Towards Topology-Rich Visualization

Attila GyulassySCI Institute, University of Utah

Why Use Topology Representations?

Scalar function Structural representation

Topology-based Representations of Scalar

Functions

2D Scalar function

Reeb Graph/Contour Tree

Morse-Smale Complex

The state of the art

Computation

Analysis

Visualization

Combinatorial Construction

Harish Doraiswamy and Vijay Natarajan. Efficient output-sensitive construction of Reeb graphs. Proc. Intl. Symp. Algorithms and Computation, LNCS 5369, Springer-Verlag, 2008, 557-568.

Carr H, Snoeyink J, Axen U (2003) 'Computing Contour Trees in All Dimensions'. Computational Geometry, 24 (2):75-94.

Harish Doraiswamy and Vijay Natarajan. Efficient algorithms for computing Reeb graphs. Computational Geometry: Theory and Applications, 42, 2009, 606-616.

Valerio Pascucci , Kree Cole-McLaughlin, Parallel Computation of the Topology of Level Sets, Algorithmica, v.38 n.1, p.249-268, October 2003

Valerio Pascucci , Giorgio Scorzelli , Peer-Timo Bremer , Ajith Mascarenhas, Robust on-line computation of Reeb graphs: simplicity and speed, ACM Transactions on Graphics (TOG), v.26 n.3, July 2007

Contour Tree Reeb Graph

Julien Tierny , Attila Gyulassy , Eddie Simon , Valerio Pascucci, Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees, IEEE Transactions on Visualization and Computer Graphics, v.15 n.6, p.1177-1184, November 2009

Combinatorial Construction

Morse-Smale Complex

Data Structures

Analysis/Visualization

Hamish Carr , Jack Snoeyink , Michiel van de Panne, Simplifying Flexible Isosurfaces Using Local Geometric Measures, Proceedings of the conference on Visualization '04, p.497-504, October 10-15, 2004

Gunther H. Weber, Scott E. Dillard, Hamish Carr, Valerio Pascucci, and Bernd Hamann. Topology-Controlled Volume Rendering, IEEE Transactions on Visualization and Computer Graphics. 13 (2), pp. 330-341. 10.1109/TVCG.2007.47

Outline

From topology to visualization Modified visualization pipeline? Motivation: as more complex features need to be

visualized, more sophisticated classification T Rep is a roadmap to a scalar function What we do with roadmap? Analysis vs vis.

Overview of CT and MSC Literature Review Current Work with MSC

Background

Ct and msc are our roadmaps to compute What is a ct What is an msc

Algorithms to compute Ct – carr, reeb graphs – streaming, 2dms – bremer,

3dms – gyulassy Description of result

Data structure with nodes, arcs, etc. - discrete can be queried

analysis/visualization of result

Literature review

How has roadmap been used in vis? Vis of the reeb graph? Carr and extracting different isosurfaces Scott's paper using segmentation 2d MS complex – bubbles 3d merge trees – flame 3d MS complex – porous media

What we're working on

Formalizing the space of visualizations that can be achieved using MS complex Querying Each component – what space of visualizations

does this afford? Vertex, arcs, surfaces, volumes

Demo Highlight that it's surfaces we're playing with