700 research outputs found

    Anisotropic Total Variation Regularized L^1-Approximation and Denoising/Deblurring of 2D Bar Codes

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    We consider variations of the Rudin-Osher-Fatemi functional which are particularly well-suited to denoising and deblurring of 2D bar codes. These functionals consist of an anisotropic total variation favoring rectangles and a fidelity term which measure the L^1 distance to the signal, both with and without the presence of a deconvolution operator. Based upon the existence of a certain associated vector field, we find necessary and sufficient conditions for a function to be a minimizer. We apply these results to 2D bar codes to find explicit regimes ---in terms of the fidelity parameter and smallest length scale of the bar codes--- for which a perfect bar code is recoverable via minimization of the functionals. Via a discretization reformulated as a linear program, we perform numerical experiments for all functionals demonstrating their denoising and deblurring capabilities.Comment: 34 pages, 6 figures (with a total of 30 subfigures); errors corrected in Version 3, see Errata 1.1, 4.4, and 6.6 (v3 numbering) for more informatio

    Subdivision surface fitting to a dense mesh using ridges and umbilics

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    Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original features. The natural ridge-joined connectivity of umbilics and ridge-crossings is used as the connectivity of the control mesh for subdivision, so that the edges follow salient features on the surface. Furthermore, the chosen features and connectivity characterise the overall shape of the original mesh, since ridges capture extreme principal curvatures and ridges start and end at umbilics. A metric of Hausdorff distance including curvature vectors is proposed and implemented in a distance transform algorithm to construct the connectivity. Ridge-colour matching is introduced as a criterion for edge flipping to improve feature alignment. Several examples are provided to demonstrate the feature-preserving capability of the proposed approach

    On Deterministic Sketching and Streaming for Sparse Recovery and Norm Estimation

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    We study classic streaming and sparse recovery problems using deterministic linear sketches, including l1/l1 and linf/l1 sparse recovery problems (the latter also being known as l1-heavy hitters), norm estimation, and approximate inner product. We focus on devising a fixed matrix A in R^{m x n} and a deterministic recovery/estimation procedure which work for all possible input vectors simultaneously. Our results improve upon existing work, the following being our main contributions: * A proof that linf/l1 sparse recovery and inner product estimation are equivalent, and that incoherent matrices can be used to solve both problems. Our upper bound for the number of measurements is m=O(eps^{-2}*min{log n, (log n / log(1/eps))^2}). We can also obtain fast sketching and recovery algorithms by making use of the Fast Johnson-Lindenstrauss transform. Both our running times and number of measurements improve upon previous work. We can also obtain better error guarantees than previous work in terms of a smaller tail of the input vector. * A new lower bound for the number of linear measurements required to solve l1/l1 sparse recovery. We show Omega(k/eps^2 + klog(n/k)/eps) measurements are required to recover an x' with |x - x'|_1 <= (1+eps)|x_{tail(k)}|_1, where x_{tail(k)} is x projected onto all but its largest k coordinates in magnitude. * A tight bound of m = Theta(eps^{-2}log(eps^2 n)) on the number of measurements required to solve deterministic norm estimation, i.e., to recover |x|_2 +/- eps|x|_1. For all the problems we study, tight bounds are already known for the randomized complexity from previous work, except in the case of l1/l1 sparse recovery, where a nearly tight bound is known. Our work thus aims to study the deterministic complexities of these problems

    Thermalization and Quantum Information in Conformal Field Theory

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    The consequences of the constraints of conformal symmetry are far-reaching withintheoretical physics. In this dissertation we address a series of questions in conformalfield theory: 1) We calculate the spectrum of qKdV charges in a large central chargeexpansion. 2) We determine the corrections to bulk information geometry from 1/Ncontributions to holographic correlators. 3) We study the higher genus partitionsfunctions of CFTs associated with classical and quantum error-correcting codes

    Robust surface modelling of visual hull from multiple silhouettes

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    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

    リーマン多様体とグラフ上の熱核の大域解析

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    平成16年度-平成18年度科学研究費補助金(基盤研究(B))研究成果報告書,課題番号:1634004
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