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# N-D Linear Time Exact Signed Euclidean Distance Transform

Tustison, Nicholas J., Siqueira, Marcelo, Gee, James C.

Fast computation of distance transforms find direct application in various computer vision problems. Currently there exists two image filters in the ITK library which can be used to generate distance maps. Unfortunately, these filters produce only approximations to the Euclidean Distance Transform (EDT). We introduce into the ITK library a third EDT filter which was developed by Maurer {\em et al.} \cite{Maurer2003}. In contrast to other algorithms, this algorithm produces the exact signed squared EDT using integer arithmetic. The complexity, which is formally verified, is $O(n)$ with a small time constant where $n$ is the number of image pixels.