# 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

- Mathematics
- 1997

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…

### Frequency selective filtering using weighted order statistic admitting real-valued weights

- Computer Science
- 2010

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.

### Fuzzy Ordering Theory and Its Use in Filter Generalization

- Computer ScienceEURASIP J. Adv. Signal Process.
- 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.

### Multiresolution permutation filters based on decision trees

- MathematicsProceedings 2000 International Conference on Image Processing (Cat. No.00CH37101)
- 2000

A more general multiresolution approach based on decision trees is developed that allows the level of ordering information utilized to automatically adjust to the problem at hand.

### Fuzzy Rank LUM Filters

- Computer ScienceIEEE Transactions on Image Processing
- 2006

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 Generalization of WOSF and Corresponding Outputs

- Computer Science, MathematicsJ. Softw.
- 2010

This paper constructs equivalent classes of WOSF, the BF equivalent class and the global equivalent class, and proposes 3 translated formulas to fast generate corresponding outputs of BF equivalent classes, not perform extra machine training or mathematical computation.

### 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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