imcombine input output
input
List of input images to combine. All images must have the same dimensionality
but they may be of different sizes.
output
Output combined image or list of images. If the project parameter is
no then there will be one output image while if it is yes there will be one
output image for each input image.
plfile = (optional)
Output pixel list file or list of files. If no name is given or the
list ends prematurely then no file is produced. The pixel list file
is a map of the number of pixels rejected or, equivalently,
the total number of input images minus the number of pixels actually used.
The file name is also added to the output image header under the
keyword BPM.
sigma = (optional)
Output sigma image or list of images. If no name is given or the list ends
prematurely then no image is produced. The sigma is standard deviation,
corrected for a finite population, of the input pixel values (excluding
rejected pixels) about the output combined pixel values.
logfile = STDOUT (optional)
Output log file. If no file is specified then no log information is produced.
The special filename "STDOUT" prints log information to the terminal.
combine = average (average|median)
Type of combining operation performed on the final set of pixels (after
offsetting, masking, thresholding, and rejection). The choices are
"average" or "median". The median uses the average of the two central
values when the number of pixels is even.
reject = none (none|minmax|ccdclip|crreject|sigclip|avsigclip|pclip)
Type of rejection operation performed on the pixels remaining after offsetting,
masking and thresholding. The algorithms are described in the
DESCRIPTION section. The rejection choices are:
none - No rejection
minmax - Reject the nlow and nhigh pixels
ccdclip - Reject pixels using CCD noise parameters
crreject - Reject only positive pixels using CCD noise parameters
sigclip - Reject pixels using a sigma clipping algorithm
avsigclip - Reject pixels using an averaged sigma clipping algorithm
pclip - Reject pixels using sigma based on percentiles
project = no
Project (combine) across the highest dimension of the input images? If
no then all the input images are combined to a single output image. If
yes then the highest dimension elements of each input image are combined to
an output image and optional pixel list and sigma images. Each element of
the highest dimension may have a separate offset but there can only be one
mask image.
outtype = real (short|ushort|integer|long|real|double)
Output image pixel datatype. The pixel datatypes are "double", "real",
"long", "integer", unsigned short "ushort", and "short" with highest
precedence first. If none is specified then the highest precedence
datatype of the input images is used. The datatypes may be abbreviated to
a single character.
offsets = none (none|grid|
Input image offsets. The offsets may be specified in a file consisting
of one line per image with the offsets in each dimension forming the
columns. The special case of a grid may be specified by the string:
grid [n1] [s1] [n2] [s2] ...
where ni is the number of images in dimension i and si is the step in dimension i. For example "grid 5 100 5 100" specifies a 5x5 grid with origins offset by 100 pixels.
masktype = none (none|goodvalue|badvalue|goodbits|badbits)
Type of pixel masking to use. If "none" then no pixel masking is done
even if an image has an associated pixel mask. The other choices
are to select the value in the pixel mask to be treated as good
(goodvalue) or bad (badvalue) or the bits (specified as a value)
to be treated as good (goodbits) or bad (badbits). The pixel mask
file name comes from the image header keyword BPM.
maskvalue = 0
Mask value used with the masktype parameter. If the mask type
selects good or bad bits the value may be specified using IRAF notation
for decimal, octal, or hexidecimal; i.e 12, 14b, 0cx to select bits 3
and 4.
blank = 0.
Output value to be used when there are no pixels.
scale = none (none|mode|median|mean|exposure|@
Multiplicative image scaling to be applied. The choices are none, multiply
by the reciprocal of the mode, median, or mean of the specified statistics
section, multiply by the reciprocal of the exposure time in the image header,
multiply by the values in a specified file, or multiply by a specified
image header keyword. When specified in a file the scales must be one per
line in the order of the input images.
zero = none (none|mode|median|mean|@
Additive zero level image shifts to be applied. The choices are none, add
the negative of the mode, median, or mean of the specified statistics
section, add the values given in a file, or add the values given by an
image header keyword. When specified in a file the zero values must be one
per line in the order of the input images.
weight = none (none|mode|median|mean|exposure|@
Weights to be applied during the final averaging. The choices are none,
the mode, median, or mean of the specified statistics section, the exposure
time, values given in a file, or values given by an image header keyword.
