
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
nonlinear 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 alphatrimmed 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", JongSen
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

