCA) which omits high-frequency information by its nature. While this does not curtail shape, which is often smooth in the original data, texture models are heavily afflicted by losing high-frequency details and photorealism. Secondly, the existing 3DMM fitting approaches rely on very primitive (i.e. RGB values, sparse landmarks) or hand-crafted features (i.e. HOG, SIFT) as supervision that are sensitive to "in-the-wild" images (i.e. lighting, pose, occlusion), or somewhat missing identity/expression resemblance with the target image. Finally, shape, texture, and expression modalities are separately modelled by ignoring the correlation among them, placing a fundamental limit to the synthesization of semantically meaningful 3D faces. Moreover, photorealistic 3D face synthesis has not been studied thoroughly in the literature. This thesis attempts to address the above-mentioned issues by harnessing the power of deep neural network and generative adversarial networks as explained below: Due to the linear texture models, many of the state-of-the-art methods are still not capable of reconstructing facial textures with high-frequency details. For this, we take a radically different approach and build a high-quality texture model by Generative Adversarial Networks (GANs) that preserves details. That is, we utilize GANs to train a very powerful generator of facial texture in the UV space. And then show that it is possible to employ this generator network as a statistical texture prior to 3DMM fitting. The resulting texture reconstructions are plausible and photorealistic as GANs are faithful to the real-data distribution in both low- and high- frequency domains. Then, we revisit the conventional 3DMM fitting approaches making use of non-linear optimization to find the optimal latent parameters that best reconstruct the test image but under a new perspective. We propose to optimize the parameters with the supervision of pretrained deep identity features through our end-to-end differentiable framework. In order to be robust towards initialization and expedite the fitting process, we also propose a novel self-supervised regression-based approach. We demonstrate excellent 3D face reconstructions that are photorealistic and identity preserving and achieve for the first time, to the best of our knowledge, facial texture reconstruction with high-frequency details. In order to extend the non-linear texture model for photo-realistic 3D face synthesis, we present a methodology that generates high-quality texture, shape, and normals jointly. To do so, we propose a novel GAN that can generate data from different modalities while exploiting their correlations. Furthermore, we demonstrate how we can condition the generation on the expression and create faces with various facial expressions. Additionally, we study another approach for photo-realistic face synthesis by 3D guidance. This study proposes to generate 3D faces by linear 3DMM and then augment their 2D rendering by an image-to-image translation network to the photorealistic face domain. Both works demonstrate excellent photorealistic face synthesis and show that the generated faces are improving face recognition benchmarks as synthetic training data. Finally, we study expression reconstruction for personalized 3D face models where we improve generalization and robustness of expression encoding. First, we propose a 3D augmentation approach on 2D head-mounted camera images to increase robustness to perspective changes. And, we also propose to train generic expression encoder network by populating the number of identities with a novel multi-id personalized model training architecture in a self-supervised manner. Both approaches show promising results in both qualitative and quantitative experiments.Open Acces
    • …
    corecore