Computational complexity of combinatorial surfaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
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
Level set diagrams of polyhedral objects
Proceedings of the fifth ACM symposium on Solid modeling and applications
Computing Morse functions on triangulated manifolds
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Isosurface extraction in time-varying fields using a temporal branch-on-need tree (T-BON)
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
The digital Michelangelo project: 3D scanning of large statues
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Introduction to Modern Information Retrieval
Introduction to Modern Information Retrieval
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
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
Trekking in the Alps Without Freezing or Getting Tired
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
Loops in reeb graphs of 2-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
An overview on properties and efficacy of topological skeletons in Shape Modelling
SMI '03 Proceedings of the Shape Modeling International 2003
Topology Recognition of 3D Closed Freeform Objects Based on Topological Graphs
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
Topological quadrangulations of closed triangulated surfaces using the Reeb graph
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Removing excess topology from isosurfaces
ACM Transactions on Graphics (TOG)
Time-varying reeb graphs for continuous space-time data
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Reeb Graph Representation of Surfaces with Boundary
SMI '04 Proceedings of the Shape Modeling International 2004
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Topological manipulation of isosurfaces
Topological manipulation of isosurfaces
Local and Global Comparison of Continuous Functions
VIS '04 Proceedings of the conference on Visualization '04
Simplifying Flexible Isosurfaces Using Local Geometric Measures
VIS '04 Proceedings of the conference on Visualization '04
Feature-based surface parameterization and texture mapping
ACM Transactions on Graphics (TOG)
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
Stability of persistence diagrams
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
IEEE Transactions on Visualization and Computer Graphics
Laplace-Beltrami Eigenfunctions Towards an Algorithm That "Understands" Geometry
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Robust 3D Shape Correspondence in the Spectral Domain
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Topology-Controlled Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
Two-Dimensional Critical Point Configuration Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
A comparison framework for 3d object classification methods
MRCS'06 Proceedings of the 2006 international conference on Multimedia Content Representation, Classification and Security
A functional-based segmentation of human body scans in arbitrary postures
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Computing geometry-aware handle and tunnel loops in 3D models
ACM SIGGRAPH 2008 papers
Complex Fiedler Vectors for Shape Retrieval
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Advanced Homology Computation of Digital Volumes Via Cell Complexes
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Technical Section: Semantics-driven best view of 3D shapes
Computers and Graphics
Recognition of Occluded Shapes Using Size Functions
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
Technical Section: Shape approximation by differential properties of scalar functions
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
High-dimensional spectral feature selection for 3D object recognition based on reeb graphs
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
Artwork 3D model database indexing and classification
Pattern Recognition
Detecting critical regions in multidimensional data sets
Computers & Mathematics with Applications
Measuring 3D shape similarity by graph-based matching of the medial scaffolds
Computer Vision and Image Understanding
Reeb graphs: approximation and persistence
Proceedings of the twenty-seventh annual symposium on Computational geometry
Unsupervised co-segmentation of a set of shapes via descriptor-space spectral clustering
Proceedings of the 2011 SIGGRAPH Asia Conference
Graph-based representations of point clouds
Graphical Models
A 3D shape segmentation approach for robot grasping by parts
Robotics and Autonomous Systems
A deterministic o(m log m) time algorithm for the reeb graph
Proceedings of the twenty-eighth annual symposium on Computational geometry
The hitchhiker's guide to the galaxy of mathematical tools for shape analysis
ACM SIGGRAPH 2012 Courses
Co-Segmentation of 3D Shapes via Subspace Clustering
Computer Graphics Forum
ConTopo: non-rigid 3D object retrieval using topological information guided by conformal factors
EG 3DOR'11 Proceedings of the 4th Eurographics conference on 3D Object Retrieval
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
Information-theoretic selection of high-dimensional spectral features for structural recognition
Computer Vision and Image Understanding
Approximate partitioning of 2D objects into orthogonally convex components
Computer Vision and Image Understanding
Exploiting 3d part-based analysis, description and indexing to support medical applications
MCBR-CDS'12 Proceedings of the Third MICCAI international conference on Medical Content-Based Retrieval for Clinical Decision Support
An efficient computation of handle and tunnel loops via Reeb graphs
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Graph matching and clustering using kernel attributes
Neurocomputing
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Learning kernels on extended Reeb graphs for 3d shape classification and retrieval
3DOR '13 Proceedings of the Sixth Eurographics Workshop on 3D Object Retrieval
| Hi-index | 5.23 |
Reeb graphs are compact shape descriptors which convey topological information related to the level sets of a function defined on the shape. Their definition dates back to 1946, and finds its root in Morse theory. Reeb graphs as shape descriptors have been proposed to solve different problems arising in Computer Graphics, and nowadays they play a fundamental role in the field of computational topology for shape analysis. This paper provides an overview of the mathematical properties of Reeb graphs and reconstructs its history in the Computer Graphics context, with an eye towards directions of future research.