NDLI: Shape dimension and intrinsic metric from samples of manifolds with high co-dimension

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

Fault-tolerant geometric spanners

Shape fitting with outliers

Polygon decomposition based on the straight line skeleton

Topological graphs with no self-intersecting cycle of length 4

Long monotone paths in line arrangements

Spatial embedding of pseudo-triangulations

Local polyhedra and geometric graphs

Proximate planar point location

Near-optimal parameterization of the intersection of quadrics

Optimized color gamuts for tiled displays

Curve reconstruction from noisy samples

An optimal algorithm for the minimum edge cardinality cut surface problem

The asteroid surveying problem and other puzzles

Euclidean bounded-degree spanning tree ratios

High-dimensional shape fitting in linear time

Efficient algorithms for shared camera control

Distinct distances in homogeneous sets

New constructions of weak epsilon-nets

Planar minimally rigid graphs and pseudo-triangulations

Updating and constructing constrained delaunay and constrained regular triangulations by flips

Cost-driven octree construction schemes: an experimental study

Constructive root bound for k-ary rational input numbers

Hausdorff distance under translation for points and balls

Restricted delaunay triangulations and normal cycle

Loops in reeb graphs of 2-manifolds

VASCO: visualizing and animating spatial constructs and operations

Approximation algorithms for aligning points

Smooth kinetic maintenance of clusters

Good NEWS: partitioning a simple polygon by compass directions

A tight bound for the number of different directions in three dimensions

Curve-sensitive cuttings

The complexity of (un)folding

Anisotropic voronoi diagrams and guaranteed-quality anisotropic mesh generation

Cache-oblivious data structures for orthogonal range searching

Controlled perturbation for arrangements of circles

The smallest enclosing ball of balls: combinatorial structure and algorithms

Estimating surface normals in noisy point cloud data

Molecular shape analysis based upon the morse-smale complex and the connolly function

Billboard clouds

Geometric algorithms for static leaf sequencing problems in radiation therapy

On conflict-free coloring of points and simple regions in the plane

Complexity of the delaunay triangulation of points on surfaces the smooth case

Shape dimension and intrinsic metric from samples of manifolds with high co-dimension

Morse-smale complexes for piecewise linear 3-manifolds

A 3-D visualization of kirkpatrick's planar point location algorithm

Incremental constructions con BRIO

Morphing between shapes by using their straight skeletons

3DTreeDraw: a three dimensional tree drawing system

Online dispersion algorithms for swarms of robots

Finding a curve in a map

Fast penetration depth estimation using rasterization hardware and hierarchical refinement

Shape dimension and intrinsic metric from samples of manifolds with high co-dimension

Content Provider	ACM Digital Library
Author	Giesen, Joachim Wagner, Uli
Abstract	We introduce the adaptive neighborhood graph as a data structure for modeling a smooth manifold M embedded in some (potentially very high-dimensional) Euclidean space $R^{d}.$ We assume that M is known to us only through a finite sample P? M, as it is often the case in applications. The adaptive neighborhood graph is a geometric graph on P. Its complexity is at most $min[2^{O(k)}n,$ $n^{2}],$ where n=\|P\| and k=dim M, as opposed to the $n^{[d/2]}$ complexity of the Delaunay triangulation, which is often used to model manifolds. We show that we can provably correctly infer the connectivity of M and the dimension of M from the adaptive neighborhood graph provided a certain standard sampling condition is fulfilled. The running time of the dimension detection algorithm is $d2^{O(k^{7}log$ k) for each connected component of M. If the dimension is considered constant, this is a constant-time operation, and the adaptive neighborhood graph is of linear size. Moreover, the exponential dependence of the constants is only on theintrinsic dimension k, not on the ambient dimension d. This is of particular interest if the co-dimension is high, i.e., if k is much smaller than d, as is the case in many applications. The adaptive neighborhood graph also allows us to approximate the geodesic distances between the points in P.
Starting Page	329
Ending Page	337
Page Count	9
File Format	PDF
ISBN	1581136633
DOI	10.1145/777792.777841
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2003-06-08
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Dimension detection Geodesic distance Manifold learning
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