Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Discrete distance operator on rectangular grids
Pattern Recognition Letters
On digital distance transforms in three dimensions
Computer Vision and Image Understanding
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
Computing 3D Medial Axis for Chamfer Distances
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Weighted Distance Transforms in Rectangular Grids
ICIAP '01 Proceedings of the 11th International Conference on Image Analysis and Processing
Weighted distance transforms for volume images digitized in elongated voxel grids
Pattern Recognition Letters - Special issue: Discrete geometry for computer imagery (DGCI'2002)
Surface area estimation of digitized 3D objects using weighted local configurations
Image and Vision Computing
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
Distance transforms on anisotropic surfaces for surface roughness measurement
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Supercover model and digital straight line recognition on irregular isothetic grids
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
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In this paper we investigate weighted distance transforms in 3D images using elongated voxel grids. We use a local neighbourhood of size 3 脳 3 脳 3 and assume a voxel grid with equal resolution along two axes and lower along the third. The weights (local distances) in the local neighbourhood are optimized by minimizing the maximum error over linear trajectories, which is a completely digital approach. General solutions are presented, as well as numerical solutions for the cases when the voxels are 1.5 and 2.58 times longer in one direction. Integer solutions for both real and integer scale factors are presented. As an application example, the medial axis of an object is computed in an image with elongated voxels and compared to the medial axis computed on the same image interpolated to equal resolution along all axes.