Homology functionality for grayscale image segmentation

Authors

  • Rabih Assaf CReSTIC, University of Reims Champagne-Ardenne, Reims, France; MathematicsDepartment, Holy Spirit University of KASLIK,Jounieh, Lebanon
  • Alban Goupil CReSTIC, University of Reims Champagne-Ardenne, Reims
  • Valeriu Vrabie
  • Mohammad Kacim Department of Mathematics, Holy Spirit University of KASLIK, Jounieh

DOI:

https://doi.org/10.26713/jims.v8i4.563

Keywords:

Algebraic topology, persistent homology, image processing

Abstract

Topological tools provide features about spaces, which are insensitive to continuous deformations. Applied to images, the topological analysis reveals important characteristics: how many connected components are present, which ones have holes and how many, how are they related one to another, how to measure them and find their locations. We show in this paper that the extraction of such features by computing persistent homology is suitable for grayscale image segmentation.

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References

C. Adams and R. Franzosa.Introduction to Topology: Pure and Applied. Prentice Hall (2007).

G. Carlsson et al., Topological data analysis and machine learning theory, BIRS Workshop, Alberta, October 15–19 (2012).

C. Chen and M. Kerber, Persistent homology computation with a twist, 27th European Workshop on Computational Geometry, Switzerland, March 28–30 (2011).

H. Edelsbrunner and J. L. Harer, Computational topology. American Mathematical Society (2010).

H. Edelsbrunner, D. Letscher, and A. Zomorodian. Topological persistence and simplification. Discreteand Computational Geometry, 28(4) (2002), 511–533.

R. Ghrist, "Elementary Applied Topology", ed. 1.0, Createspace, 2014.

A. Hatcher, Algebraic Topology. Cambridge University Press (2001).

J. Macqueen, Some methods for classification and analysis of multivariate observations, 5-th Berkeley Symposium on Mathematical Statistics and Probability (1967), 281–297.

E. Merelli,et al, Topological Characterization of Complex Systems: Using Persistent Entropy, Entropy 17 (2015), 6872-6892.

A.Zomorodian, G. Carlsson. Computing Persistent Homology. Discrete and Computational Geometry,33 (2005), 249-274.

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Published

2016-12-31
CITATION

How to Cite

Assaf, R., Goupil, A., Vrabie, V., & Kacim, M. (2016). Homology functionality for grayscale image segmentation. Journal of Informatics and Mathematical Sciences, 8(4), 281–286. https://doi.org/10.26713/jims.v8i4.563

Issue

Vol. 8 No. 4 (2016)

Section

Research Articles

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