Title :
Tensor product formulation for Hilbert space-filling curves
Author :
Lin, Shen-Yi ; Chen, Chih-Shen ; Liu, Li ; Huang, Chua-Huang
Author_Institution :
Dept. of Inf. Eng. & Comput. Sci., Feng Chia Univ., Taichung
Abstract :
We present a tensor product formulation for Hilbert space-filling curves. Both recursive and iterative formulas are expressed. We view a Hilbert space-filling curve as a permutation which maps two-dimensional 2ntimes2n data elements stored in the row major or column major order to the order of traversing a Hilbert space-filling curve. The tensor product formula of Hilbert space-filling curves uses several permutation operations: stride permutation, radix-2 gray permutation, transposition, and antidiagonal transposition. The iterative tensor product formula can be manipulated to obtain the inverse Hilbert permutation. Also, the formulas are directly translated into computer programs which can be used in various applications including R-tree indexing, image processing, and process allocation, etc
Keywords :
Hilbert spaces; matrix algebra; tensors; Hilbert space-filling curves; R-tree indexing; antidiagonal transposition; image processing; inverse Hilbert permutation; iterative formulas; process allocation; radix-2 gray permutation; recursive approach; stride permutation; tensor product formulation; transposition; Application software; Biomedical engineering; Biomedical imaging; Biomedical informatics; Computer science; Grid computing; Hilbert space; Image processing; Indexing; Tensile stress;
Conference_Titel :
Parallel Processing, 2003. Proceedings. 2003 International Conference on
Conference_Location :
Kaohsiung
Print_ISBN :
0-7695-2017-0
DOI :
10.1109/ICPP.2003.1240570