Distances defined by neighborhood sequences
Pattern Recognition
Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
A note on “distance transformations in digital images"
Computer Vision, Graphics, and Image Processing
A comment on “a note on `distance transformations in digital images”'
Computer Vision, Graphics, and Image Processing
Another comment on “a note on distance transformation in digital images”
CVGIP: Image Understanding
The Euclidean distance transform in arbitrary dimensions
Pattern Recognition Letters
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
Medial axis lookup table and test neighborhood computation for 3D chamfer norms
Pattern Recognition
Discrete topology on N-dimensional square tessellated grids
Image and Vision Computing
Medial axis LUT computation for chamfer norms using H-polytopes
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Integer approximation of 3D chamfer mask coefficients using a scaling factor in anisotropic grids
Pattern Recognition Letters
Surface volume estimation of digitized hyperplanes using weighted local configurations
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Hyperspheres of weighted distances in arbitrary dimension
Pattern Recognition Letters
Linear combination of norms in improving approximation of Euclidean norm
Pattern Recognition Letters
Linear combination of weighted t-cost and chamfering weighted distances
Pattern Recognition Letters
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A digital distance transformation converts a binary image in Zn to a distance transform, where each picture element in the foreground (background) has a value measuring the closest distance to the background (foreground). In a weighted distance transform, the distance between two points is defined by a minimal 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 transforms are illustrated by their associated balls.