Anti-aliased Euclidean distance transform

We present a modified distance measure for use with distance transforms of anti-aliased, area sampled grayscale images of arbitrary binary contours. The modified measure can be used in any vector-propagation Euclidean distance transform. Our test implementation in the traditional SSED8 algorithm shows a considerable improvement in accuracy and homogeneity of the distance field compared to a traditional binary image transform. At the expense of a 10× slowdown for a particular image resolution, we achieve an accuracy comparable to a binary transform on a supersampled image with 16 × 16 higher resolution, which would require 256 times more computations and memory.

Research highlights
► The Euclidean distance transform is extended to anti-aliased contours.
► Accuracy of the distance field is significantly improved.
► Accuracy is greatly improved near edges.
► Extra memory requirements and added complexity are reasonable.