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.