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Flat zones filtering, connected operators, and filters by reconstruction
1Dept. de Teoria del Senyal i Comunicacions, Univ. Politecnica de Catalunya, Barcelona.
Summary
This study introduces connected operators for functions, extending set-based definitions. These operators enlarge flat zones in functions, enabling nested structures and applications in image processing via filters by reconstruction.
Area of Science:
- Mathematical Morphology
- Image Analysis
- Set Theory
Background:
- Connected operators are fundamental in image analysis and mathematical morphology.
- Extending these operators from sets to functions is crucial for advanced image processing tasks.
Purpose of the Study:
- To extend the concept of connected operators from sets to functions.
- To introduce and formalize the concept of pyramids based on connected operators.
- To define and present properties of filters by reconstruction.
Main Methods:
- Definition of connected operators acting on functions by extending set-based definitions.
- Formal introduction of pyramids constructed using connected operators.
- Definition of filters by reconstruction and analysis of their properties.
Main Results:
- A method to construct connected operators for functions from set-based operators is presented.
- Pyramids based on connected operators exhibit increasing flat zones at higher levels (nested flat zones).
- Properties of filters by reconstruction are defined and illustrated.
Conclusions:
- Connected operators offer a powerful framework for analyzing and transforming functions, particularly concerning their flat zones.
- The proposed pyramid structures and filters by reconstruction have potential applications in image analysis and signal processing.
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