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Proceedings Paper

Low-discrepancy sampling of parametric surface using adaptive space-filling curves (SFC)
Author(s): Charles Hsu; Harold Szu
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Paper Abstract

Space-Filling Curves (SFCs) are encountered in different fields of engineering and computer science, especially where it is important to linearize multidimensional data for effective and robust interpretation of the information. Examples of multidimensional data are matrices, images, tables, computational grids, and Electroencephalography (EEG) sensor data resulting from the discretization of partial differential equations (PDEs). Data operations like matrix multiplications, load/store operations and updating and partitioning of data sets can be simplified when we choose an efficient way of going through the data. In many applications SFCs present just this optimal manner of mapping multidimensional data onto a one dimensional sequence. In this report, we begin with an example of a space-filling curve and demonstrate how it can be used to find the most similarity using Fast Fourier transform (FFT) through a set of points. Next we give a general introduction to space-filling curves and discuss properties of them. Finally, we consider a discrete version of space-filling curves and present experimental results on discrete space-filling curves optimized for special tasks.

Paper Details

Date Published: 24 June 2014
PDF: 8 pages
Proc. SPIE 9118, Independent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering XII, 91180P (24 June 2014); doi: 10.1117/12.2053306
Show Author Affiliations
Charles Hsu, Trident Systems Inc. (United States)
Harold Szu, The Catholic Univ. of America (United States)


Published in SPIE Proceedings Vol. 9118:
Independent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering XII
Harold H. Szu; Liyi Dai, Editor(s)

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