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
Introduction to Algorithms
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
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)
Loops in Reeb Graphs of 2-Manifolds
Discrete & Computational Geometry
Topological manipulation of isosurfaces
Topological manipulation of isosurfaces
Feature-based surface parameterization and texture mapping
ACM Transactions on Graphics (TOG)
Design of data structures for mergeable trees
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Extreme Elevation on a 2-Manifold
Discrete & Computational Geometry
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Time-varying Reeb graphs for continuous space--time data
Computational Geometry: Theory and Applications
Extending Persistence Using Poincaré and Lefschetz Duality
Foundations of Computational Mathematics
Efficient Output-Sensitive Construction of Reeb Graphs
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Efficient algorithms for computing Reeb graphs
Computational Geometry: Theory and Applications
Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees
IEEE Transactions on Visualization and Computer Graphics
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
An output-sensitive algorithm for persistent homology
Proceedings of the twenty-seventh annual symposium on Computational geometry
Reeb graphs: approximation and persistence
Proceedings of the twenty-seventh annual symposium on Computational geometry
Graph-based representations of point clouds
Graphical Models
A deterministic o(m log m) time algorithm for the reeb graph
Proceedings of the twenty-eighth annual symposium on Computational geometry
An output-sensitive algorithm for persistent homology
Computational Geometry: Theory and Applications
An efficient computation of handle and tunnel loops via Reeb graphs
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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Given a continuous scalar field ƒ: X → where X is a topological space, a level set of ƒ is a set {x ∈ X : ƒ (x) = α} for some value α ∈ IR. The level sets of ƒ can be subdivided into connected components. As α changes continuously, the connected components in the level sets appear, disappear, split and merge. The Reeb graph of ƒ encodes these changes in connected components of level sets. It provides a simple yet meaningful abstraction of the input domain. As such, it has been used in a range of applications in fields such as graphics and scientific visualization. In this paper, we present the first sub-quadratic algorithm to compute the Reeb graph for a function on an arbitrary simplicial complex K. Our algorithm is randomized with an expected running time O(m log n), where m is the size of the 2-skeleton of K (i.e, total number of vertices, edges and triangles), and n is the number of vertices. This presents a significant improvement over the previous Θ(mn) time complexity for arbitrary complex, matches (although in expectation only) the best known result for the special case of 2-manifolds, and is faster than current algorithms for any other special cases (e.g, 3-manifolds). Our algorithm is also very simple to implement. Preliminary experimental results show that it performs well in practice.