NDLI: Cut locus and topology from surface point data

Please wait, while we are loading the content...

Lower bounds for weak epsilon-nets and stair-convexity

Coresets for polytope distance

Computing hereditary convex structures

An IP solution to the art gallery problem

The scale axis transform

An improved bound on the number of unit area triangles

Visibility maps of realistic terrains have linear smoothed complexity

Divide-and-conquer for Voronoi diagrams revisited

Persistent cohomology and circular coordinates

Distributed vision with smart pixels

A proof of the molecular conjecture

k-means requires exponentially many iterations even in the plane

Adaptive isotopic approximation of nonsingular curves: the parametrizability and nonlocal isotopy approach

Diameter of polyhedra: limits of abstraction

Computational origami: from flapping birds to space telescopes

Epsilon nets and union complexity

Kinetic spanners in $R^{d}$

Binary plane partitions for disjoint line segments

Quadrilateral meshes with bounded minimum angle

Integral estimation from point cloud in d-dimensional space: a geometric view

Halving lines and measure concentration in the plane

Embedding rivers in polyhedral terrains

The geodesic farthest-site Voronoi diagram in a polygonal domain with holes

Proximity of persistence modules and their diagrams

Area-universal rectangular layouts

Flattening single-vertex origami: the non-expansive case

Approximation algorithms for maximum independent set of pseudo-disks

On the topology of planar algebraic curves

Minimum Manhattan network is NP-complete

PTAS for geometric hitting set problems via local search

Shooting permanent rays among disjoint polygons in the plane

Optimal in-place algorithms for 3-D convex hulls and 2-D segment intersection

Animating a continuous family of two-site Voronoi diagrams (and a proof of a bound on the number of regions)

Cut locus and topology from surface point data

Candle in the woods: asymptotic bounds on minimum blocking sets

The Euclidean degree-4 minimum spanning tree problem is NP-hard

Incremental construction of the delaunay triangulation and the delaunay graph in medium dimension

Zigzag persistent homology and real-valued functions

Cache-oblivious range reporting with optimal queries requires superlinear space

Arrangements of double pseudolines: extended abstract

On the set multi-cover problem in geometric settings

Randomly removing g handles at once

On grids in topological graphs

Near-linear approximation algorithms for geometric hitting sets

The scale axis picture show

Approximate center points with proofs

Parallel geometric algorithms for multi-core computers

A general approach for cache-oblivious range reporting and approximate range counting

Minimum cuts and shortest homologous cycles

Rectangular cartograms: the game

Geometric tomography: a limited-view approach for computed tomography

Straight skeletons of three-dimensional polyhedra

Reconstructing sharp features of triangular meshes

High resolution surface reconstruction from overlapping multiple-views

Cut locus and topology from surface point data

Content Provider	ACM Digital Library
Author	Dey, Tamal K. Li, Kuiyu
Abstract	A cut locus of a point p in a compact Riemannian manifold M is defined as the set of points where minimizing geodesics issued from p stop being minimizing. It is known that a cut locus contains most of the topological information of M. Our goal is to utilize this property of cut loci to decipher the topology of M from a point sample. Recently it has been shown that Rips complexes can be built from a point sample P of M systematically to compute the Betti numbers, the rank of the homology groups of M. Rips complexes can be computed easily and therefore are favored over others such as restricted Delaunay, alpha, Cech, and witness complex. However, the sizes of the Rips complexes tend to be large. Since the dimension of a cut locus is lower than that of the manifold M, a subsample of P approximating the cut locus is usually much smaller in size and hence admits a relatively smaller Rips complex. In this paper we explore the above approach for point data sampled from surfaces embedded in any high dimensional Euclidean space. We present an algorithm that computes a subsample P' of a sample P of a 2-manifold where P' approximates a cut locus. Empirical results show that the first Betti number of M can be computed from the Rips complexes built on these subsamples. The sizes of these Rips complexes are much smaller than the one built on the original sample of M.
Starting Page	125
Ending Page	134
Page Count	10
File Format	PDF
ISBN	9781605585017
DOI	10.1145/1542362.1542390
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2009-06-08
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Cut locus Differential geometry Rips complex Surface point cloud Topology
Content Type	Text
Resource Type	Article

Central Library (ISO-9001:2015 Certified)
Indian Institute of Technology Kharagpur
Kharagpur, West Bengal, India | PIN - 721302

See location in the Map
03222 282435
Mail: support@ndl.gov.in

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in