# Permutation weighted order statistic filter lattices

@article{Arce1995PermutationWO, title={Permutation weighted order statistic filter lattices}, author={Gonzalo R. Arce and Timothy A. Hall and Kenneth E. Barner}, journal={IEEE transactions on image processing : a publication of the IEEE Signal Processing Society}, year={1995}, volume={4 8}, pages={ 1070-83 } }

We introduce and analyze a new class of nonlinear filters called permutation weighted order statistic (PWOS) filters. These filters extend the concept of weighted order statistic (WOS) filters, in which filter weights associated with the input samples are used to replicate the corresponding samples, and an order statistic is chosen as the filter output. PWOS filters replicate each input sample according to weights determined by the temporal-order and rank-order of samples within a window. Hence…

## 27 Citations

### Permutation filters: a class of nonlinear filters based on set permutations

- Engineering, MathematicsIEEE Trans. Signal Process.
- 1994

An adaptive design algorithm that minimizes the mean absolute error criterion is described as well as a more flexible adaptive algorithm that attains the optimal permutation filter under a deterministic least normed error criterion.

### Design of permutation order statistic filters through group colorings

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In this paper, we develop a group theoretic method for reducing the class cardinality of Permutation (P) filters. P filters are a recently introduced class of nonlinear filters that have their roots…

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The proposed filtering approach can effectively address a number of signal and image processing applications that require robust bandpass or highpass operations where the underlying contamination follows a nonsymmetric heavy-tailed distribution.

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- 2001

By exploiting fuzzy methodologies real-valued SR orderings can be defined that not only relate the spatial and rank orderings of samples, but also includes information on sample spread.

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- Computer ScienceIEEE Transactions on Image Processing
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The experimental results show that the F-LUM smoothers can achieve a better tradeoff between noise removal and detail preservation than the Lum smoothers, and shows that utilizing fuzzy ranks in filter generalization is a promising methodology.

### The fuzzy transformation and its applications in image processing

- Computer ScienceIEEE Transactions on Image Processing
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The fuzzy transformation (FZT) is introduced, which refers to the mapping of the crisp samples, order statistics, and SR ordering indexes to their fuzzy counterparts, and the element invariant and order invariant properties of the FZT are established.

### Characterization of WOSF by Equivalent Classes through Support Vector Machine

- Mathematics, Computer ScienceJ. Inf. Sci. Eng.
- 2011

A different representation of WOSF induced from SVM is proposed, and equivalent classes for WOSf are constructed based on the maximal margin classification of SVM.

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- Computer Science1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings
- 1996

Generalized selection probabilities are introduced in order to achieve even faster implementations for PCDOS-filters via using generalized orderings by stack filter banks.

### Weighted median image sharpeners for the World Wide Web

- Computer ScienceIEEE Trans. Image Process.
- 2002

A class of robust weighted median (WM) sharpening algorithms is developed that can prove useful in the enhancement of compressed or noisy images posted on the World Wide Web as well as in other applications where the underlying images are unavoidably acquired with noise.

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