Family of RankOrder Filters
Rankorder filters are spatialdomain 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
rankorder family with the supplement based on a combination
of rankorder filtering and multivalued nonlinear filtering.
A particular rankorder filter is defined
by a method of local histogram correction. Rankorder filters
are adaptive to the signal local statistics. Image processing
with rankorder 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 multivalued mean are used as averaging methods.
A type of rankorder 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 rankorder filters: Rankorder EV filter,
Rankorder KNV filter and Rankorder ER filter
(classification of L. Yaroslavsky). These are also expanded
by impulsive noise detector and remover.
Rankorder 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.
Rankorder 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.
Rankorder 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 rankorder 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 
Rankorder EV multivalued filtering,
3x3 window, EV=30. (The image boundaries are preserved
with the highest accuracy PSNR=8.28) 
Rankorder KNV multivalued filtering, 5x5, KNV=12.
(The image boundaries are preserved with the highest
accuracy PSNR=10.09) 
