Non-linear image processing Page: 2 of 9
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NON-LINEAR IMAGE PROCESSING
P. R. Bell, R. S. Dillon, and M. R. Bell
Linear image smoothing methods are often applied to data with low
statistical weight to improve the quality of the image so that details of the
imaged structure will be more apparent to the observer. One effect of such
smoothing, although details may be more visible, is the lumpy or "buttermilk"
appearance of regions of the image that were expected to be smooth. This effect
is produced by the removal of higher frequency noise components that had con-
cealed these lower frequency components of the statistical fluctuation of the
data. In essence, a data point that is so high or low as to have low probabil-
ity will likely be surrounded by points closer to the mean and will appear
in the processed image as a positive or negative delta function response of
the processing function superimposed on a mildly fluctuating background. If
the processing function has been chosen to fit the resolution of the imaging
system for optimum signal/noise ratios, these noise lumps will resemble the
image of a point source. Linear methods, whether in the signal or frequency
domains, are powerless to suppress these fluctuation effects.
It was noted that data bounding, that is, the modification of data points
of statistically improbably high or low values, had a noticeable beneficial
effect upon the mottling or "buttermilk" effect in images with low counting
rate. A recent article by Rempel (1) detailing an inherently non-linear pro-
cedure approximating a least-difference method demonstrated a strong beneficial
effect in the smoothing of geophysical data. Data bounding is clearly a sort
of black and white version of this method when applied using a least-squares
fit against which to test the data points to be bounded.
Our bounding method performs a least-squares fit of a two-dimensional
quadratic (or quartic) equation to a 7 x 7 (or 5 x 5) element array of tha data
at each point (2). The routine compares the data value with the fitted value
0.7, 1.0, or 1.4 times the square root of the fitted value. If the data
point lies outside the chosen range, it is replaced by the fitted value; other-
wise it is left unchanged.
A 64 x 32 element field (2048 points) of Poisson distribution noise with
n = 5 was prepared as a test object with a "detail," a 3 x 20 element bar of
n = 8 noise. The FOCAL program used to produce this noise is gihen in Fig. 1.
The random number generator used was the FRAN8 (DECUS FOCAL 8-150) not the
standard FRAN FOCAL function which is not sufficiently random for this use.
Figure 2 displays this raw noise field together with a Z-cut of the line through
the long dimension of the signal bar. The background corresponds to a level of
45 counts/cm2 in the usual 3-element/cm camera image while the signal bar
corresponds to a 1 cm x 7 cm area at 72 counts/cm2. The image was processed
by multiple passes of various processing methods: 1) The usual 9-point (3 x 3)
averaging, marked A4 in the image tags; 2) a 7 x 7 element Gaussian averager
(Table 1) indicated as A5 in the tags; 3) a 7 x. 7 element least-squares
quadratic (Table 2) indicated as A2 in the tags. All these smoothers have a
weight of 4 in the program so that the resulting processed data can display the
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Bell, P.R.; Dillon, R.S. & Bell, M.R. Non-linear image processing, article, January 1, 1976; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc864758/m1/2/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.