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Optical Engineering

Study of compression efficiency for three-dimensional discrete curves
Author(s): Hermilo Sanchez-Cruz; Ernesto Bribiesca
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Paper Abstract

A study of compression efficiency of 3-D chain codes to represent discrete curves is described. The 3-D Freeman chain code and the five orthogonal change chain directions (5OT) chain code are compared. The 3-D Freeman chain code consists of 26 directions, in 3-D Euclidean space, with no invariance under rotation. The 5OT chain elements represent the orthogonal direction changes of the contiguous straight-line segments of the discrete curve. This chain code only considers relative direction changes, which allows us to have a curve descriptor invariant under rotation, and mirroring curves may be obtained with ease. In the 2-D domain, Freeman chain codes are widely used to represent contour curves. Until now, the authors have had no information of implementing Freeman chain codes to compress 3-D curves. Our contribution is how to implement the Freeeman chain code in 3-D and how to compare it with the recently proposed 5OT code. Finally, to probe our results, we apply the proposed method to three different cases: arbitrary curves, cube-filling Hilbert curves, and lattice knots.

Paper Details

Date Published: 1 July 2008
PDF: 9 pages
Opt. Eng. 47(7) 077206 doi: 10.1117/1.2957963
Published in: Optical Engineering Volume 47, Issue 7
Show Author Affiliations
Hermilo Sanchez-Cruz, Univ. Autonoma de Aguascalientes (Mexico)
Ernesto Bribiesca, Univ. Nacional Autónoma de México (Mexico)

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