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Helplog #38 -- zscale, display and autoscaling

  • Monday, December 05 2005 @ 11:23 PM GMT
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Help Logs/Tips Question: I can't find a description of the 'zscale' scaling algorithm anywhere.Do you have a reference for how it determines the proper scaling of the pixels?

NUMBER: 38
KEYWORDS: zscale, display, autoscaling
DATE: Mon Dec 5 15:37:00 MST 2005
FROM: valdes

Q: I can't find a description of the 'zscale' scaling algorithm anywhere.
Do you have a reference for how it determines the proper scaling of
the pixels?


A: The algorithm is described in the IRAF help for the DISPLAY task
in a section on the algorithm. I include the section below for your
convenience. In summary, the algorithm consists of selecting a subset
of pixels (using masks if defined to exclude data), sorting the values,
chopping off the ends, and fitting a linear function.


>From the DISPLAY help page:

ZSCALE ALGORITHM
The zscale algorithm is designed to display the image values near
the median image value without the time consuming process of
computing a full image histogram. This is particularly useful for
astronomical images which generally have a very peaked histogram
corresponding to the background sky in direct imaging or the
continuum in a two dimensional spectrum.

The sample of pixels, specified by values greater than zero in the
sample mask zmask or by an image section, is selected up to a
maximum of nsample pixels. If a bad pixel mask is specified by the
bpmask parameter then any pixels with mask values which are greater
than zero are not counted in the sample. Only the first pixels up
to the limit are selected where the order is by line beginning from
the first line. If no mask is specified then a grid of pixels with
even spacing along lines and columns that make up a number less
than or equal to the maximum sample size is used.

If a contrast of zero is specified (or the zrange flag is used and
the image does not have a valid minimum/maximum value) then the
minimum and maximum of the sample is used for the intensity mapping
range.

If the contrast is not zero the sample pixels are ranked in
brightness to form the function I(i) where i is the rank of the
pixel and I is its value. Generally the midpoint of this function
(the median) is very near the peak of the image histogram and there
is a well defined slope about the midpoint which is related to the
width of the histogram. At the ends of the I(i) function there are
a few very bright and dark pixels due to objects and defects in the
field. To determine the slope a linear function is fit with
iterative rejection;

I(i) = intercept + slope * (i - midpoint)

If more than half of the points are rejected then there is no well
defined slope and the full range of the sample defines z1 and z2.
Otherwise the endpoints of the linear function are used (provided
they are within the original range of the sample):

z1 = I(midpoint) + (slope / contrast) * (1 - midpoint)
z2 = I(midpoint) + (slope / contrast) * (npoints - midpoint)

As can be seen, the parameter contrast may be used to adjust the
contrast produced by this algorithm.


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