Computational geometry: an introduction
Computational geometry: an introduction
Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Finding local maxima in a pseudo-Euclidean distance transform
Computer Vision, Graphics, and Image Processing
A bridging model for parallel computation
Communications of the ACM
Simulating the Grassfire Transform Using an Active Contour Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
An introduction to parallel algorithms
An introduction to parallel algorithms
Thinning Methodologies-A Comprehensive Survey
IEEE Transactions on Pattern Analysis and Machine Intelligence
Serial and Parallel Algorithms for the Medial Axis Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
A fast algorithm for Euclidean distance maps of a 2-D binary image
Information Processing Letters
ACM Computing Surveys (CSUR)
International Journal of Computer Vision
Computation of the Medial Axis Transform of 3-D polyhedra
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
A fully parallel 3D thinning algorithm and its applications
Computer Vision and Image Understanding
Computing the Medial Axis Transform in Parallel With Eight Scan Operations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Accurate computation of the medial axis of a polyhedron
Proceedings of the fifth ACM symposium on Solid modeling and applications
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)
Computer representation of planar regions by their skeletons
Communications of the ACM
Medial axis for chamfer distances: computing look-up tables and neighbuorhoods in 2D or 3D
Pattern Recognition Letters
A 3-subiteration 3D thinning algorithm for extracting medial surfaces
Pattern Recognition Letters
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
The Chessboard Distance Transform and the Medial Axis Transform are Interchangeable
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
Constant-Time Algorithm for Medial Axis Transform on the Reconfigurable Mesh
IPPS '99/SPDP '99 Proceedings of the 13th International Symposium on Parallel Processing and the 10th Symposium on Parallel and Distributed Processing
The Shock Scaffold for Representing 3D Shape
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
Parallel Computation on Interval Graphs Using PC CLusters: Algorithms and Experiments
Euro-Par '98 Proceedings of the 4th International Euro-Par Conference on Parallel Processing
On the Local Form and Transitions of Symmetry Sets, Medial Axes, and Shocks
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
ICPADS '02 Proceedings of the 9th International Conference on Parallel and Distributed Systems
A Formal Classification of 3D Medial Axis Points and Their Local Geometry
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Effective Skeletonization Method Based on Adaptive Selection of Contour Points
ICITA '05 Proceedings of the Third International Conference on Information Technology and Applications (ICITA'05) Volume 2 - Volume 02
PDCAT '05 Proceedings of the Sixth International Conference on Parallel and Distributed Computing Applications and Technologies
The Medial Scaffold of 3D Unorganized Point Clouds
IEEE Transactions on Pattern Analysis and Machine Intelligence
A 3D fully parallel surface-thinning algorithm
Theoretical Computer Science
3D Block-Based Medial Axis Transform and Chessboard Distance Transform on the CREW PRAM
ICA3PP '08 Proceedings of the 8th international conference on Algorithms and Architectures for Parallel Processing
Discrete 2D and 3D euclidean medial axis in higher resolution
Image and Vision Computing
Transitions of the 3D Medial Axis under a One-Parameter Family of Deformations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Medial Axis Transformation of a Planar Shape
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
An O(1) time algorithm for the 3D Euclidean distance transform on the CRCW PRAM model
IEEE Transactions on Parallel and Distributed Systems
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Traditionally, the block-based medial axis transform (BB-MAT) and the chessboard distance transform (CDT) were usually viewed as two completely different image computation problems, especially for three dimensional (3D) space. In fact, there exist some equivalent properties between them. The relationship between both of them is first derived and proved in this paper. One of the significant properties is that CDT for 3D binary image V is equal to BB-MAT for image V' where it denotes the inverse image of V. In a parallel algorithm, a cost is defined as the product of the time complexity and the number of processors used. The main contribution of this work is to reduce the costs of 3D BB-MAT and 3D CDT problems proposed by Wang [65]. Based on the reverse-dominance technique which is redefined from dominance concept, we achieve the computation of the 3D CDT problem by implementing the 3D BB-MAT algorithm first. For a 3D binary image of size N^3, our parallel algorithm can be run in O(logN) time using N^3 processors on the concurrent read exclusive write (CREW) parallel random access machine (PRAM) model to solve both 3D BB-MAT and 3D CDT problems, respectively. The presented results for the cost are reduced in comparison with those of Wang's. To the best of our knowledge, this work is the lowest costs for the 3D BB-MAT and 3D CDT algorithms known. In parallel algorithms, the running time can be divided into computation time and communication time. The experimental results of the running, communication and computation times for the different problem sizes are implemented in an HP Superdome with SMP/CC-NUMA (symmetric multiprocessor/cache coherent non-uniform memory access) architecture. We conclude that the parallel computer (i.e., SMP/CC-NUMA architecture or cluster system) is more suitable for solving problems with a large amount of input size.