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Appendix to the paper “On the Billingsley dimension of Birkhoff average in the countable symbolic space”

Comptes Rendus. Mathématique, 2020
This appendix gives a lower bound of the Billingsley-Hausdorff dimension of a level set related to Birkhoff average in the “non-compact” symbolic space $\mathbb{N}^{\mathbb{N}}$, defined by Gibbs measure.
Selmi, Bilel
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A Multi‐Sequence Adversarial Fusion U‐Net for Brain Tumor Image Segmentation

IEEJ Transactions on Electrical and Electronic Engineering, EarlyView.
In the field of brain tumor image segmentation, in order to avoid the impact of insufficient number of training samples, the method of fusing multi‐modal MRI information before segmentation is widely used. However, when fusing different modal features, existing methods only add fixed weights to the features of each modality, resulting in insufficient ...
Jie Wang, Jinglu Hu
wiley   +1 more source

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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Artificial Intelligence in Intraoral Scanning: A Narrative Review

Australian Dental Journal, EarlyView.
ABSTRACT Intraoral scanning (IOS) enables the acquisition of three‐dimensional surface models of dental and oral structures, supporting diagnosis, treatment planning and digital workflows. However, many processing steps remain operator‐dependent and time‐consuming. The integration of artificial intelligence (AI) with intraoral scanning (IOS) represents
Camila Tirapelli, Bree Jones, Caio Uehara Martins, Bruna Neves de Freitas, Alessandra Alaniz Macedo, Ruben Pauwels   +5 more
wiley   +1 more source

SDFs from Unoriented Point Clouds using Neural Variational Heat Distances

Computer Graphics Forum, EarlyView.
We propose a novel variational approach for computing neural Signed Distance Fields (SDF) from unoriented point clouds. We first compute a small time step of heat flow (middle) and then use its gradient directions to solve for a neural SDF (right). Abstract We propose a novel variational approach for computing neural Signed Distance Fields (SDF) from ...
Samuel Weidemaier, Florine Hartwig, Josua Sassen, Sergio Conti, Mirela Ben‐Chen, Martin Rumpf   +5 more
wiley   +1 more source

Compact operators on the Motzkin sequence space $c_0(\mathcal{M})$

Journal of New Results in Science
The concept of non-compactness measure is extremely beneficial for functional analysis in theories, such as fixed point and operator equations. Apart from these, the Hausdorff measure of non-compactness also has some applications in the theory of ...
Sezer Erdem
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Basis Networks: Learning basis functions for free‐form triangulations

Computer Graphics Forum, EarlyView.
Abstract We present a framework for learning compactly supported basis functions that define tangent continuous surfaces based on coarse irregular triangle meshes. The basis functions are represented as MLPs. Smoothness of the basis functions is achieved by using the values of Loop basis functions as the parameterization of the surface.
T. Djuren, M. Alexa
wiley   +1 more source

LeafFit: Plant Assets Creation from 3D Gaussian Splatting

Computer Graphics Forum, EarlyView.
Abstract We propose LeafFit, a pipeline that converts 3D Gaussian Splatting (3DGS) of individual plants into editable, instanced mesh assets. While 3DGS faithfully captures complex foliage, its high memory footprint and lack of mesh topology make it incompatible with traditional game production workflows. We address this by leveraging the repetition of
Chang Luo, Nobuyuki Umetani
wiley   +1 more source

Calculation of Hausdorff dimensions of basins of ergodic measures in encoding spaces

Журнал Белорусского государственного университета: Математика, информатика, 2018
In the article we consider spaces XN of sequences of elements of finite alphabet X (encoding spaces) and ergodic measures on them, basins of ergodic measures and Hausdorff dimensions of such basins with respect to ultrametrics defined by a product of ...
Pavel N. Varabei
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О хаусдорфовой мере однородного треугольного (С, θ)-ковра Серпинского [PDF]

Проблемы анализа, 2011
В работе рассматривается однородный треугольный (с,θ)-ковер Серпинского.Для значений параметра с ⊂(0,1/3] при θ⊂(π/3, π) получено точное значение хаусдорфовой s-меры, а при θ⊂(0, π/3] её оценка.The generalized homogeneous Sierpinski (c, θ)-gasket is ...
Светова Н. Ю.
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