57,450 research outputs found

    Geometric Tomography With Topological Guarantees

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    We consider the problem of reconstructing a compact 3-manifold (with boundary) embedded in R3\mathbb{R}^3 from its cross-sections with a given set of cutting planes having arbitrary orientations. Under appropriate sampling conditions that are satisfied when the set of cutting planes is dense enough, we prove that the algorithm presented by Liu et al. in [1] preserves the homotopy type of the object. Using the homotopy equivalence, we also show that the reconstructed object is homeomorphic (and isotopic) to the original object. This is the first time that 3D shape reconstruction from cross-sections comes with such theoretical guarantees. [1] L. Liu, C.L. Bajaj, J.O. Deasy, D.A. Low, and T. Ju. Surface reconstruction from non-parallel curve networks. Computer Graphics Forum, 27:155-163, 2008

    Three-dimensional reconstruction of stenosed coronary artery segments with assessment of the flow impedance

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    In this paper preliminary results of a study about the diagnostic benefits of 3D visualization and quantitation of stenosed coronary artery segments are presented. As is well known, even biplane angiographic images do not provide enough information for binary reconstruction. Therefore,a priori information about the slice to be reconstructed must be incorporated into the reconstruction algorithm. One approach is to assume a circular cross-section of the coronary artery. Hence, the diameter is estimated from the contours of the vessels in both projections. Another approach is to search for a solution of the reconstruction problem close to the previously reconstructed adjacent slice. In this paper we follow the first method based on contour information. The reconstructed coronary segment is visualized in three dimensions. Based on the obtained geometry of the obstruction the pertinent blood flow impedance is estimated on the basis of fluid dynamic principles. The results of applying the reconstruction algorithms to clinical coronary biplane exposures are presented with an indication of the assessed flow impedance

    EPiK-a Workflow for Electron Tomography in Kepler.

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    Scientific workflows integrate data and computing interfaces as configurable, semi-automatic graphs to solve a scientific problem. Kepler is such a software system for designing, executing, reusing, evolving, archiving and sharing scientific workflows. Electron tomography (ET) enables high-resolution views of complex cellular structures, such as cytoskeletons, organelles, viruses and chromosomes. Imaging investigations produce large datasets. For instance, in Electron Tomography, the size of a 16 fold image tilt series is about 65 Gigabytes with each projection image including 4096 by 4096 pixels. When we use serial sections or montage technique for large field ET, the dataset will be even larger. For higher resolution images with multiple tilt series, the data size may be in terabyte range. Demands of mass data processing and complex algorithms require the integration of diverse codes into flexible software structures. This paper describes a workflow for Electron Tomography Programs in Kepler (EPiK). This EPiK workflow embeds the tracking process of IMOD, and realizes the main algorithms including filtered backprojection (FBP) from TxBR and iterative reconstruction methods. We have tested the three dimensional (3D) reconstruction process using EPiK on ET data. EPiK can be a potential toolkit for biology researchers with the advantage of logical viewing, easy handling, convenient sharing and future extensibility

    A mathematical model and inversion procedure for Magneto-Acousto-Electric Tomography (MAET)

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    Magneto-Acousto-Electric Tomography (MAET), also known as the Lorentz force or Hall effect tomography, is a novel hybrid modality designed to be a high-resolution alternative to the unstable Electrical Impedance Tomography. In the present paper we analyze existing mathematical models of this method, and propose a general procedure for solving the inverse problem associated with MAET. It consists in applying to the data one of the algorithms of Thermo-Acoustic tomography, followed by solving the Neumann problem for the Laplace equation and the Poisson equation. For the particular case when the region of interest is a cube, we present an explicit series solution resulting in a fast reconstruction algorithm. As we show, both analytically and numerically, MAET is a stable technique yilelding high-resolution images even in the presence of significant noise in the data

    Nanometer-scale Tomographic Reconstruction of 3D Electrostatic Potentials in GaAs/AlGaAs Core-Shell Nanowires

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    We report on the development of Electron Holographic Tomography towards a versatile potential measurement technique, overcoming several limitations, such as a limited tilt range, previously hampering a reproducible and accurate electrostatic potential reconstruction in three dimensions. Most notably, tomographic reconstruction is performed on optimally sampled polar grids taking into account symmetry and other spatial constraints of the nanostructure. Furthermore, holographic tilt series acquisition and alignment have been automated and adapted to three dimensions. We demonstrate 6 nm spatial and 0.2 V signal resolution by reconstructing various, previously hidden, potential details of a GaAs/AlGaAs core-shell nanowire. The improved tomographic reconstruction opens pathways towards the detection of minute potentials in nanostructures and an increase in speed and accuracy in related techniques such as X-ray tomography
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