Exact linear time euclidean distance transforms of grid line sampled shapes

Abstract

We propose a method for computing, in linear time, the exact Euclidean distance transform of sets of points s. t. one coordinate of a point can be assigned any real value, whereas other coordinates are restricted to discrete sets of values. The proposed distance transform is applicable to objects represented by grid line sampling, and readily provides sub-pixel precise distance values. The algorithm is easy to implement; we present complete pseudo code. The method is easy to parallelize and extend to higher dimensional data. We present two ways of obtaining approximate grid line sampled representations, and evaluate the proposed EDT on synthetic examples. The method is competitive w. r. t. state-of-the-art methods for sub-pixel precise distance evaluation.