Medial Axis for Euclidean Distance in nD

by Eric Remy and Edouard Thiel

This page is an appendix to our paper:

Image and Vision Computing

Here you can download the program sources (in C langage) to compute the Look-Up Tables and the Neighbourhoods in several dimensions: LutEucli2D.c , LutEucli3D.c ; for larger dimensions, see npic-mlut.c.

To compile, type cc LutEucli2D.c -O2 -o LutEucli2D and to run, type ./LutEucli2D (the same for 3D). The program will print its usage with command line arguments.

The beginning of the Lut masks are presented in the paper in 2D and 3D, Figures 10 and 13. Here are wider Lut masks saved in text files (first column the appearance rank i, next columns the coordinates x,y or x,y,z or ... or x,y,z,t,s,r, last column the appearance radius R) ; same datas are also given in Npic .nmask format :

Dimension	Vector number	Rverified	radius in pixels	Text format "i x y z R"	Npic format "z y x R"	OEIS reference
2	350	23500000	4847	txt	nmask	A171988
3	10000	126929	356	txt	nmask
4	144979	30000	173	txt.gz	nmask.gz
5	491945	10000	100	txt.gz	nmask.gz
6	158129	2500	50	txt.gz	nmask.gz

Erratum:

Page 168, section 2.3, 1^st paragraph, 2^nd line: replace v^g = G(v) with v^g = G( sigma(v) : sigma in S_G(n) ) .
Page 172, 1^st paragraph, 2^nd line: replace 4^a(8^b+7) with 4^a(8b+7) .

Last update 25 may 2009