When specified in a file the weights must be one per line in the order of
the input images.
statsec =
Section of images to use in computing image statistics for scaling and
weighting. If no section is given then the entire region of the input is
sampled (for efficiency the images are sampled if they are big enough).
When the images are offset relative to each other one can precede the image
section with one of the modifiers "input", "output", "overlap". The first
interprets the section relative to the input image (which is equivalent to
not specifying a modifier), the second interprets the section relative to
the output image, and the last selects the common overlap and any following
section is ignored.
expname =
Image header keyword to be used with the exposure scaling and weighting
options. Also if an exposure keyword is specified that keyword will be
added to the output image using a weighted average of the input exposure
values.
nlow = 1, nhigh = 1 (minmax)
The number of low and high pixels to be rejected by the "minmax" algorithm.
These numbers are converted to fractions of the total number of input images
so that if no rejections have taken place the specified number of pixels
are rejected while if pixels have been rejected by masking, thresholding,
or nonoverlap, then the fraction of the remaining pixels, truncated
to an integer, is used.
nkeep = 1
The minimum number of pixels to retain or the maximum number to reject
when using the clipping algorithms (ccdclip, crreject, sigclip,
avsigclip, or pclip). When given as a positive value this is the minimum
number to keep. When given as a negative value the absolute value is
the maximum number to reject. The latter is in addition to pixels
missing due to non-overlapping offsets, bad pixel masks, or thresholds.
mclip = yes (ccdclip, crreject, sigclip, avsigcliip)
Use the median as the estimate for the true intensity rather than the
average with high and low values excluded in the "ccdclip", "crreject",
"sigclip", and "avsigclip" algorithms? The median is a better estimator
in the presence of data which one wants to reject than the average.
However, computing the median is slower than the average.
lsigma = 3., hsigma = 3. (ccdclip, crreject, sigclip, avsigclip, pclip)
Low and high sigma clipping factors for the "ccdclip", "crreject", "sigclip",
"avsigclip", and "pclip" algorithms. They multiply a "sigma" factor
produced by the algorithm to select a point below and above the average or
median value for rejecting pixels. The lower sigma is ignored for the
"crreject" algorithm.
rdnoise = 0. , gain = 1. , snoise = 0. (ccdclip, crreject)
CCD readout noise in electrons, gain in electrons/DN, and sensitivity noise
as a fraction. These parameters are used with the "ccdclip" and "crreject"
algorithms. The values may be either numeric or an image header keyword
which contains the value.
sigscale = 0.1 (ccdclip, crreject, sigclip, avsigclip)
This parameter determines when poisson corrections are made to the
computation of a sigma for images with different scale factors. If all
relative scales are within this value of unity and all relative zero level
offsets are within this fraction of the mean then no correction is made.
The idea is that if the images are all similarly though not identically
scaled, the extra computations involved in making poisson corrections for
variations in the sigmas can be skipped. A value of zero will apply the
corrections except in the case of equal images and a large value can be
used if the sigmas of pixels in the images are independent of scale and
zero level.
pclip = -0.5 (pclip)
Percentile clipping algorithm parameter. If greater than
one in absolute value then it specifies a number of pixels above or
below the median to use for computing the clipping sigma. If less
than one in absolute value then it specifies the fraction of the pixels
above or below the median to use. A positive value selects a point
above the median and a negative value selects a point below the median.
The default of -0.5 selects approximately the quartile point.
See the DESCRIPTION section for further details.
grow = 0
Number of pixels to either side of a rejected pixel along image lines
to also be rejected. This applies only to pixels rejected by one of
the rejection algorithms and not the masked or threshold rejected pixels.
