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
Finding local maxima in a pseudo-Euclidean distance transform
Computer Vision, Graphics, and Image Processing
Local distances for distance transformations in two and three dimensions
Pattern Recognition Letters
The Euclidean distance transform in arbitrary dimensions
Pattern Recognition Letters
On digital distance transforms in three dimensions
Computer Vision and Image Understanding
Geometry of Digital Spaces
Digital distance transforms in 3D images using information from neighbourhoods up to 5 × 5 × 5
Computer Vision and Image Understanding
Weighted distance transforms for volume images digitized in elongated voxel grids
Pattern Recognition Letters - Special issue: Discrete geometry for computer imagery (DGCI'2002)
Distances based on neighbourhood sequences in non-standard three-dimensional grids
Discrete Applied Mathematics
Discrete Applied Mathematics
On approximating Euclidean metrics by weighted t-cost distances in arbitrary dimension
Pattern Recognition Letters
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Distance transforms on the face-centered cubic (fcc) grid and the body-centered cubic (bcc) grid are examined. Since the voxels on the fcc and bcc grids are better approximations of a Euclidean ball than the cube, the distance transforms (DTs) on these grids can be less rotation dependent than those in Z3, which is a desirable feature. Optimal (according to the error function) weights are calculated and integer approximations of these weights are found. Also, the two-dimensional city block distance is generalized to the fcc and bcc grids by considering a unit distance between gridpoints whose corresponding voxels share a face. A method to compute the DTs is presented. The results are evaluated both theoretically and by actually computing some DTs.