An efficient algorithm for complete Euclidean distance transform on mesh-connected SIMD

• Published in: Parallel computing Vol. 21; no. 5; pp. 841 - 852
• Main Authors: Chen, Ling, Chuang, Henry Y.H.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-05-1995; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Artificial intelligence; Complexity analysis; Computer science; control theory; systems; Euclidean distance transform; Exact sciences and technology; Image analysis; Mesh-connected SIMD computer; Pattern recognition. Digital image processing. Computational geometry; Theoretical computing; Image analysis; Complexity analysis; Mesh-connected SIMD computer; Euclidean distance transform; Computer vision; Parallel algorithm; Euclidean geometry; Array processor; Program transformation; SIMD computer; Algorithm; Computational complexity; Implementation; Sequential; Analysis; Time complexity
• ISSN: 0167-8191; 1872-7336
• DOI: 10.1016/0167-8191(94)00103-H

The Euclidean distance transform (EDT) converts a binary image into one where each pixel has a value equal to its Euclidean distance to the nearest foreground pixel. It has important uses in image analysis, computer vision, and robotics where high speed computation is essential. In this paper, a sequential algorithm which does not require global operations is first presented. We then apply a sequence of algorithm transformations to convert it into a parallel algorithm for mesh-connected SIMD computers. For an
n ×
n image on an equal-sized processor array, the time complexity is
O(
n). An algorithm for computing large EDT problems on smaller processor arrays is also given. For an
n ×
n image on a
g ×
g processor array, the time complexity is
O((
n
2
g
)
log(
n
g
))
.