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.

scholarly journals Distance functions and umbilic submanifolds of hyperbolic space

1979 ◽  
Vol 74 ◽  
pp. 67-75 ◽  
Author(s):  
Thomas E. Cecil ◽  
Patrick J. Ryan
Keyword(s):  
Riemannian Manifold ◽  
Euclidean Space ◽  
Hyperbolic Space ◽  
Critical Points ◽  
Morse Function ◽  
Complete Riemannian Manifold ◽  
Distance Functions

In 1972, Nomizu and Rodriguez [5] found the following characterization of the complete umbilic submanifolds of Euclidean space.Theorem A. Let Mn, n ≥ 2, be a connected, complete Riemannian manifold isometrically immersed in a Euclidean space Em. Every Morse function of the form Lp has index 0 or n at all of its critical points if and only if Mnis embedded as a Euclidean n-subspace or a Euclidean n-sphere in Em.

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.

A New Surface Reconstruction Algorithm for Noisy 3D Unorganized Points

2012 ◽  
Vol 217-219 ◽  
pp. 1312-1317
Author(s):  
Jun Song
Keyword(s):  
Surface Reconstruction ◽  
Point Cloud ◽  
Sampling Method ◽  
Reconstruction Algorithm ◽  
Improved Method ◽  
Feature Size ◽  
Data Set ◽  
Good Surface ◽  
Fuzzy C Means Clustering ◽  
Local Feature Size

This paper puts forward a new method of surface reconstruction. Power crust algorithm can reconstruct a good surface that is topological valid and be proved theoretically. But when the point cloud is noisy, the surface reconstructed is not good and its running time is long. This paper proposes a improved method of fuzzy c-means clustering to delete the noisy points and a non-uniformly sampling method to resample the input data set according to the local feature size before reconstruction. Experimental results show that the efficiency of the algorithm has been improved much more.

CRITICAL POINTS OF DISTANCE TO AN ε-SAMPLING OF A SURFACE AND FLOW-COMPLEX-BASED SURFACE RECONSTRUCTION

2008 ◽  
Vol 18 (01n02) ◽  
pp. 29-61 ◽  
Author(s):  
TAMAL K. DEY ◽  
JOACHIM GIESEN ◽  
EDGAR A. RAMOS ◽  
BARDIA SADRI
Keyword(s):  
Surface Reconstruction ◽  
Distance Function ◽  
Critical Points ◽  
Geometric Modeling ◽  
Medial Axis ◽  
Reconstruction Algorithm ◽  
Three Dimensions ◽  
Distance Functions ◽  
Curve Reconstruction ◽  
Discrete Sample

The distance function to surfaces in three dimensions plays a key role in many geometric modeling applications such as medial axis approximations, surface reconstructions, offset computations and feature extractions among others. In many cases, the distance function induced by the surface can be approximated by the distance function induced by a discrete sample of the surface. The critical points of the distance functions are known to be closely related to the topology of the sets inducing them. However, no earlier theoretical result has found a link between topological properties of a geometric object and critical points of the distance to a discrete sample of it. We provide this link by showing that the critical points of the distance function induced by a discrete sample of a surface fall into two disjoint classes: those that lie very close to the surface and those that are near its medial axis. This closeness is precisely quantified and is shown to depend on the sampling density. It turns out that critical points near the medial axis can be used to extract topological information about the sampled surface. Based on this, we provide a new flow-complex-based surface reconstruction algorithm that, given a tight ε-sample of a surface, approximates the surface geometrically, both in distance and normals, and captures its topology. Furthermore, we show that the same algorithm can be used for curve reconstruction.

