Weighted distance transforms in rectangular grids

We investigate weighted distance transforms in 2D images in rectangular grids. We use a local neighborhood of size 3×3 and assume a rectangular grid with arbitrary ratio between the sides. The weights (local distances) are optimized by minimizing the maximum error over linear trajectories, which is an all-digital approach. General solutions for all ratios are presented. We also present numeric results for the cases when the ratio between the sides equals 1 (comparable with studies of weighted distance transforms in the square grid), 4/3 and 3. Integer solutions for both real and integer scale factors are presented