Distances defined by neighborhood sequences
Pattern Recognition
Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
On digital distance transforms in three dimensions
Computer Vision and Image Understanding
Regularity properties of distance transformations in image analysis
Computer Vision and Image Understanding
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
On Skeletonization in 4D Images
SSPR '96 Proceedings of the 6th International Workshop on Advances in Structural and Syntactical Pattern Recognition
Topology-Preserving Deletion of 1's from 2-, 3- and 4-Dimensional Binary Images
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Iso-surface extraction in 4D with applications related to scale space
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
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In a digital distance transform, each picture element in the shape (background) has a value measuring the distance to the background (shape). In a weighted distance transform, the distance between two points is defined by path consisting of a number of steps between neighbouring picture elements, where each type of possible step is given a length-value, or a weight. In 4D, using 3×3×3×3 neighbourhoods, there are four different 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.