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Extended permutation filters and their application to edge enhancement
1Dept. of Electr. Eng., Dayton Univ., OH.
Summary
Extended permutation rank selection (EPRS) filters unify smoothing and edge enhancement. Including the sample mean in EPRS filters significantly improves edge enhancement capabilities, outperforming other sharpening filters.
Area of Science:
- Digital Image Processing
- Signal Processing
- Computer Vision
Background:
- Rank-order-based filters are crucial for image processing tasks like smoothing and edge enhancement.
- Existing filters often specialize in either smoothing or sharpening, lacking a unified framework.
- Extended permutation (EP) filters offer a new approach to filter design.
Purpose of the Study:
- To define and analyze extended permutation (EP) filters, with a focus on extended permutation rank selection (EPRS) filters.
- To demonstrate the edge enhancement capabilities of EPRS filters, particularly when incorporating the sample mean.
- To establish EPRS filters as a unifying framework for various existing rank-order-based filters.
Main Methods:
- Definition and theoretical analysis of Extended Permutation (EP) filters.
- Formulation of Extended Permutation Rank Selection (EPRS) filters using an extended observation vector (N samples + K statistics).
- Development of edge enhancement properties and an L(n) norm optimization procedure for EPRS filters.
- Comparative computer simulations to evaluate EPRS filter performance against existing sharpening filters.
Main Results:
- EPRS filters, when including the sample mean, exhibit excellent edge enhancement properties.
- Several existing edge enhancers (CS, LUM, WMMR) are shown to be subclasses of EPRS filters.
- EPRS filters provide a unified framework encompassing both smoothing and sharpening subclasses.
Conclusions:
- EPRS filters offer a versatile and unified framework for a wide range of rank-order-based image processing operations.
- The inclusion of the sample mean is key to achieving superior edge enhancement with EPRS filters.
- This novel class of filters unifies previously disparate smoothing and sharpening filter designs.
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