Abstract: In this paper we investigate weighted distance transforms in 2D images in rectangular grids. We use a local neighbor-hood of size 3 x 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.