Simple and Fast Parallel Algorithms for the Voronoi Map and the Euclidean Distance Map, with GPU Implementations

2017 ◽  
Author(s):  
Takumi Honda ◽  
Shinnosuke Yamamoto ◽  
Hiroaki Honda ◽  
Koji Nakano ◽  
Yasuaki Ito
Keyword(s):  
Parallel Algorithms ◽  
Euclidean Distance ◽  
Distance Map ◽  
Voronoi Map ◽  
Euclidean Distance Map

Richardson Plots for Fractal Dimension Characterization of Bound Aries of Digitized Grains and Particles

1997 ◽  
Vol 3 (S2) ◽  
pp. 1145-1146 ◽  
Author(s):  
D.S. Bright
Keyword(s):  
Fractal Dimension ◽  
Euclidean Distance ◽  
Additional Measurement ◽  
Step Size ◽  
Distance Map ◽  
Band Area ◽  
Measurement Resolution ◽  
Sem Micrograph ◽  
Euclidean Distance Map

Fractal dimension is useful for characterizing objects with tortuous boundaries, providing an additional measurement to characterize shape beyond the commonly used area, perimeter, caliper diameter and their combinations. The fractal dimension of the boundary describes the increase of the measured value of the perimeter of an object resulting from increasing measurement resolution, i.e., decreasing step size. We desire to characterize and classify shapes such as soot particles, as shown in the TEM micrograph in Fig. 1a, and crystalline grains of metal alloys, as shown in the SEM micrograph of Raney nickel in Fig. 4.This investigation involves evaluation of the Minkowski-sausage or dilation technique (Fig. 1) using the histogram of the Euclidean distance map of the perimeter of the object. The distance map gives bands of various widths that follow the perimeter - greater widths lose detail. Perimeter length is sausage (band) area divided by sausage width, w.

scholarly journals Identification of protein pockets and cavities by Euclidean Distance Transform

2018 ◽  
Author(s):  
Sebastian Daberdaku
Keyword(s):  
Ligand Binding ◽  
Active Sites ◽  
Euclidean Distance ◽  
Protein Structures ◽  
Ligand Docking ◽  
Distance Transform ◽  
Structure Based Drug Design ◽  
Distance Map ◽  
Euclidean Distance Transform ◽  
Protein Pockets

Protein pockets and cavities usually coincide with the active sites of biological processes, and their identification is significant since it constitutes an important step for structure-based drug design and protein-ligand docking applications. This paper presents a novel purely geometric algorithm for the detection of ligand binding protein pockets and cavities based on the Euclidean Distance Transform (EDT). The EDT can be used to compute the Solvent-Excluded surface for any given probe sphere radius value at high resolutions and in a timely manner. The algorithm is adaptive to the specific candidate ligand: it computes two voxelised protein surfaces using two different probe sphere radii depending on the shape of the candidate ligand. The pocket regions consist of the voxels located between the two surfaces, which exhibit a certain minimum depth value from the outer surface. The distance map values computed by the EDT algorithm during the second surface computation can be used to elegantly determine the depth of each candidate pocket and to rank them accordingly. Cavities on the other hand, are identified by scanning the inside of the protein for voids. The algorithm determines and outputs the best k candidate pockets and cavities, i.e. the ones that are more likely to bind to the given ligand. The method was applied to a representative set of protein-ligand complexes and their corresponding unbound protein structures to evaluate its ligand binding site prediction capabilities, and was shown to outperform most of the previously developed purely geometric pocket and cavity search methods.

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