Statistical Estimators for Image
Combining
Mira provides many mathematical choices for
combining a set of images. This command produces a final image in
which the pixel at each coordinate is a mathematical combination of
the pixels at the same coordinate in all of the source images.
In considering the combining methods described
below, keep in mind that each method works by processing all the
values at each (column,row) location in turn. At each point, the
value is drawn from each image and combined using the selected
method to create 1 output pixel. This is repeated for each point
until the entire image is processed.
Averaging Methods
These methods vary from simple linear pixel merging
methods to non-linear weighted averaging methods. Use them to
Combine Image Set into a single, higher image having higher
signal-to-noise ratio.
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Mean
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Creates an image containing the arithmetic mean
value over all images at each point. The Mean method combines the
pixels as a straight average with no weighting or rejection of bad
values. This is the preferred method if the images can be
considered to contain only well-behaved statistical noise.
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Mean - Masked by 0
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Creates an image containing the mean value of
pixels from all images except those with a value of 0, which are
interpreted as "don't use". Pixels with a value of zero are not
included in calculating the mean value. See the
Image Registration command for an application of this
method. This also can be used in combination with the
Clean Image Set and
Apply Pixel Mask commands.
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Mean - Keyword weighted
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Weights the images by the value of a keyword
loaded from the image headers. For example, this might be used to
weight by exposure time using the EXPTIME keyword. The keyword name can be
specified and does not have to be a "standard" name.
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Sum of Values
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Creates an image containing the sum of the values
from all images at each point. If using this method, be sure the
output pixel type has greater sufficient numeric range to handle
the resulting values. For example, combining 100 16-bit images
having peak intensity of 50,000 may result in some output pixels
being as high as 5,000,000. Clearly 5,000,000 is not within the
0-65535 range of a 16-bit unsigned integer image. To handle this
change the output pixel type to 32-bit integer or 32-bit real.
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Rejection Methods
These methods remove deviant pixels from the sample
at each point. The result is a "cleaner" image of higher
signal-to-noise ratio and without abnormally bright or dark values.
Use these methods to Combine Image Set when some of the pixel
values are not from the same statistical population as the
majority.
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Mean - Min/Max Clipped
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Creates an image containing the mean value at each
point after rejection of the minimum and maximum values. At each
point, the minimum and maximum values are not included in computing
the mean value. This is an excellent way to remove noise by
discarding only 2 of the total number of images being combined. In
this method, even the statistically insignificant deviations, or
"true noise" at the extremes are rejected from the mean value. This
method works well for bad pixel rejection using a large number of
images in which it is likely that a dark or bright non-noise pixel
is likely to be found at most locations. If the number of images is
small, e.g., fewer than 5, do not use this method.
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Mean - Alpha Clipped
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This is a general case of the Min/Max clipping method. Here, you specify the
number of high values to clip and the number of low values to clip.
In comparison, the Min/Max method
rejects only the 1 highest and 1 lowest values.
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Mean - Sigma Clipped
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Creates an image containing the sigma-clipped mean
value over all images at each point. Sigma clipping discards high
and low extreme values in a way you can control with the clipping
Properties. This method requires a large number of images, on the
order of 20 or more in order to compute good clipping criteria at
each coordinate.
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Mean - Modified Trimmed
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Computes the Modified Trimmed Mean, which is a
hybrid of the sigma-clipped mean and median methods.
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Ranking Methods
These methods create a single image in which each
point contains the ranked value of pixels in all images.
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Median
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Creates an image containing the median values of all images at each point. This
method has good ability to reject extreme values. For a given
number of input images, the noise in the resulting image is not as
low as that which can result from Mean combining methods.
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Minimum
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Creates an image containing the minimum value of all images at each point. This
is a good way to bright artifacts that affect a large fraction of
the images at the same coordinates. For example, if 5 of 8 images
have large bright areas or defects, you can remove them using this
method. The advantage over simply throwing away the 5 images is
that there can still be some filtering done to areas that do not
show the bright defects.
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Maximum
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Creates an image containing the maximum value of all images at each point.
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Rank Statistic
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The rank statistic selects the pixel with the
desired percentile value from the
population of pixels at each location. For example, the median
method selects the pixels with 98th percentile rank and the minimum
method selects pixels with 0-th percentile rank. The Rank Statistic
method can select any of these by setting the percentile to value in the range of 0 to 100.
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Other Methods
These operations Combine Image Set to show
differences or particular details from among the image set. For
example, the combined image may contain the range of values in the
image set at every point.
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Range of Values
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Creates an image in which each pixel value is the
numeric range between the minimum and maximum values of all images
at that point. This method is useful for showing the variation
among images at each location.
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Standard Deviation
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Creates an image containing the standard deviation
among pixels at each point. This method is useful for measuring the
variation among similar images. This method requires at least 3
images. Also see the description of the "clipped" version of this
command.
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Standard Deviation, Clipped
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Creates an image of the standard deviation at each
pixel position, but excludes both the highest and lowest values at
each point. This is useful for measuring the variation among images
when the images contain randomly located transients such as cosmic
ray events. In addition, if a "dithered" set of images is
registered before using this command, it gives the
standard deviation independent of fixed pixel artifacts such as hot
and cold pixels and other defects that end up at different
coordinates after registration. Since this method discards the
minimum and maximum values, it requires at least 5 images.
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Related Topics
Combine Image Set
Combine Files
Image Registration
Region Statistics Estimators
Clean Image Set
Apply Pixel Mask
Statistics Properties
Mira Pro x64 User's Guide, Copyright Ⓒ 2023 Mirametrics, Inc. All
Rights Reserved.
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