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Given a 2-D binary image of size nxn, Euclidean Distance Map (EDM) is a 2-D array of the same size such that each element is storing the Euclidean distance to the nearest black pixel. It is known that a sequential algorithm can compute the EDM in O(n2) and thus this algorithm is optimal. Also, work-time optimal parallel algorithms for shared memory model have been presented. However, these algorithms are too complicated to implement in existing shared memory parallel machines. The main contribution of this paper is to develop a simple parallel algorithm for the EDM and implement it in two parallel platforms: multicore processors and a Graphics Processing Unit (GPU). More specifically, we have implemented our parallel algorithm in a Linux server with four Intel hexad-core processors (Intel Xeon X7460 2.66GHz). We have also implemented it in a modern GPU system, Tesla C1060, respectively. The experimental results have shown that, for an input binary image with size of 10000 × 10000, our implementation in the multi-core system achieves a speedup factor of 18 over the performance of a sequential algorithm using a single processor in the same system. Meanwhile, for the same input binary image, our implementation on the GPU achieves a speedup factor of 5 over the sequential algorithm implementation.