Parallel Three-Dimensional Distance Transform for Railway Alignment Optimization Using OpenMP

2020 ◽  
Vol 146 (5) ◽  
pp. 04020029 ◽  
Author(s):  
Taoran Song ◽  
Hao Pu ◽  
Paul Schonfeld ◽  
Wei Li ◽  
Hong Zhang ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Distance Transform

A three‐dimensional distance transform for optimizing constrained mountain railway alignments

2019 ◽  
Vol 34 (11) ◽  
pp. 972-990 ◽  
Author(s):  
Hao Pu ◽  
Taoran Song ◽  
Paul Schonfeld ◽  
Wei Li ◽  
Hong Zhang ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Distance Transform

Three-dimensional skeletonization using distance transform

1998 ◽  
Author(s):  
Kai Qian ◽  
Siqi Cao ◽  
Prabir Bhattacharya
Keyword(s):  
Three Dimensional ◽  
Distance Transform

scholarly journals Parallel N-Dimensional Exact Signed Euclidean Distance Transform

2006 ◽  
Author(s):  
Robert Staubs ◽  
Andriy Fedorov ◽  
Leonidas Linardakis ◽  
Benjamin Dunton ◽  
Nikos Chrisochoides
Keyword(s):  
Data Structures ◽  
Euclidean Distance ◽  
Parallel Implementation ◽  
Three Dimensional ◽  
Distance Transform ◽  
Distance Transforms ◽  
Euclidean Distance Transform ◽  
Use Of Data ◽  
Computation Speed ◽  
Standard Tests

The computation speed for distance transforms becomes important in a wide variety of image processing applications. Current ITK library filters do not see any benefit from a multithreading environment. We introduce a three-dimensional signed parallel implementation of the exact Euclidean distance transform algorithm developed by Maurer et al. with a theoretical complexity of O(n/p) for n voxels and p threads. Through this parallelization and efficient use of data structures we obtain approximately 3 times mean speedup on standard tests on a 4-processor machine compared with the current ITK exact Euclidean distance transform filter.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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