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 SI...

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Bibliographic Details
Published in:IEEE transactions on image processing Vol. 28; no. 11; pp. 5322 - 5335
Main Authors: Manduhu, Manduhu, Jones, Mark W.
Format: Journal Article
Language:English
Published: United States IEEE 01.11.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
1D EDT
2D EDT
Algorithms
Approximation algorithms
binary operations on GPU
Computer architecture
Euclidean geometry
Graphics processing units
Parallel algorithms
Parallel processing
Phase change random access memory
Random access
SIMD architecture
Time complexity
Transforms
Work-time optimal parallel algorithm
ISSN:1057-7149, 1941-0042, 1941-0042
Online Access:Get full text
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Summary: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.
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ISSN:1057-7149
1941-0042
1941-0042
DOI:10.1109/TIP.2019.2916741