Invariant representative cocycles of cohomology generators using irregular graph pyramids

Authors:
Rocio Gonzalez-Diaz;Adrian Ion;Mabel Iglesias-Ham;Walter G. Kropatsch
Affiliations:
Applied Math Department, School of Computer Engineering, University of Seville, Reina Mercedes Avenue, CP: 41012 Seville, Spain;Pattern Recognition and Image Processing Group, Vienna University of Technology, Faculty of Informatics, Institute of Computer Aided Automation, Favoritenstr. 9/1832, A-1040 Vienna, Austria and In ...;Pattern Recognition and Image Processing Group, Vienna University of Technology, Faculty of Informatics, Institute of Computer Aided Automation, Favoritenstr. 9/1832, A-1040 Vienna, Austria and Pa ...;Pattern Recognition and Image Processing Group, Vienna University of Technology, Faculty of Informatics, Institute of Computer Aided Automation, Favoritenstr. 9/1832, A-1040 Vienna, Austria
Venue:
Computer Vision and Image Understanding
Year:
2011

Citing 13
Cited 2

The Dual Irregular Pyramid

CAIP '93 Proceedings of the 5th International Conference on Computer Analysis of Images and Patterns
Removing excess topology from isosurfaces

ACM Transactions on Graphics (TOG)
Vision pyramids that do not grow too high

Pattern Recognition Letters - Special issue: In memoriam Azriel Rosenfeld
nD generalized map pyramids: Definition, representations and basic operations

Pattern Recognition
Notes on shape orientation where the standard method does not work

Pattern Recognition
Topological analysis of shapes using Morse theory

Computer Vision and Image Understanding
Computing geometry-aware handle and tunnel loops in 3D models

ACM SIGGRAPH 2008 papers
Integral Operators for Computing Homology Generators at Any Dimension

CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
Delineating Homology Generators in Graph Pyramids

CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
Directly computing the generators of image homology using graph pyramids

Image and Vision Computing
Irregular Graph Pyramids and Representative Cocycles of Cohomology Generators

GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Euclidean eccentricity transform by discrete arc paving

DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Hardness results for homology localization

SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms

Cup products on polyhedral approximations of 3D digital images

IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Removal operations in nd generalized maps for efficient homology computation

CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context

Quantified Score

Hi-index	0.00

Visualization

Abstract

Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns 'quantities' to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. An extension to obtain scanning and rotation invariant cocycles is given.