Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Local distances for distance transformations in two and three dimensions
Pattern Recognition Letters
Discrete distance operator on rectangular grids
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
Fast Euclidean distance transformation by propagation using multiple neighborhoods
Computer Vision and Image Understanding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital distance transforms in 3D images using information from neighbourhoods up to 5 × 5 × 5
Computer Vision and Image Understanding
Weighted Distance Transforms for Images Using Elongated Voxel Grids
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Weighted digital distance transforms in four dimensions
Discrete Applied Mathematics
Weighted Distance Transforms in Rectangular Grids
ICIAP '01 Proceedings of the 11th International Conference on Image Analysis and Processing
Weighted distances based on neighbourhood sequences
Pattern Recognition Letters
3-D chamfer distances and norms in anisotropic grids
Image and Vision Computing
Chordal axis on weighted distance transforms
DGCI'06 Proceedings of the 13th 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
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For 3D images composed of successive scanner slices (e.g. medical imaging, confocal microscopy or computed tomography), the sampling step may vary according to the axes, and specially according to the depth which can take values lower or higher than 1. Hence, the sampling grid turns out to be parallelepipedic. In this paper, 3D anisotropic local distance operators are introduced. The problem of coefficient optimization is addressed for arbitrary mask size. Lower and upper bounds of scaling factors used for integer approximation are given. This allows, first, to derive analytically the maximal normalized error with respect to Euclidean distance, in any 3D anisotropic lattice, and second, to compute optimal chamfer coefficients. As far as large images or volumes are concerned, 3D anisotropic operators are adapted to the measurement of distances between objects sampled on non-cubic grids as well as for quantitative comparison between grey level images.