mation smoothing, edge enhancement.

This program is part of

multiple pixels near the corresponding location in an input image.

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

the image and processes it according to the values of it and its sur-

rounding pixels. Rather than using a square block of surrounding pix-

els (e.g. the subject pixel and its 8 immediate neighbors, in a 3x3

square),

hexagons with the radius parameter. A radius value of 1/3 means that

the 7 hexagons essentially fit into the subject pixel (ie. there will

be no filtering effect). A radius value of 1.0 means that the 7

hexagons essentially cover the 3x3 immediate neighbor square.

Your choice of 'alpha' parameter selects among the three modes.

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 propor-

tional 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 parame-

ter to get the desired effect. This type of filter is best for filter-

ing 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 parame-

ter 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

the desired result. For instance to turn a monochrome dithered image

into a grayscale image you could try one or two passes of the smooth-

ing 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 declin-

ing alpha values are more effective than a single pass with a large

alpha value. As usual, there is a tradeoff between filtering effec-

tiveness 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 Jour-

nal, 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

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.

The parameters are:

Graeme W. Gill

netpbm documentation 24 October 2006 Pnmnlfilt User Manual(0)