A Work Efficient Parallel Algorithm for Exact Euclidean Distance Transform

A fully-parallelized work-time optimal algorithm is presented for computing the exact Euclidean Distance Transform (EDT) of a 2D binary image with the size of n × n. Unlike existing PRAM (Parallel Random Access Machine) and other algorithms, this algorithm is suitable for implementation on modern SIMD (Single Instruction Multiple Data) architectures such as GPUs. As a fundamental operation of 2D EDT, 1D EDT is efficiently parallelized first. Specifically, the GPU algorithm for the 1D EDT, which uses CUDA (Compute Unified Device Architecture) binary functions, such as ballotO, ffs(), clzO, and shflO, runs in O(log
₃₂
n) time and performs O(n) work. Using the 1D EDT as a fundamental operation, the fully-parallelized work-time optimal 2D EDT algorithm is designed. This algorithm consists of three steps. Step 1 of the algorithm runs in O(log
₃₂
n) time and performs O(N) (N=
ⁿ²
) of total work on GPU. Step 2 performs O(N) of total work and has an expected time complexity of O(logn) on GPU. Step 3 runs in O(log
₃₂
n) time and performs O(N) of total work on GPU. As far as we know, this algorithm is the first fully-parallelized and realized work-time optimal algorithm for GPUs. The experimental results show that this algorithm outperforms the prior state-of-the-art GPU algorithms.