Updated: 5 February 1993

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This program works on multi-image streams.

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.

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

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.

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
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.

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.