Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
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
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Simplicial subdivisions and sampling artifacts
Proceedings of the conference on Visualization '01
Efficient computation of the topology of level sets
Proceedings of the conference on Visualization '02
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
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Topological Volume Skeletonization Using Adaptive Tetrahedralization
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
Topological manipulation of isosurfaces
Topological manipulation of isosurfaces
A Multi-resolution Data Structure for Two-dimensional Morse-Smale Functions
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Proceedings of the 2006 ACM symposium on Solid and physical modeling
A Topological Approach to Simplification of Three-Dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Understanding the Structure of the Turbulent Mixing Layer in Hydrodynamic Instabilities
IEEE Transactions on Visualization and Computer Graphics
Topology-Controlled Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
Computer-Aided Design
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
Topological Landscapes: A Terrain Metaphor for Scientific Data
IEEE Transactions on Visualization and Computer Graphics
Topologically Clean Distance Fields
IEEE Transactions on Visualization and Computer Graphics
Efficient Computation of Morse-Smale Complexes for Three-dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Reeb spaces of piecewise linear mappings
Proceedings of the twenty-fourth annual symposium on Computational geometry
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Efficient algorithms for computing Reeb graphs
Computational Geometry: Theory and Applications
3D Mesh decomposition using Reeb graphs
Image and Vision Computing
Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree
Computational Geometry: Theory and Applications
I/O-Efficient Contour Tree Simplification
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Tessellation of quadratic elements
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Smooth Shape-Aware Functions with Controlled Extrema
Computer Graphics Forum
Flexible and topologically localized segmentation
EUROVIS'07 Proceedings of the 9th Joint Eurographics / IEEE VGTC conference on Visualization
Introducing topological attributes for objective-based visualization of simulated datasets
VG'05 Proceedings of the Fourth Eurographics / IEEE VGTC conference on Volume Graphics
Topological landscape ensembles for visualization of scalar-valued functions
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
Topology-based smoothing of 2D scalar fields with C1-continuity
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
Topology-based visualization of transformation pathways in complex chemical systems
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
A gradient-based comparison measure for visual analysis of multifield data
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
Proceedings of the 18th ACM SIGPLAN symposium on Principles and practice of parallel programming
Technical Section: Topological saliency
Computers and Graphics
Technical note: Kinematic skeleton extraction from 3D articulated models
Computer-Aided Design
Evaluating isosurfaces with level-set-based information maps
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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The contour tree, an abstraction of a scalar field that encodes the nesting relationships of isosurfaces, can be used to accelerate isosurface extraction, to identify important isovalues for volume-rendering transfer functions, and to guide exploratory visualization through a flexible isosurface interface. Many real-world data sets produce unmanageably large contour trees which require meaningful simplification. We define local geometric measures for individual contours, such as surface area and contained volume, and provide an algorithm to compute these measures in a contour tree. We then use these geometric measures to simplify the contour trees, suppressing minor topological features of the data. We combine this with a flexible isosurface interface to allow users to explore individual contours of a dataset interactively.