Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Computing Voronoi diagrams in digital pictures
Pattern Recognition Letters
The design and analysis of parallel algorithms
The design and analysis of parallel algorithms
An introduction to parallel algorithms
An introduction to parallel algorithms
Distance transforms: properties and machine vision applications
CVGIP: Graphical Models and Image Processing
Serial and Parallel Algorithms for the Medial Axis Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parallel computational geometry
Parallel computational geometry
A unified distance transform algorithm and architecture
Machine Vision and Applications
A fast algorithm for Euclidean distance maps of a 2-D binary image
Information Processing Letters
An optimal parallel algorithm for the Euclidean distance maps of 2-D binary images
Information Processing Letters
Parallel computation of exact Euclidean distance transform
Parallel Computing
A unified linear-time algorithm for computing distance maps
Information Processing Letters
On digital distance transforms in three dimensions
Computer Vision and Image Understanding
Collision detection for volumetric objects
VIS '97 Proceedings of the 8th conference on Visualization '97
Computer Vision and Image Understanding
Optimal computing the chessboard distance transform on parallel processing systems
Computer Vision and Image Understanding
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
Digital Picture Processing
Fast Computation of the 3-D Euclidean Distance Transform on the EREW PRAM Model
ICPP '02 Proceedings of the 2001 International Conference on Parallel Processing
The Chessboard Distance Transform and the Medial Axis Transform are Interchangeable
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
A Parallel Algorithm for Weighted Distance Transforms
IPPS '97 Proceedings of the 11th International Symposium on Parallel Processing
Fast parallel chessboard distance transform algorithms
ICPADS '96 Proceedings of the 1996 International Conference on Parallel and Distributed Systems
DCC '98 Proceedings of the Conference on Data Compression
Euclidean distance transform for binary images on reconfigurablemesh-connected computers
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IEEE Transactions on Parallel and Distributed Systems
Parallel Banding Algorithm to compute exact distance transform with the GPU
Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games
Parallel re-initialization of level set functions on distributed unstructured tetrahedral grids
Journal of Computational Physics
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In a two- or three-dimensional image array, the computation of Euclidean distance transform (EDT) is an important task. With the increasing application of 3D voxel images, it is useful to consider the distance transform of a 3D digital image array. Because the EDT computation is a global operation, it is prohibitively time consuming when performing the EDT for image processing. In order to provide the efficient transform computations, parallelism is employed. In this paper, we first derive several important geometry relations and properties among parallel planes. We then, develop a parallel algorithm for the three-dimensional Euclidean distance transform (3D_EDT) on the EREW PRAM computation model. The time complexity of our parallel algorithm isO(\log^2 N)for anN \times N \times Nimage array and this is currently the best known result. A generalized parallel algorithm for the 3D-EDT is also proposed. We implement the proposed algorithms sequentially, the performance of which exceeds the existing algorithms (proposed by Yamada, Toriwaki). Finally, we develop the corresponding parallel programs on both the emulated EREW PRAM model computer and the IBM SP2 to verify the speed-up properties of the proposed algorithms.