Alpha trimmed mean filter. (0.0 <= alpha <= 0.5)
The value of the center pixel
will be replaced by the mean of the 7 hexagon values, but
the 7 values are sorted by size and the top and bottom alpha
portion of the 7 are excluded from the mean. This implies
that an alpha value of 0.0 gives the same sort of output as
a normal convolution (ie. averaging or smoothing filter),
where radius will determine the "strength" of the
filter. A good value to start from for subtle filtering is
alpha = 0.0, radius = 0.55 For a more blatant effect, try
alpha 0.0 and radius 1.0
An alpha value
of 0.5 will cause the median value of the 7 hexagons to be
used to replace the center pixel value. This sort of filter
is good for eliminating "pop" or single pixel
noise from an image without spreading the noise out or
smudging features on the image. Judicious use of the radius
parameter will fine tune the filtering. Intermediate values
of alpha give effects somewhere between smoothing and
"pop" noise reduction. For subtle filtering try
starting with values of alpha = 0.4, radius = 0.6 For a more
blatant effect try alpha = 0.5, radius = 1.0
Optimal estimation smoothing. (1.0 <= alpha <= 2.0)
This type of
filter applies a smoothing filter adaptively over the image.
For each pixel the variance of the surrounding hexagon
values is calculated, and the amount of smoothing is made
inversely proportional to it. The idea is that if the
variance is small then it is due to noise in the image,
while if the variance is large, it is because of
"wanted" image features. As usual the radius
parameter controls the effective radius, but it probably
advisable to leave the radius between 0.8 and 1.0 for the
variance calculation to be meaningful. The alpha parameter
sets the noise threshold, over which less smoothing will be
done. This means that small values of alpha will give the
most subtle filtering effect, while large values will tend
to smooth all parts of the image. You could start with
values like alpha = 1.2, radius = 1.0 and try increasing or
decreasing the alpha parameter to get the desired effect.
This type of filter is best for filtering out dithering
noise in both bitmap and color images.
Edge enhancement. (-0.1 >= alpha >= -0.9)
This is the
opposite type of filter to the smoothing filter. It enhances
edges. The alpha parameter controls the amount of edge
enhancement, from subtle (-0.1) to blatant (-0.9). The
radius parameter controls the effective radius as usual, but
useful values are between 0.5 and 0.9. Try starting with
values of alpha = 0.3, radius = 0.8
Combination use.
The various
modes of pnmnlfilt can be used one after the other to
get the desired result. For instance to turn a monochrome
dithered image into a grayscale image you could try one or
two passes of the smoothing filter, followed by a pass of
the optimal estimation filter, then some subtle edge
enhancement. Note that using edge enhancement is only likely
to be useful after one of the non-linear filters (alpha
trimmed mean or optimal estimation filter), as edge
enhancement is the direct opposite of smoothing.
For reducing
color quantization noise in images (ie. turning .gif files
back into 24 bit files) you could try a pass of the optimal
estimation filter (alpha 1.2, radius 1.0), a pass of the
median filter (alpha 0.5, radius 0.55), and possibly a pass
of the edge enhancement filter. Several passes of the
optimal estimation filter with declining alpha values are
more effective than a single pass with a large alpha value.
As usual, there is a tradeoff between filtering
effectiveness and loosing detail. Experimentation is
encouraged.
References:
The
alpha-trimmed mean filter is based on the description in
IEEE CG&A May 1990 Page 23 by Mark E. Lee and Richard A.
Redner, and has been enhanced to allow continuous alpha
adjustment.
The optimal
estimation filter is taken from an article "Converting
Dithered Images Back to Gray Scale" by Allen Stenger,
Dr Dobb’s Journal, November 1992, and this article
references "Digital Image Enhancement and Noise
Filtering by Use of Local Statistics", Jong-Sen Lee,
IEEE Transactions on Pattern Analysis and Machine
Intelligence, March 1980.
The edge
enhancement details are from pgmenhance(1), which is taken
from Philip R. Thompson’s "xim" program,
which in turn took it from section 6 of "Digital
Halftones by Dot Diffusion", D. E. Knuth, ACM
Transaction on Graphics Vol. 6, No. 4, October 1987, which
in turn got it from two 1976 papers by J. F. Jarvis et.
al.
SEE ALSO
pgmenhance(1),
pnmconvol(1), pnm(5)
BUGS
Integers and
tables may overflow if PPM_MAXMAXVAL is greater than
255.
AUTHOR
Graeme W. Gill
graeme@labtam.oz.au
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pnmnlfilt(1) |
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