3,331 research outputs found

    Spectral Convergence of the connection Laplacian from random samples

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    Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as Diffusion Maps and Laplacian Eigenmaps are often used for manifold learning and non-linear dimensionality reduction. It was previously shown by Belkin and Niyogi \cite{belkin_niyogi:2007} that the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions and eigenvalues of the Laplace-Beltrami operator of the manifold in the limit of infinitely many data points sampled independently from the uniform distribution over the manifold. Recently, we introduced Vector Diffusion Maps and showed that the connection Laplacian of the tangent bundle of the manifold can be approximated from random samples. In this paper, we present a unified framework for approximating other connection Laplacians over the manifold by considering its principle bundle structure. We prove that the eigenvectors and eigenvalues of these Laplacians converge in the limit of infinitely many independent random samples. We generalize the spectral convergence results to the case where the data points are sampled from a non-uniform distribution, and for manifolds with and without boundary

    On the Reliability of Diffusion Neuroimaging

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    Over the last years, diffusion imaging techniques like DTI, DSI or Q-Ball received increasin

    Robust numerical analysis of fibrous composites from X-ray computed tomography image data enabling low resolutions

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    X-ray computed tomography scans can provide detailed information about the state of the material after manufacture and in service. X-ray computed tomography aided engineering (XAE) was recently introduced as an automated process to transfer 3D image data to finite element models. The implementation of a structure tensor code for material orientation analysis in combination with a newly developed integration point-wise fibre orientation mapping allows an easy applicable, computationally cheap, fast, and accurate model set-up. The robustness of the proposed approach is demonstrated on a non-crimp fabric glass fibre reinforced composite for a low resolution case with a voxel size of 64 μm corresponding to more than three times the fibre diameter. Even though 99.8% of the original image data is removed, the simulated elastic modulus of the considered non-crimp fabric composite is only underestimated by 4.7% compared to the simulation result based on the original high resolution scan

    Robust numerical analysis of fibrous composites from X-ray computed tomography image data enabling low resolutions

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    X-ray computed tomography scans can provide detailed information about the state of the material after manufacture and in service. X-ray computed tomography aided engineering (XAE) was recently introduced as an automated process to transfer 3D image data to finite element models. The implementation of a structure tensor code for material orientation analysis in combination with a newly developed integration point-wise fibre orientation mapping allows an easy applicable, computationally cheap, fast, and accurate model set-up. The robustness of the proposed approach is demonstrated on a non-crimp fabric glass fibre reinforced composite for a low resolution case with a voxel size of 64 μm corresponding to more than three times the fibre diameter. Even though 99.8% of the original image data is removed, the simulated elastic modulus of the considered non-crimp fabric composite is only underestimated by 4.7% compared to the simulation result based on the original high resolution scan

    Interactive volumetric segmentation for textile micro-tomography data using wavelets and nonlocal means

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    This work addresses segmentation of volumetric images of woven carbon fiber textiles from micro-tomography data. We propose a semi-supervised algorithm to classify carbon fibers that requires sparse input as opposed to completely labeled images. The main contributions are: (a) design of effective discriminative classifiers, for three-dimensional textile samples, trained on wavelet features for segmentation; (b) coupling of previous step with nonlocal means as simple, efficient alternative to the Potts model; and (c) demonstration of reuse of classifier to diverse samples containing similar content. We evaluate our work by curating test sets of voxels in the absence of a complete ground truth mask. The algorithm obtains an average 0.95 F1 score on test sets and average F1 score of 0.93 on new samples. We conclude with discussion of failure cases and propose future directions toward analysis of spatiotemporal high-resolution micro-tomography images

    X-ray computer tomography based numerical modelling of fibre reinforced composites

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    Non-crimp fabric reinforced polymers are commonly used to manufacture the load carrying parts in wind turbine blades. Since wind turbine blades have a large material usage, the favourable stiffness to price ratio of non-crimp fabric reinforced polymers is highly attractive for manufactures. Additionally, they are easy to manufacture, which is essential for mould sizes of up to approximately 100 m. Smaller turbine blades up to 75 m use glass fibres, lager blades require carbon fibres to meet the stiffness requirements.\ua0Wind turbine blades are ever increasing in length since the generated power is proportional to the length squared. In addition to the challenge to reduce the material usage, longer blades demand higher stiffness. Furthermore, wind turbines are one of the man-made structures that have to endure the highest numbers of load cycles. Even though wind turbine blades are mainly loaded in tension there are compressive loads present on the leeward side of the blade. Those three main material requirements demand highly tailored high-performance materials. At the same time wind turbine manufactures are under a high cost pressure as governments all over the world are cutting subsidies. As for any other high-performance material a constant production quality is essential. However, in particular composites are susceptible for manufacture flaws.\ua0X-ray computer tomography allows for the detection of some of the defects present after manufacture. X-ray computer tomography is a very promising tool for materials quality control and quantification when combined with numerical modelling. In the last years the image acquisition and analysis process has seen enormous progress that can now be exploited.\ua0In this research project the X-ray computer tomography aided engineering (XAE) process has been established. XAE systemically combines all work-steps from material image acquisition to the final finite element analysis results. The process provides an automated, accurate and fast image analysis and an element-wise and integration point-wise material orientation mapping. The analysis of the detailed stress and strain distributions after manufacture with XAE will allow for more reliable and low-cost wind turbine blades

    A Vignetting Model for Light Field Cameras with an Application to Light Field Microscopy

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    International audienceIn standard photography, vignetting is considered mainly as a radiometric effect because it results in a darkening of the edges of the captured image. In this paper, we demonstrate that for light field cameras, vignetting is more than just a radio-metric effect. It modifies the properties of the acquired light field and renders most of the calibration procedures from the literature inadequate. We address the problem by describing a model-and camera-agnostic method to evaluate vignetting in phase space. This enables the synthesis of vignetted pixel values, that, applied to a range of pixels yield images corresponding to the white images that are customarily recorded for calibrating light field cameras. We show that the commonly assumed reference points for microlens-based systems are incorrect approximations to the true optical reference, i.e. the image of the center of the exit pupil. We introduce a novel calibration procedure to determine this optically correct reference point from experimental white images. We describe the changes vignetting imposes on the light field sampling patterns and, therefore, the optical properties of the corresponding virtual cameras using the ECA model [1] and apply these insights to a custom-built light field microscope

    Oscillatory and Fourier Integral operators with degenerate canonical relations

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    We mostly survey results concerning the L2L^2 boundedness of oscillatory and Fourier integral operators. This article does not intend to give a broad overview; it mainly focusses on a few topics directly related to the work of the authors.Comment: 37 pages, to appear in Publicacions Mathematiques (special issue, Proceedings of the 2000 El Escorial Conference in Harmonic Analysis and Partial Differential Equations
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