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A generalized fuzzy mathematical morphology and its application in robust 2-D and 3-D object representation
1Dept. of Inf., Aristotelian Univ. of Thessaloniki, Thessaloniki, Greece. chatzis@zeus.csd.auth.gr
Summary
A novel generalized fuzzy mathematical morphology (GFMM) was developed using a fuzzy inclusion indicator (FII). GFMM offers a flexible tool for object analysis, outperforming binary morphology in reconstruction tasks.
Area of Science:
- Computer Science
- Image Processing
- Fuzzy Logic
Background:
- Mathematical morphology is crucial for image analysis.
- Existing methods like binary and grayscale morphology have limitations.
- Fuzzy set theory offers potential for more robust image processing.
Purpose of the Study:
- To introduce a Generalized Fuzzy Mathematical Morphology (GFMM).
- To define a novel Fuzzy Inclusion Indicator (FII) for measuring set inclusion.
- To demonstrate GFMM's advantages in object analysis and reconstruction.
Main Methods:
- Definition of a new Fuzzy Inclusion Indicator (FII) as a fuzzy set.
- Development of Generalized Fuzzy Mathematical Morphology (GFMM) axioms.
- Application of GFMM to skeletonization and shape decomposition of 2D and 3D objects.
Main Results:
- The proposed FII satisfies extended axioms for inclusion indicators.
- GFMM encompasses binary and grayscale morphology as special cases.
- GFMM-based object reconstruction from skeletal subsets showed superior performance compared to binary morphology.
Conclusions:
- GFMM is a powerful and flexible tool for morphological operations.
- GFMM effectively preserves shape and location during skeletonization and decomposition.
- GFMM provides enhanced object reconstruction capabilities.
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