Feature line extraction from unorganized noisy point clouds using truncated Fourier series

2013 ◽  
Vol 29 (6-8) ◽  
pp. 617-626 ◽  
Author(s):  
Enkhbayar Altantsetseg ◽  
Yuta Muraki ◽  
Katsutsugu Matsuyama ◽  
Kouichi Konno
Keyword(s):  
Fourier Series ◽  
Point Clouds ◽  
Line Extraction ◽  
Feature Line ◽  
Truncated Fourier Series

scholarly journals Feature Line Extraction and Matching for Modeling Artificial Buildings Using Measured Point Clouds

2006 ◽  
Vol 5 (3) ◽  
pp. 80-91 ◽  
Author(s):  
Tetsuji KONNO ◽  
Kouichi KONNO ◽  
Tadahiro FUJIMOTO ◽  
Norishige CHIBA
Keyword(s):  
Point Clouds ◽  
Line Extraction ◽  
Feature Line

Investigation of discontinuous periodic signals using the measuring labview complex

2020 ◽  
pp. 72-79
Author(s):  
E.B. Solovyeva ◽  
◽  
Yu.M. Inshakov ◽  
Keyword(s):  
Fourier Series ◽  
Laboratory Experiment ◽  
Gibbs Phenomenon ◽  
Electrical Signals ◽  
Measuring Complex ◽  
Universal Measuring ◽  
Depth Study ◽  
Periodic Signals ◽  
Truncated Fourier Series

General approaches to the analysis of the Gibbs phenomenon for discontinuous periodic signals approximated by the truncated Fourier series are considered. Methods for smoothing the truncated Fourier series and improving its convergence are discussed. The software means for modeling is a universal measuring complex LabVIEW, which possesses a convenient environment for analyzing electrical signals, on the basis of this complex a laboratory experiment is carried out. The advantages of the measuring LabVIEW complex and its capabilities for in-depth study of discontinuous periodic signals are noted.

scholarly journals Dynamics of Fourier Modes in Torus Generative Adversarial Networks

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 325
Author(s):  
Ángel González-Prieto ◽  
Alberto Mozo ◽  
Edgar Talavera ◽  
Sandra Gómez-Canaval
Keyword(s):  
Fourier Series ◽  
Generative Adversarial Networks ◽  
Learning Models ◽  
Training Process ◽  
Small Perturbations ◽  
Adversarial Networks ◽  
Novel Method ◽  
Truncated Fourier Series ◽  
Real Flow ◽  
Machine Learning Models

Generative Adversarial Networks (GANs) are powerful machine learning models capable of generating fully synthetic samples of a desired phenomenon with a high resolution. Despite their success, the training process of a GAN is highly unstable, and typically, it is necessary to implement several accessory heuristics to the networks to reach acceptable convergence of the model. In this paper, we introduce a novel method to analyze the convergence and stability in the training of generative adversarial networks. For this purpose, we propose to decompose the objective function of the adversary min–max game defining a periodic GAN into its Fourier series. By studying the dynamics of the truncated Fourier series for the continuous alternating gradient descend algorithm, we are able to approximate the real flow and to identify the main features of the convergence of GAN. This approach is confirmed empirically by studying the training flow in a 2-parametric GAN, aiming to generate an unknown exponential distribution. As a by-product, we show that convergent orbits in GANs are small perturbations of periodic orbits so the Nash equillibria are spiral attractors. This theoretically justifies the slow and unstable training observed in GANs.

Automatic Hexahedral Mesh Generation with Feature Line Extraction

2007 ◽  
pp. 453-467 ◽  
Author(s):  
Masayuki Hariya ◽  
Ichiro Nishigaki ◽  
Ichiro Kataoka ◽  
Yoshimitsu Hiro
Keyword(s):  
Mesh Generation ◽  
Hexahedral Mesh ◽  
Line Extraction ◽  
Feature Line ◽  
Hexahedral Mesh Generation
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