Flow Complexity: Fast Polytopal Graph Complexity and 3D Object Clustering

Authors:
Francisco Escolano;Daniela Giorgi;Edwin R. Hancock;Miguel A. Lozano;Bianca Falcidieno
Affiliations:
Departamento de Ciencia de la Computación e Inteligencia Artificial, University of Alicante, Spain;Istituto di Matematica Applicata e Tecnologie Informatiche Consiglio Nazionale delle Ricerche, Italy;Department of Computer Science, University of York, UK;Departamento de Ciencia de la Computación e Inteligencia Artificial, University of Alicante, Spain;Istituto di Matematica Applicata e Tecnologie Informatiche Consiglio Nazionale delle Ricerche, Italy
Venue:
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Year:
2009

Citing 7
Cited 4

Topology matching for fully automatic similarity estimation of 3D shapes

Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Constructing a Reeb graph automatically from cross sections

IEEE Computer Graphics and Applications
Learning Shape-Classes Using a Mixture of Tree-Unions

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Riemannian approach to graph embedding

Pattern Recognition
Protein classification by matching and clustering surface graphs

Pattern Recognition
Graph simplification and matching using commute times

Pattern Recognition
Polytopal Graph Complexity, Matrix Permanents, and Embedding

SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition

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
What is the complexity of a network? the heat flow-thermodynamic depth approach

SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
Information-geometric graph indexing from bags of partial node coverages

GbRPR'11 Proceedings of the 8th international conference on Graph-based representations in pattern recognition
Information-theoretic selection of high-dimensional spectral features for structural recognition

Computer Vision and Image Understanding

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we introduce a novel descriptor of graph complexity which can be computed in real time and has the same qualitative behavior of polytopal (Birkhoff) complexity, which has been successfully tested in the context of Bioinformatics. We also show how the phase-change point may be characterized in terms of the Laplacian spectrum, by analyzing the derivatives of the complexity function. In addition, the new complexity notion (flow complexity ) is applied to cluster a database of Reeb graphs coming from analyzing 3D objects.