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Family of Rank-Order Filters

Rank-order filters are spatial-domain nonlinear filters, which are based on the correction of the local histogram within the filtering window. There are many filters belonging to this family, as there are also many different implementations of them.

We utilize three powerful filters from the rank-order family with the supplement based on a combination of rank-order filtering and multi-valued nonlinear filtering.

A particular rank-order filter is defined by a method of local histogram correction. Rank-order filters are adaptive to the signal local statistics. Image processing with rank-order filters is reduced to the creation of the filtering interval from the limited number of pixels belonging to the filtering window with the further correction of the central pixel within the window using some kind of averaging of the selected pixels. Usually arithmetic mean, median, slicing and multi-valued mean are used as averaging methods.

A type of rank-order filter is defined by the method of the signal value selection, which composes a filtering interval. This interval contains some subset of the signal values set corresponding to the n x m local window around the analyzed pixel. As mentioned above, there are three rank-order filters: Rank-order EV filter, Rank-order KNV filter and Rank-order ER filter (classification of L. Yaroslavsky). These are also expanded by impulsive noise detector and remover.

Rank-order EV filter. A filtering interval for this filter is composed of all brightness values belonging to the pixels within the filtering window whose absolute difference from the central pixel brightness value is less than or equal to EV (which is a main control parameter for this filter). The most important property of this filter is that it smoothes the brightness jumps which are less than or equal to EV, and preserves the brightness jumps that are greater than EV. This property may be used for the highly effective preservation of image boundaries and small details from the smoothing. Knowing statistical characteristics of a type of noise, it is always possible to choose such an EV value that will ensure the effective noise reduction together with maximal preservation of image boundaries. The EV filter is highly effective for reduction of white noise. It is also dramatically effective for speckle noise reduction.

Rank-order ER filter. A filtering interval for this filter is composed of all brightness values belonging to the pixels within the filtering window whose rank difference from the central pixel brightness value rank in the variational series is less than or equal to ER, which is a main control parameter for this filter. This filter is effective for the reduction of complicated noise types with unknown statistics, and for the reduction of any complicated noise containing an impulsive component. The user keeps control over the filtering process using the parameter ER. The choice of the long filtering interval (larger ER) defines a strong filtering, while the choice of the short filtering interval (smaller ER) defines a light filtering.

Rank-order KNV filter. A filtering interval for this filter is composed of the number of brightness values (belonging to the pixels within the filtering window) which is equal to KNV and whose values are closest to the central pixel brightness value (KNV is a main control parameter for this filter). The most important property of this filter is that it smoothes only the objects whose area is less than the number of square pixels that are equal to KNV, and preserves the objects whose area is greater than KNV. This property may be used for the highly effective preservation of image boundaries and small details from the smoothing. Knowing the area of detailsthat must be preserved, it is always possible to choose such a KNV value to ensure the effective noise reduction together with maximal preservation of image boundaries. The KNV filter is highly effective for reduction of white noise. It is also very effective for the speckle noise reduction.

It should be also noted that rank-order filters can be used iteratively (especially EV and KNV filters) to get better results both from the point of view of noise reduction and preservation of image boundaries.

Examples

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White Noise Reduction

Input noisy image, PSNR=5.3 Rank-order EV multi-valued filtering, 3x3 window, EV=30. (The image boundaries are preserved with the highest accuracy PSNR=8.28) Rank-order KNV multi-valued filtering, 5x5, KNV=12. (The image boundaries are preserved with the highest accuracy PSNR=10.09)

 

Multi-valued nonlinear filtering Overview of the Original Image Processing Algorithms Nonlinear Image processing Combined Spatial-Frequency Domain Two-Stage Filtering

 

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Last Updated
Mon, November 01, 2009 13:18