Weighted Distance Transforms for Images Using Elongated Voxel Grids

Abstract

In this paper we investigate weighted distance transforms in 3D images using elongated voxel grids. We use a local neighbourhood of size 3 × 3 × 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.

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