pnmnlfilt General Commands Manual pnmnlfilt

### NAME

pnmnlfilt – non-linear filters: smooth, alpha trim mean, optimal esti‐

mation smoothing, edge enhancement.

### SYNOPSIS

pnmnlfilt alpha radius [pnmfile]

### DESCRIPTION

pnmnlfilt produces an output image where the pixels are a summary 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 oper‐

ating 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 3×3 block, 7 hexagonal area samples are

taken, the size of the hexagons being controlled by the radius parame‐

ter. 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 3×3 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 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 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 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. Sev‐

eral passes of the optimal estimation filter with declining alpha val‐

ues 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 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 Enhance‐

ment 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, 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, pnmconvol, pnm(5)

### BUGS

Integers and tables may overflow if PPM_MAXMAXVAL is greater than 255.

### AUTHOR

Graeme W. Gill graeme@labtam.oz.au

5 February 1993 pnmnlfilt