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Combinatorial Homology in a Perspective of Image Analysis
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Marco Grandis
Published/Copyright:
February 26, 2010
Abstract
This is the sequel of a paper where we introduced an intrinsic ho-motopy theory and homotopy groups for simplicial complexes. We study here the relations of this homotopy theory with the well-known homology theory of simplicial complexes. Also, our investigation is aimed at applications in image analysis. A metric space 𝑋 representing an image, has a structure of simplicial complex at each resolution ε > 0, and the corresponding combinatorial homology groups
give information on the image. Combining the methods developed here with programs for automatic computation of combinatorial homology might open the way to realistic applications.
Key words and phrases:: Homology groups; image processing; simplicial complex; digital topology; mathematical morphology
Received: 2002-05-28
Revised: 2002-12-14
Published Online: 2010-02-26
Published in Print: 2003-March
© Heldermann Verlag
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Keywords for this article
Homology groups;
image processing;
simplicial complex;
digital topology;
mathematical morphology
Articles in the same Issue
- On One Theorem of S. Warschawski
- Investigation of Two-Dimensional Models of Elastic Prismatic Shell
- Branched Coverings and Minimal Free Resolution for Infinite-Dimensional Complex Spaces
- Operational Identities for Circular and Hyperbolic Functions and Their Generalizations
- Bi-Hamiltonian Structure as a Shadow of Non-Noether Symmetry
- On the Oscillation of Solutions of First Order Differential Equations with Retarded Arguments
- Combinatorial Homology in a Perspective of Image Analysis
- Internal Crossed Modules
- Cochain Operations Defining Steenrod ⌣𝑖-Products in the Bar Construction
- On Maximal 𝑜𝑡-Subsets of the Euclidean Plane
- Inversion of the Cauchy Integral Taken over the Double Periodic Line
- Singular Integrals in Weighted Lebesgue Spaces with Variable Exponent
- Local Growth of Weierstrass σ-Function and Whittaker-Type Derivative Sampling
- Sturm–Liouville and Focal Higher Order BVPs with Singularities in Phase Variables
- On Some Convexity Properties of Generalized Cesáro Sequence Spaces