A Efficient Surface Reconstruction Method for Noisy Samples Based on Bilateral Filtering and down Sampling

2014 ◽  
Vol 950 ◽  
pp. 145-149
Author(s):  
Wen Rui Wan
Keyword(s):  
Surface Reconstruction ◽  
Sampling Method ◽  
Reconstruction Algorithm ◽  
Bilateral Filter ◽  
Reconstruction Method ◽  
Bilateral Filtering ◽  
Triangle Mesh ◽  
Feature Size ◽  
Original Surface ◽  
Local Feature Size

Surface reconstruction is a hot topic in the field of computer graphics. Power Crust algorithm can reconstruct a triangle mesh that is topologically valid and convergent to the original surface. But it can not handle the points with noised and its running time is long. In this paper an efficient surface reconstruction algorithm for noisy samples is proposed. Firstly, we delete the noise by bilateral filter. Secondly, a non-uniformly sampling method is used to resample the input data in order decrease the number of the samples to the local feature size before reconstruction. Finally, Power crust algorithm is be used to reconstructed the surface. From the experiments, it can be seen the speed of reconstruction is increased and the features of the surface are preserved.

Applications of the Global Coordinate System

2011 ◽  
Author(s):  
Yves Balasko
Keyword(s):  
Coordinate System ◽  
Critical Points ◽  
Global Coordinate System ◽  
Coordinate Systems ◽  
Analytical Characterization ◽  
Equilibrium Manifold ◽  
System P ◽  
Definition Of

The global coordinate system for the equilibrium manifold follows from: (1) the determination of the unique fiber F(b) through the equilibrium (ρ‎, ω‎) where b = φ‎((ρ‎, ω‎) = (ρ‎, ρ‎ · ρ‎1, …, ρ‎ · ρ‎m); and (2) the determination of the location of the equilibrium (ρ‎, ω‎) within the fiber F(b) viewed as a linear space of dimension (ℓ − 1)(m − 1) and, therefore, parameterized by (ℓ − 1)(m − 1) coordinates. If there is little leeway in determining the fiber F(b) through the equilibrium (ρ‎, ω‎), there are different ways of representing the equilibrium (ρ‎, ω‎) within its fiber F(b). This leads to the definition of coordinate systems (A) and (B) for the equilibrium manifold. This chapter defines these two coordinate systems and applies them to obtain an analytical characterization of the critical equilibria, i.e., the critical points of the natural projection.

scholarly journals An ACT-R Based Humanoid Social Robot to Manage Storytelling Activities

Robotics ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 25
Author(s):  
Adriana Bono ◽  
Agnese Augello ◽  
Giovanni Pilato ◽  
Filippo Vella ◽  
Salvatore Gaglio
Keyword(s):  
Primary School ◽  
School Children ◽  
Critical Points ◽  
Cognitive Architecture ◽  
Humanoid Robots ◽  
Primary School Children ◽  
Interactive Storytelling ◽  
Future Experimentation ◽  
Definition Of ◽  
The Impact

This paper describes an interactive storytelling system, accessible through the SoftBank robotic platforms NAO and Pepper. The main contribution consists of the interpretation of the story characters by humanoid robots, obtained through the definition of appropriate cognitive models, relying on the ACT-R cognitive architecture. The reasoning processes leading to the story evolution are based on the represented knowledge and the suggestions of the listener in critical points of the story. They are disclosed during the narration, to make clear the dynamics of the story and the feelings of the characters. We analyzed the impact of such externalization of the internal status of the characters to set the basis for future experimentation with primary school children.

scholarly journals Umbilical Submanifolds and Morse Functions

1972 ◽  
Vol 48 ◽  
pp. 197-201 ◽  
Author(s):  
Katsumi Nomizu ◽  
Lucio Rodríguez
Keyword(s):  
Euclidean Space ◽  
Differentiable Function ◽  
Critical Points ◽  
Morse Function ◽  
Differentiable Manifold ◽  
Morse Functions

Let Mn be a differentiable manifold (of class C∞). By a Morse function on Mn we mean a differentiable function whose critical points are all non-degenerate. If f is an immersion of Mn into a Euclidean space Rm, we may obtain Morse functions on Mn in the following way.

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