21 research outputs found

    Cellular Skeletons: A New Approach to Topological Skeletons with Geometric Features

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    This paper introduces a new kind of skeleton for binary volumes called the cellular skeleton. This skeleton is not a subset of voxels of a volume nor a subcomplex of a cubical complex: it is a chain complex together with a reduction from the original complex. Starting from the binary volume we build a cubical complex which represents it regarding 6 or 26-connectivity. Then the complex is thinned using the proposed method based on elementary collapses, which preserves significant geometric features. The final step reduces the number of cells using Discrete Morse Theory. The resulting skeleton is a reduction which preserves the homology of the original complex and the geometrical information of the output of the previous step. The result of this method, besides its skeletonization content, can be used for computing the homology of the original complex, which usually provides well shaped homology generators

    Mathematics in Medical Diagnostics - 2022 Proceedings of the 4th International Conference on Trauma Surgery Technology

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    The 4th event of the Giessen International Conference Series on Trauma Surgery Technology took place on April, the 23rd 2022 in Warsaw, Poland. It aims to bring together practical application research, with a focus on medical imaging, and the TDA experts from Warsaw. This publication contains details of our presentations and discussions

    26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

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    This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)

    A novel technique for cohomology computations in engineering practice

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    The problem of computing cohomology generators of a cell complex is gaining more and more interest in various branches of science ranging from computational physics to biology. Focusing on engineering applications, cohomology generators are currently used in computer aided design (CAD) and in potential definition for computational electromagnetics and fluid dynamics. The aim of this paper is to introduce a novel technique to effectively compute cohomology generators focusing on the application involving the potential definition for h-oriented eddy-current formulations. This technique, which has been called Thinned Current Technique (TCT), is completely automatic, computationally efficient and general. The TCT runs in most cases in linear time and exhibits a speed up of orders of magnitude with respect to the best alternative documented implementation

    Efficient cohomology computation for electromagnetic modeling

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    The systematic potential design is of high importance in computational electromagnetics. For example, it is well known that when the efficient eddy-current formulations based on a magnetic scalar potential are employed in problems which involve conductive regions with holes, the so-called thick cuts are needed to make the boundary value problem well defined. Therefore, a considerable effort has been invested over the past twenty-five years to develop fast and general algorithms to compute thick cuts automatically. Nevertheless, none of the approaches proposed in literature meet all the requirements of being automatic, computationally efficient and general. In this paper, an automatic, computationally efficient and provably general algorithm is presented. It is based on a rigorous algorithm to compute a cohomology basis of the insulating region with state-of-art reductions techniques-the acyclic sub-complex technique, among others-expressly designed for cohomology computations over simplicial complexes. Its effectiveness is demonstrated by presenting a number of practical benchmarks. The automatic nature of the proposed approach together with its low computational time enable the routinely use of cohomology computations in computational electromagnetics

    Efficient generalized source field computation forh-oriented magnetostatic formulations

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    A technique based on a tree-cotree decomposition, called Spanning Tree Technique (STT) in this paper, has been shown to be simple and efficient to compute the generalized source magnetic fields for h-oriented magnetostatic formulations when solenoidal source electric currents over the faces of the mesh are given as input. Yet, it has been recently shown that STT may frequently fail in practice. Other techniques, which circumvent STT problems, have been proposed in literature. However, all of them greatly worsen the computational complexity and memory requirements regarding the source field computation. The aim of this paper is to present a generalization of STT called Extended Spanning Tree Technique (ESTT), which is provably general and it retains the STT computational efficiency

    Voltage and current sources for massive conductors suitable with the A-chi Geometric Formulation

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    The aim of the paper is to present an automatic and general technique, suitable with the A-chi geometric eddy-current formulation, to impose sources over massive conductors of any shape. For this purpose, the localized source approach is used, which does not require the solutions of steady-state conduction problems in the preprocessing stage. Nevertheless, this approach needs a thick cut in each active conductor, which is usually found by hand. In this paper, an automatic and general algorithm to compute such thick cuts is introduced. Some benchmark problems are presented to demonstrate the generality and the robustness of the algorithm

    Automatic generation of cuts on large-sized meshes for the T–Ω geometric eddy-current formulation

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    In this paper a Geometric T-\u3a9 formulation to solve eddy-current problems on a tetrahedral mesh is presented. When non-simply-connected conducting regions are considered, the formulation requires the so-called thick cuts, while, in the literature, more attention is usually given to the so-called thin cuts. While the automatic construction of thin cuts has been theoretically solved many years ago, no implementation of an algorithm to compute the thick cuts which can be used in practice exists so far. In this paper, we propose how to fill this gap by introducing an algorithm to automatically compute the thick cuts on real-sized meshes, based on a belted tree and a tree-cotree decomposition. The belted tree is constructed by means of a homology computation by exploiting efficient reduction methods. A number of benchmarks are presented to demonstrate the generality and the robustness of the algorithm. A rigorous definition of thick cuts, which necessarily has to rely on cohomology, is presented in addition
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