pnmnlfilt - non-linear filters: smooth, alpha trim mean, optimal estimation smoothing,
pnmnlfilt alpha radius [pnmfile]
This is something of a swiss army knife filter. It has 3 distinct operating modes. In all
of the modes each pixel in the image is examined and processed according to it and its
surrounding pixels values. Rather than using the 9 pixels in a 3x3 block, 7 hexagonal area
samples are taken, the size of the hexagons being controlled by the radius parameter. A
radius value of 0.3333 means that the 7 hexagons exactly fit into the center pixel (ie.
there will be no filtering effect). A radius value of 1.0 means that the 7 hexagons
exactly fit a 3x3 pixel array.
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 fil-
tering 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 mean-
ingful. 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
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 fil-
ter, 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 encour-
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 adjust-
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 refer-
ences "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. Thomp-
son'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.
pgmenhance(1), pnmconvol(1), pnm(5)
Integers and tables may overflow if PPM_MAXMAXVAL is greater than 255.
Graeme W. Gill firstname.lastname@example.org
5 February 1993 pnmnlfilt(1)