Detecting critical regions in multidimensional data sets

Authors:
Madjid Allili;David Corriveau;Sara Derivière;Marc Ethier;Tomasz Kaczynski
Affiliations:
Department of Computer Science, Bishop's University, Sherbrooke (Québec), Canada J1M 1Z7;Département de mathématiques, Université de Sherbrooke, Sherbrooke (Québec), Canada J1K 2R1;Département de mathématiques, Université de Sherbrooke, Sherbrooke (Québec), Canada J1K 2R1;Département de mathématiques, Université de Sherbrooke, Sherbrooke (Québec), Canada J1K 2R1;Département de mathématiques, Université de Sherbrooke, Sherbrooke (Québec), Canada J1K 2R1
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 6
Cited 0

Constructing a Reeb graph automatically from cross sections

IEEE Computer Graphics and Applications
Detecting critical regions in scalar fields

VISSYM '03 Proceedings of the symposium on Data visualisation 2003
Discrete Dynamical System Framework for Construction of Connections between Critical Regions in Lattice Height Data

Journal of Mathematical Imaging and Vision
Reeb graphs for shape analysis and applications

Theoretical Computer Science
The Theory of Multidimensional Persistence

Discrete & Computational Geometry - 23rd Annual Symposium on Computational Geometry
Coreduction Homology Algorithm for Regular CW-Complexes

Discrete & Computational Geometry

Quantified Score

Hi-index	0.09

Visualization

Abstract

We propose a new approach, based on the Conley index theory, for the detection and classification of critical regions in multidimensional data sets. The use of homology groups makes this method consistent and successful in all dimensions and allows us to generalize visual classification techniques based solely on the notion of connectedness which may fail in higher dimensions.