Some Weighted Distance Transforms in Four Dimensions
In a digital distance transform,each picture element in the shape (background)has a va ue measuring the distance to the background (shape).In a weighted distance transform,the distance between two points is de .ned by path consisting of a number of steps between neighbouring picture e ements,where each type of possible step is given a ength-va ue,or a weight.In 4D,using 3 ×3 ×3 ×3 neighbourhoods,there are four di .erent weights.In this paper,optimal real and integer weights are computed for one type of 4D weighted distance transforms.The most useful integer transform is probably (3 , 4 , 5 , 6) , but there are a number of other ones listed.Two integer distance transform are illustrated by their associated balls.
- 4.H. S. M. Coxeter, Regular polytopes, Dover Publications, Inc., New York, 1973. 332Google Scholar
- 5.G. Borgefors, H. Guo, Weighted distance transform hyperspheres in four dimensions, Proc. SSAB Symposium on Image Analysis 1997, Stockholm, Sweden, March 1997, pp.71–76. 332Google Scholar
- 6.M. Fidrich: Iso-surface extraction in 4D with applications related to scale space, In Miguet, Montanvert, Ubéda, Eds., Discrete Geometry for Computer Imagery, Springer 1996 (LNCS 1176), pp.257–268. 325Google Scholar
- 7.P. P. Jonker and O. Vermeij, On skeletonization in 4D images,In Perner, Wang, Rosenfeld, Eds., Advances in Structura and Syntactica Pattern Recognition, Springer 1996 (LNCS 1121), pp.79–89. 325Google Scholar
- 9.T.Y. Kong, Topology-preserving deletion of 1’ s from 2-, 3-, and 4-dimensional binary images,In Ahronovitz and Fiorio, Eds., Discrete Geometry for Computer Imagery,Springer 1997 (LNCS 1347), pp. 3–18. 325Google Scholar