TY - JOUR
T1 - N-dimensional hilbert scanning and its application to data compression
AU - Perez, Arnulfo
AU - Kamata, Seiichiro
AU - Kawaguchi, Eiji
N1 - Funding Information:
This work was supported in part by Grant—in—Md for Scientific Research by the Ministry of Education, Science and Culture (Project No. 01633524) and also by the Inamori Foundation, as well as the Japan Society for the Promotion of Science Postdoctoral Fellowship for Foreign Researchers program. Thanks are due to Mrs. Yamashita for her invaluable assistance in the editing of the final version of the paper.
Publisher Copyright:
© 1991 SPIE. All rights reserved.
PY - 1991/6/1
Y1 - 1991/6/1
N2 - Hubert scanning defines a mapping, h :-U, that maps the unit interval onto the n-dimensional unit hypercube continuously. In the discrete case the mapping can be described in terms of Reflected Binary Gray Codes (RBGC). In order to extend the quantized mapping to arbitrary precision it is necessary to define induction rules. Induction rules are defined in terms of a single canonical sequence and a set of rotations. In general, in an n-dimensional hypercube there are n2" possible orientations of a canonical form. Beyond two dimensions, it is possible to have non-trivially different paths between two possible orientations and it is better to define the induction rule in terms of the end points of the RBGC subsequences. Hilbert coding is used for n-dimensional binary data compression. The effectiveness of this method to data compression is confirmed. Experimental evaluation shows Hilbert-Wyle coding to be consistently better than other standard compression methods.
AB - Hubert scanning defines a mapping, h :-U, that maps the unit interval onto the n-dimensional unit hypercube continuously. In the discrete case the mapping can be described in terms of Reflected Binary Gray Codes (RBGC). In order to extend the quantized mapping to arbitrary precision it is necessary to define induction rules. Induction rules are defined in terms of a single canonical sequence and a set of rotations. In general, in an n-dimensional hypercube there are n2" possible orientations of a canonical form. Beyond two dimensions, it is possible to have non-trivially different paths between two possible orientations and it is better to define the induction rule in terms of the end points of the RBGC subsequences. Hilbert coding is used for n-dimensional binary data compression. The effectiveness of this method to data compression is confirmed. Experimental evaluation shows Hilbert-Wyle coding to be consistently better than other standard compression methods.
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U2 - 10.1117/12.45401
DO - 10.1117/12.45401
M3 - Conference article
AN - SCOPUS:0025758008
VL - 1452
SP - 430
EP - 441
JO - Proceedings of SPIE - The International Society for Optical Engineering
JF - Proceedings of SPIE - The International Society for Optical Engineering
SN - 0277-786X
T2 - Image Processing Algorithms and Techniques II 1991
Y2 - 1 February 1991 through 7 February 1991
ER -