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Optimal filtering of digital binary images corrupted by union/intersection noise.
N D Sidiropoulos1, J S Baras, C A Berenstein
1Inst. for Syst. Res., Maryland Univ., College Park, MD.
Summary
This study models digital images as discrete random sets and develops optimal filters for noise removal. Morphological filters are shown to be effective MAP estimators for degraded images, offering universal optimality characterizations.
Area of Science:
- Mathematical imaging
- Set theory
- Image processing
Background:
- Digital images are modeled as discrete random sets on finite lattices.
- Image degradation is addressed using a union/intersection noise model.
- Estimating degraded discrete random sets is a key challenge.
Purpose of the Study:
- To develop optimal filtering approaches for estimating degraded discrete random sets.
- To analyze mask filters and morphological filters for image restoration.
- To establish universal characterizations of filter optimality.
Main Methods:
- Modeling digital binary images as uniformly bounded discrete random sets.
- Applying set-theoretic analysis to derive optimal mask filters.
- Investigating morphological filters (openings, closings) as MAP estimators.
- Expanding optimal filters for universal optimality characterizations.
Main Results:
- Two optimal filtering approaches: mask filters and morphological filters.
- Morphological operations (openings, closings, unions, intersections) are MAP estimators under i.i.d. noise.
- Universal characterizations of filter optimality are achieved without strong spatial assumptions.
- The methods are generalizable to gray-level images.
Conclusions:
- Optimal filtering strategies for discrete random sets are presented.
- Morphological filters provide effective MAP estimation for image restoration.
- The developed framework offers robust and generalizable image restoration techniques.
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