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## Helplog #38 -- zscale, display and autoscaling

- Monday, December 05 2005 @ 11:23 PM GMT
- Contributed by: admin
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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.

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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