Making data structures persistent
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
A feature-based approach for smooth surfaces
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Contour trees and small seed sets for isosurface traversal
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Level set diagrams of polyhedral objects
Proceedings of the fifth ACM symposium on Solid modeling and applications
Semi-regular mesh extraction from volumes
Proceedings of the conference on Visualization '00
Topology recognition of 3D closed freeform objects based on topological graphs
Proceedings of the sixth ACM symposium on Solid modeling and applications
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Cutting 3D freeform objects with genus-n into single boundary surfaces using topological graphs
Proceedings of the seventh ACM symposium on Solid modeling and applications
Exploring scalar fields using critical isovalues
Proceedings of the conference on Visualization '02
Surface Coding Based on Morse Theory
IEEE Computer Graphics and Applications
Constructing a Reeb graph automatically from cross sections
IEEE Computer Graphics and Applications
Computing contour trees in all dimensions
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Loops in reeb graphs of 2-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Topological persistence and simplification
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Re-Meshing Techniques for Topological Analysis
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Removing excess topology from isosurfaces
ACM Transactions on Graphics (TOG)
Parallel Computation of the Topology of Level Sets
Algorithmica
Extreme elevation on a 2-manifold
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Simplifying Flexible Isosurfaces Using Local Geometric Measures
VIS '04 Proceedings of the conference on Visualization '04
Simple and optimal output-sensitive construction of contour trees using monotone paths
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
Shape-based retrieval and analysis of 3D models
ACM SIGGRAPH 2004 Course Notes
Streaming compression of tetrahedral volume meshes
GI '06 Proceedings of Graphics Interface 2006
Skeleton extraction by mesh contraction
ACM SIGGRAPH 2008 papers
Computing geometry-aware handle and tunnel loops in 3D models
ACM SIGGRAPH 2008 papers
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Harmonic 1-form based skeleton extraction from examples
Graphical Models
Efficient algorithms for computing Reeb graphs
Computational Geometry: Theory and Applications
Technical Section: Geometry-aware domain decomposition for T-spline-based manifold modeling
Computers and Graphics
Rig retargeting for 3D animation
Proceedings of Graphics Interface 2009
Technical Section: Shape approximation by differential properties of scalar functions
Computers and Graphics
Technical Section: Feature-aligned harmonic volumetric mapping using MFS
Computers and Graphics
A randomized O(m log m) time algorithm for computing Reeb graphs of arbitrary simplicial complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Technical Section: Exoskeleton: Curve network abstraction for 3D shapes
Computers and Graphics
Local Orthogonal Cutting Method for Computing Medial Curves and Its Biomedical Applications
SIAM Journal on Scientific Computing
A mobile environment for sketching-based skeleton generation
World Wide Web
Reeb graphs: approximation and persistence
Proceedings of the twenty-seventh annual symposium on Computational geometry
Image skeletonization based on curve skeleton extraction
HCII'11 Proceedings of the 14th international conference on Human-computer interaction: design and development approaches - Volume Part I
Graph-based representations of point clouds
Graphical Models
SMI 2012: Full Local approximation of scalar functions on 3D shapes and volumetric data
Computers and Graphics
A deterministic o(m log m) time algorithm for the reeb graph
Proceedings of the twenty-eighth annual symposium on Computational geometry
Centroidal Voronoi Tessellation of Line Segments and Graphs
Computer Graphics Forum
SkelTre - fast skeletonisation for imperfect point cloud data of botanic trees
EG 3DOR'09 Proceedings of the 2nd Eurographics conference on 3D Object Retrieval
Combining in-situ and in-transit processing to enable extreme-scale scientific analysis
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Analytic Curve Skeletons for 3D Surface Modeling and Processing
Computer Graphics Forum
PRICAI'12 Proceedings of the 12th Pacific Rim international conference on Trends in Artificial Intelligence
Simplified reeb graph as effective shape descriptor for the striatum
MeshMed'12 Proceedings of the 2012 international conference on Mesh Processing in Medical Image Analysis
Streaming-enabled parallel dataflow architecture for multicore systems
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
An efficient computation of handle and tunnel loops via Reeb graphs
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Invariant surface-based shape descriptor for dynamic surface encoding
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part I
Exploring power behaviors and trade-offs of in-situ data analytics
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Pose analysis using spectral geometry
The Visual Computer: International Journal of Computer Graphics
Optimizing polycube domain construction for hexahedral remeshing
Computer-Aided Design
Technical note: Kinematic skeleton extraction from 3D articulated models
Computer-Aided Design
Semantizing complex 3D scenes using constrained attribute grammars
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
| Hi-index | 0.00 |
Reeb graphs are a fundamental data structure for understanding and representing the topology of shapes. They are used in computer graphics, solid modeling, and visualization for applications ranging from the computation of similarities and finding defects in complex models to the automatic selection of visualization parameters. We introduce an on-line algorithm that reads a stream of elements (vertices, triangles, tetrahedra, etc.) and continuously maintains the Reeb graph of all elements already reed. The algorithm is robust in handling non-manifold meshes and general in its applicability to input models of any dimension. Optionally, we construct a skeleton-like embedding of the Reeb graph, and/or remove topological noise to reduce the output size. For interactive multi-resolution navigation we also build a hierarchical data structure which allows real-time extraction of approximated Reeb graphs containing all topological features above a given error threshold. Our extensive experiments show both high performance and practical linear scalability for meshes ranging from thousands to hundreds of millions of triangles. We apply our algorithm to the largest, most general, triangulated surfaces available to us, including 3D, 4D and 5D simplicial meshes. To demonstrate one important application we use Reeb graphs to find and highlight topological defects in meshes, including some widely believed to be "clean."