A lower bound on the complexity of the union-split-find problem
SIAM Journal on Computing
Introduction to algorithms
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
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
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
Time-varying reeb graphs for continuous space-time data
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
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
Families of cut-graphs for bordered meshes with arbitrary genus
Graphical Models
Harmonic skeleton for realistic character animation
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Size functions for comparing 3D models
Pattern Recognition
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
A genus oblivious approach to cross parameterization
Computer Aided Geometric Design
Harmonic 1-form based skeleton extraction from examples
Graphical Models
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 analysis using the auto diffusion function
SGP '09 Proceedings of the Symposium on Geometry Processing
Technical Section: Shape approximation by differential properties of scalar functions
Computers and Graphics
Graph-based representations of point clouds
Graphical Models
Tessellation of quadratic elements
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
A deterministic o(m log m) time algorithm for the reeb graph
Proceedings of the twenty-eighth annual symposium on Computational geometry
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
Real-Time markerless hand gesture recognition with depth camera
PCM'12 Proceedings of the 13th Pacific-Rim conference on Advances in Multimedia Information Processing
Technical note: Kinematic skeleton extraction from 3D articulated models
Computer-Aided Design
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Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(nlogn), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.