Results 21 to 30 of about 3,294 (223)
GAN‐LSTM‐3D: An efficient method for lung tumour 3D reconstruction enhanced by attention‐based LSTM
CAAI Transactions on Intelligence Technology, EarlyView., 2023 Abstract Three‐dimensional (3D) image reconstruction of tumours can visualise their structures with precision and high resolution. In this article, GAN‐LSTM‐3D method is proposed for 3D reconstruction of lung cancer tumours from 2D CT images. Our method consists of three phases: lung segmentation, tumour segmentation, and tumour 3D reconstruction. Lung
Lu Hong +12 more
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A Note on Topological Properties of Non-Hausdorff Manifolds
International Journal of Mathematics and Mathematical Sciences, 2009 The notion of compatible apparition points is introduced for non-Hausdorff manifolds, and properties of these points are studied. It is well known that the Hausdorff property is independent of the other conditions given in the standard definition of a ...
Steven L. Kent +2 more
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On the Hausdorff Dimension of CAT(κ) Surfaces
Analysis and Geometry in Metric Spaces, 2016 We prove that a closed surface with a CAT(κ) metric has Hausdorff dimension = 2, and that there are uniform upper and lower bounds on the two-dimensional Hausdorff measure of small metric balls.
Constantine David, Lafont Jean-François
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Unimodular Hausdorff and Minkowski dimensions [PDF]
Electronic Journal of Probability, 2021 This work introduces two new notions of dimension, namely the unimodular Minkowski and Hausdorff dimensions, which are inspired from the classical analogous notions. These dimensions are defined for unimodular discrete spaces, introduced in this work, which provide a common generalization to stationary point processes under their Palm version and ...
Baccelli, François +2 more
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Topological Hausdorff dimension and Poincaré inequality
Extracta Mathematicae, 2022 A relationship between Poincaré inequalities and the topological Hausdorff dimension is exposed—a lower bound on the dimension of Ahlfors regular spaces satisfying a weak (1, p)-Poincaré inequality is given.
C.A. DiMarco
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On the Fractal Measures and Dimensions of Image Measures on a Class of Moran Sets
Mathematics, 2023 In this work, we focus on the centered Hausdorff measure, the packing measure, and the Hewitt–Stromberg measure that determines the modified lower box dimension Moran fractal sets. The equivalence of these measures for a class of Moran is shown by having
Najmeddine Attia, Bilel Selmi
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Axioms, 2021 In this speculative analysis, interdimensionality is introduced as the (co)existence of universes embedded into larger ones. These interdimensional universes may be isolated or intertwined, suggesting a variety of interdimensional intrinsic phenomena ...
Karl Svozil
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A Discrete Version of Local Hausdorff Dimension on Infinite Fractal Networks
AxiomsIn this paper, we define the local Hausdorff dimension on fractal networks inspired by the idea of α-potential at a point x∈Rd. We prove some basic properties of the local Hausdorff dimension and then obtain the local Hausdorff dimension of some networks.
Cheng Zeng, Daohua Wang, Zixuan Zhao
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The Annals of Probability, 2004 We prove that the Hausdorff dimension of the trace of SLE_6 is almost surely 7/4 and give a more direct derivation of the result (due to Lawler-Schramm-Werner) that the dimension of its boundary is 4/3. We also prove that, for all κ<8, the SLE_κ trace has cut-points.
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ON THE MUTUAL MULTIFRACTAL ANALYSIS FOR SOME NON-REGULAR MORAN MEASURES
Проблемы анализа, 2023 In this paper, we study the mutual multifractal Hausdorff dimension and the packing dimension of level sets 𝐾(𝛼, 𝛽) for some non-regular Moran measures satisfying the so-called Strong Separation Condition.We obtain sufficient conditions for the valid ...
B. Selmi, N. Yu. Svetova
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