Distances defined by neighborhood sequences
Pattern Recognition
Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Local distances for distance transformations in two and three 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)
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Digital distance transforms are useful tools for many image analysis tasks. In the 2D case, the maximum difference from Euclidean distance is considerably smaller when using a 5 × 5 neighbourhood compared to using a 3 × 3 neighbourhood. In the 3D case, weighted distance transforms for neighbourhoods larger than 3 × 3 × 3 has almost not been considered so far. We present optimal local distances for an extended neighbourhood in 3D, where we use the three weights in the 3 × 3 × 3 neighbourhood together with the (2, 1, 1) weight from the 5 × 5 × 5 neighbourhood. A good integer approximation is shown to be 〈3,4,5,7〉.