AI-Powered Approaches for Hypersurface Reconstruction in Multidimensional Spaces

被引:0
|
作者
Yotov, Kostadin [1 ]
Hadzhikolev, Emil [1 ]
Hadzhikoleva, Stanka [1 ]
Milev, Mariyan [2 ]
机构
[1] Univ Plovdiv Paisii Hilendarski, Fac Math & Informat, 236 Bulgaria Blvd, Plovdiv 4027, Bulgaria
[2] Sofia Univ St Kliment Ohridski, Fac Econ, Business Adm, 125 Tsarigradsko Shosse Blvd,Bl 3, Sofia 1113, Bulgaria
关键词
hypersurface reconstruction; approximation; artificial neural networks; B & eacute; zier curves; k-nearest neighbors; principal component analysis; Markov random fields; conditional random fields; convolutional neural networks; NEURAL-NETWORK; SURFACE-ROUGHNESS; OPTIMIZATION; RECOGNITION;
D O I
10.3390/math12203285
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The present article explores the possibilities of using artificial neural networks to solve problems related to reconstructing complex geometric surfaces in Euclidean and pseudo-Euclidean spaces, examining various approaches and techniques for training the networks. The main focus is on the possibility of training a set of neural networks with information about the available surface points, which can then be used to predict and complete missing parts. A method is proposed for using separate neural networks that reconstruct surfaces in different spatial directions, employing various types of architectures, such as multilayer perceptrons, recursive networks, and feedforward networks. Experimental results show that artificial neural networks can successfully approximate both smooth surfaces and those containing singular points. The article presents the results with the smallest error, showcasing networks of different types, along with a technique for reconstructing geographic relief. A comparison is made between the results achieved by neural networks and those obtained using traditional surface approximation methods such as B & eacute;zier curves, k-nearest neighbors, principal component analysis, Markov random fields, conditional random fields, and convolutional neural networks.
引用
收藏
页数:30
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