Simple and optimal output-sensitive construction of contour trees using monotone paths

Authors:
Yi-Jen Chiang;Tobias Lenz;Xiang Lu;Günter Rote
Affiliations:
Department of Computer and Information Science, Polytechnic University, Brooklyn, NY;Institut für Informatik, Freie Universität Berlin, Takustraße 9, D-14195 Berlin, Germany;Department of Computer and Information Science, Polytechnic University, Brooklyn, NY;Institut für Informatik, Freie Universität Berlin, Takustraße 9, D-14195 Berlin, Germany
Venue:
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
Year:
2005

Citing 17
Cited 6

The contour spectrum

VIS '97 Proceedings of the 8th conference on Visualization '97
Contour trees and small seed sets for isosurface traversal

SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Construction of contour trees in 3D in O(n log n) steps

Proceedings of the fourteenth annual symposium on Computational geometry
Geometric Separators for Finite-Element Meshes

SIAM Journal on Scientific Computing
Efficiency of a Good But Not Linear Set Union Algorithm

Journal of the ACM (JACM)
Topology preserving and controlled topology simplifying multiresolution isosurface extraction

Proceedings of the conference on Visualization '00
A prototype system for visualizing time-dependent volume data

SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Introduction to Algorithms

Introduction to Algorithms
Efficient computation of the topology of level sets

Proceedings of the conference on Visualization '02
Topological Zone Organization of Scalar Volume Data

Journal of Mathematical Imaging and Vision
Controlled Topology Simplification

IEEE Transactions on Visualization and Computer Graphics
Surface Coding Based on Morse Theory

IEEE Computer Graphics and Applications
Computing contour trees in all dimensions

Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Path seeds and flexible isosurfaces using topology for exploratory visualization

VISSYM '03 Proceedings of the symposium on Data visualisation 2003
The safari interface for visualizing time-dependent volume data using iso-surfaces and contour spectra

Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Loops in reeb graphs of 2-manifolds

Proceedings of the nineteenth annual symposium on Computational geometry
Implicit modeling of swept surfaces and volumes

VIS '94 Proceedings of the conference on Visualization '94

Time-Varying Contour Topology

IEEE Transactions on Visualization and Computer Graphics
Robust on-line computation of Reeb graphs: simplicity and speed

ACM SIGGRAPH 2007 papers
Reeb graphs for shape analysis and applications

Theoretical Computer Science
Describing shapes by geometrical-topological properties of real functions

ACM Computing Surveys (CSUR)
Time-varying Reeb graphs for continuous space--time data

Computational Geometry: Theory and Applications
Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree

Computational Geometry: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

Contour trees are used when high-dimensional data are preprocessed for efficient extraction of isocontours for the purpose of visualization. So far, efficient algorithms for contour trees are based on processing the data in sorted order. We present a new algorithm that avoids sorting of the whole dataset, but sorts only a subset of so-called component-critical points. They form only a small fraction of the vertices in the dataset, for typical data that arise in practice. The algorithm is simple, achieves the optimal output-sensitive bound in running time, and works in any dimension. Our experiments show that the algorithm compares favorably with the previous best algorithm.