DELAUNAY REFINEMENT ALGORITHMS FOR ESTIMATING LOCAL FEATURE SIZE IN 2D AND 3D

2011 ◽  
Vol 21 (05) ◽  
pp. 507-543
Author(s):  
ALEXANDER RAND ◽  
NOEL WALKINGTON
Keyword(s):  
Delaunay Triangulation ◽  
Mesh Generation ◽  
Piecewise Linear ◽  
Local Information ◽  
Local Feature ◽  
Delaunay Refinement ◽  
Linear Complex ◽  
Feature Size ◽  
2D And 3D ◽  
Local Feature Size

We present Delaunay refinement algorithms for estimating local feature size on the input vertices of a 2D piecewise linear complex and on the input vertices and segments of a 3D piecewise linear complex. These algorithms are designed to eliminate the need for a local feature size oracle during quality mesh generation of domains containing acute input angles. In keeping with Ruppert's algorithm, encroachment in these algorithms can be determined through only local information in the current Delaunay triangulation. The algorithms are practical to implement and several examples are given.

scholarly journals Adaptive Metrics for Adaptive Samples

Algorithms ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 200
Author(s):  
Nicholas J. Cavanna ◽  
Donald R. Sheehy
Keyword(s):  
Euclidean Space ◽  
Surface Reconstruction ◽  
Critical Points ◽  
Adaptive Sampling ◽  
Local Feature ◽  
Distance Functions ◽  
Feature Size ◽  
Homology Inference ◽  
Definition Of ◽  
Local Feature Size

We generalize the local-feature size definition of adaptive sampling used in surface reconstruction to relate it to an alternative metric on Euclidean space. In the new metric, adaptive samples become uniform samples, making it simpler both to give adaptive sampling versions of homological inference results and to prove topological guarantees using the critical points theory of distance functions. This ultimately leads to an algorithm for homology inference from samples whose spacing depends on their distance to a discrete representation of the complement space.

A POINT-PLACEMENT STRATEGY FOR CONFORMING DELAUNAY TETRAHEDRALIZATION

2001 ◽  
Vol 11 (06) ◽  
pp. 669-682 ◽  
Author(s):  
MICHAEL MURPHY ◽  
DAVID M. MOUNT ◽  
CARL W. GABLE
Keyword(s):  
Delaunay Triangulation ◽  
Line Graph ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Linear Complex ◽  
Straight Line ◽  
Delaunay Tetrahedralization ◽  
Planar Straight Line Graph ◽  
Set Of Points ◽  
Point Placement

A strategy is presented to find a set of points that yields a Conforming Delaunay tetrahedralization of a three-dimensional Piecewise-Linear complex (PLC). This algorithm is novel because it imposes no angle restrictions on the input PLC. In the process, an algorithm is described that computes a planar conforming Delaunay triangulation of a Planar Straight-Line Graph (PSLG) such that each triangle has a bounded circumradius, which may be of independent interest.

Triangulations and meshes in computational geometry

Acta Numerica ◽  
2000 ◽  
Vol 9 ◽  
pp. 133-213 ◽  
Author(s):  
Herbert Edelsbrunner
Keyword(s):  
Twentieth Century ◽  
Computational Geometry ◽  
Delaunay Triangulation ◽  
Mesh Generation ◽  
Three Dimensional ◽  
Central Theme ◽  
Physical Processes ◽  
Finite Point ◽  
Major Application ◽  
Point Set

The Delaunay triangulation of a finite point set is a central theme in computational geometry. It finds its major application in the generation of meshes used in the simulation of physical processes. This paper connects the predominantly combinatorial work in classical computational geometry with the numerical interest in mesh generation. It focuses on the two- and three-dimensional case and covers results obtained during the twentieth century.

scholarly journals Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

2014 ◽  
Vol 36 (3) ◽  
pp. A930-A954 ◽  
Author(s):  
Zhonggui Chen ◽  
Wenping Wang ◽  
Bruno Lévy ◽  
Ligang Liu ◽  
Feng Sun
Keyword(s):  
Delaunay Triangulation ◽  
Mesh Generation ◽  
Graded Mesh

scholarly journals Local information pattern descriptor for corneal diseases diagnosis

2021 ◽  
Vol 11 (6) ◽  
pp. 4972
Author(s):  
Samer Kais Jameel ◽  
Sezgin Aydin ◽  
Nebras H. Ghaeb
Keyword(s):  
Feature Vector ◽  
Outer Part ◽  
Local Binary Patterns ◽  
Local Information ◽  
Machine Learning Algorithms ◽  
Local Feature ◽  
Human Vision ◽  
Human Cornea ◽  
Image Center ◽  
Information Pattern

<span lang="EN-US">Light penetrates the human eye through the cornea, which is the outer part of the eye, and then the cornea directs it to the pupil to determine the amount of light that reaches the lens of the eye. Accordingly, the human cornea must not be exposed to any damage or disease that may lead to human vision disturbances. Such damages can be revealed by topographic images used by ophthalmologists. Consequently, an important priority is the early and accurate diagnosis of diseases that may affect corneal integrity through the use of machine learning algorithms, particularly, use of local feature extractions for the image. Accordingly, we suggest a new algorithm called local information pattern (LIP) descriptor to overcome the lack of local binary patterns that loss of information from the image and solve the problem of image rotation. The LIP based on utilizing the sub-image center intensity for estimating neighbors' weights that can use to calculate what so-called contrast based centre (CBC). On the other hand, calculating local pattern (LP) for each block image, to distinguish between two sub-images having the same CBC. LP is the sum of transitions of neighbors' weights, from sub-image center value to one and vice versa. Finally, creating histograms for both CBC and LP, then blending them to represent a robust local feature vector. Which can use for diagnosing, detecting.</span>

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