Computing Space-Filling Curves

2010 ◽  
Vol 50 (2) ◽  
pp. 370-386 ◽  
Author(s):  
P. J. Couch ◽  
B. D. Daniel ◽  
Timothy H. McNicholl
Keyword(s):  
Space Filling ◽  
Space Filling Curves

scholarly journals On one approach to the approximation of solutions to the direct kinematics problem of parallel manipulators

2020 ◽  
Vol 10 (1) ◽  
pp. 65-70
Author(s):  
Andrei Gorchakov ◽  
Vyacheslav Mozolenko
Keyword(s):  
Neural Network ◽  
Bounded Function ◽  
Parallel Manipulators ◽  
Feedforward Neural Network ◽  
Numerical Implementation ◽  
Continuous Bounded Function ◽  
Space Filling ◽  
Space Filling Curves ◽  
Direct Kinematics

AbstractAny real continuous bounded function of many variables is representable as a superposition of functions of one variable and addition. Depending on the type of superposition, the requirements for the functions of one variable differ. The article investigated one of the options for the numerical implementation of such a superposition proposed by Sprecher. The superposition was presented as a three-layer Feedforward neural network, while the functions of the first’s layer were considered as a generator of space-filling curves (Peano curves). The resulting neural network was applied to the problems of direct kinematics of parallel manipulators.

scholarly journals Using Peano–Hilbert space filling curves for fast bidimensional ensemble EMD realization

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Paulo Costa ◽  
João Barroso ◽  
Hugo Fernandes ◽  
Leontios J Hadjileontiadis
Keyword(s):  
Hilbert Space ◽  
Space Filling ◽  
Space Filling Curves

Space-Filling Curves

2009 ◽  
pp. 2674-2675
Author(s):  
Mohamed F. Mokbel ◽  
Walid G. Aref
Keyword(s):  
Space Filling ◽  
Space Filling Curves

scholarly journals The Effect of Space-filling Curves on the Efficiency of Hand Gesture Recognition Based on sEMG Signals

2021 ◽  
Vol 12 (1) ◽  
pp. 23-31
Author(s):  
Panagiotis Tsinganos ◽  
Bruno Cornelis ◽  
Jan Cornelis ◽  
Bart Jansen ◽  
Athanassios Skodras
Keyword(s):  
Computer Vision ◽  
Gesture Recognition ◽  
Hand Gesture Recognition ◽  
Hand Gesture ◽  
Network Architectures ◽  
Hilbert Curve ◽  
Space Filling ◽  
Space Filling Curve ◽  
Space Filling Curves ◽  
Semg Signals

Over the past few years, Deep learning (DL) has revolutionized the field of data analysis. Not only are the algorithmic paradigms changed, but also the performance in various classification and prediction tasks has been significantly improved with respect to the state-of-the-art, especially in the area of computer vision. The progress made in computer vision has produced a spillover in many other domains, such as biomedical engineering. Some recent works are directed towards surface electromyography (sEMG) based hand gesture recognition, often addressed as an image classification problem and solved using tools such as Convolutional Neural Networks (CNN). This paper extends our previous work on the application of the Hilbert space-filling curve for the generation of image representations from multi-electrode sEMG signals, by investigating how the Hilbert curve compares to the Peano- and Z-order space-filling curves. The proposed space-filling mapping methods are evaluated on a variety of network architectures and in some cases yield a classification improvement of at least 3%, when used to structure the inputs before feeding them into the original network architectures.

scholarly journals Neural Network Analysis of Electroencephalograms Graphical Representation

2020 ◽  
pp. short52-1-short52-9
Author(s):  
Aleksandr Bragin ◽  
Vladimir Spitsyn
Keyword(s):  
Hilbert Space ◽  
Measurement Accuracy ◽  
Graphical Representation ◽  
Space Filling ◽  
Good Tool ◽  
Motor Patterns ◽  
Space Filling Curves ◽  
Markov Transition ◽  
Time Signals ◽  
Electroencephalogram Eeg

The article is devoted to the problem of recognition of motor imagery based on electroencephalogram (EEG) signals, which is associated with many difficulties, such as the physical and mental state of a person, measurement accuracy, etc. Artificial neural networks are a good tool in solving this class of problems. Electroencephalograms are time signals, Gramian Angular Fields (GAF), Markov Transition Field (MTF) and Hilbert space-filling curves transformations are used to represent time series as images. The paper shows the possibility of using GAF, MTF and Hilbert space-filling curves EEG signal transforms for recognizing motor patterns, which is further applicable, for example, in building a brain-computer interface.

scholarly journals Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling Curves

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Ho-Kwok Dai ◽  
Hung-Chi Su
Keyword(s):  
Random Walk ◽  
Dimensional Space ◽  
Hilbert Curve ◽  
Space Filling ◽  
Space Filling Curve ◽  
Space Filling Curves ◽  
Order Curve ◽  
Cluster Distance ◽  
The Mean ◽  
Curve Family

International audience A discrete space-filling curve provides a linear traversal/indexing of a multi-dimensional grid space.This paper presents an application of random walk to the study of inter-clustering of space-filling curves and an analytical study on the inter-clustering performances of 2-dimensional Hilbert and z-order curve families.Two underlying measures are employed: the mean inter-cluster distance over all inter-cluster gaps and the mean total inter-cluster distance over all subgrids.We show how approximating the mean inter-cluster distance statistics of continuous multi-dimensional space-filling curves fits into the formalism of random walk, and derive the exact formulas for the two statistics for both curve families.The excellent agreement in the approximate and true mean inter-cluster distance statistics suggests that the random walk may furnish an effective model to develop approximations to clustering and locality statistics for space-filling curves.Based upon the analytical results, the asymptotic comparisons indicate that z-order curve family performs better than Hilbert curve family with respect to both statistics.

Sign in / Sign up

Export Citation Format

Share Document