Study of compression efficiency for three-dimensional discrete curves

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.