A set of images or the highest dimension elements (for example the planes in an image cube) are combined by weighted averaging or medianing. Pixels may be rejected from the combining by using pixel masks, threshold levels, and rejection algorithms. The images may be scaled multiplicatively or additively based on image statistics, image header keywords, or text files before rejection. The images may be combined with integer pixel coordinate offsets to produce an image bigger than any of the input images.
The input images to be combined are specified by a list. If the project parameter is yes then the highest dimension elements of each input image are combined to make an output image of one lower dimension. There is no limit to the number of elements combined in this case. If project is no then the entire input list is combined to form a single output image. In this case the images must all have the same dimensionality but they may have different sizes. There is a software limit of approximately 100 images in this case.
The output image header is a copy of the first image in the combined set. In addition, the number of images combined is recorded under the keyword NCOMBINE, an image header keyword selected by the expname parameters (which is usually an exposure time) is updated as the weighted average of the input header keywords, and any pixel list file created is recorded under the keyword BPM. The output pixel type is set by the parameter outtype. If left blank then the input datatype of highest precision is used.
In addition to one or more output combined images there may also be a pixel list image containing the number of pixels rejected at each point in the output image, an image containing the sigmas of the pixels combined about the final output combined pixels, and a log file. The pixel list image is in the compact pixel list format which can be used as an image in other programs. The sigma computation is the standard deviation corrected for a finite population (the n/(n-1) factor) including weights if a weighted average is used.
An outline of the steps taken by the program is given below and the following sections elaborate on the steps.
o Set the input image offsets and the final output image size. o Set the input image scales and weights o Write the log file output
For each output image line:
o Get input image lines that overlap the output image line o Reject masked pixels o Reject pixels outside the threshold limits o Reject pixels using the specified algorithm o Reject neighboring pixels along each line o Combine remaining pixels using the weighted average or median o Compute sigmas of remaining pixels about the combined values o Write the output image line, rejected pixel list, and sigmas
OFFSETS
The images to be combined need not be of the same size or overlap. They do have to have the same dimensionality which will also be the dimensionality of the output image. Any dimensional images supported by IRAF may be used. Note that if the project flag is yes then the input images are the elements of the highest dimension; for example the planes of a three dimensional image.
The overlap of the images is determined by a set of integer pixel offsets with an offset for each dimension of each input image. For example offsets of 0, 10, and 20 in the first dimension of three images will result in combining the three images with only the first image in the first 10 colums, the first two images in the next 10 columns and all three images starting in the 21st column. At the 21st output column the 21st column of the first image will be combined with the 11th column of the second image and the 1st column of the third image.
The output image size is set by the maximum extent in each dimension of any input image after applying the offsets. In the above example if all the images have 100 columns then the output image will have 120 columns corresponding to the 20 column offset in the third image.
The input image offsets are set using the offset parameter. There are three ways to specify the offsets. If the word "none" or the empty string "" are used then all offsets will be zero and all pixels with the same coordinates will be combined. The output image size will be equal to the biggest dimensions of the input images.
If the input images have offsets in a regular grid or one wants to make an output image in which the input images are "mosaiced" together in a grid then the special offset string beginning with the word "grid" is used. The format is
grid [n1] [s1] [n2] [s2] ...
where ni is the number of images in dimension i and si is the step in dimension i. For example "grid 5 100 5 100" specifies a 5x5 grid with origins offset by 100 pixels. Note that one must insure that the input images are specified in the correct order. This may best be accomplished using a "@" list. One useful application of the grid is to make a nonoverlapping mosaic of a number of images for display purposes. Suppose there are 16 images which are 100x100. The offset string "grid 4 101 4 101" will produce a mosaic with a one pixel border having the value set by blank parameter between the images.
The offsets may be defined in a file by specifying the file name in the offset parameter. (Note that the special file name STDIN may be used to type in the values terminated by the end-of-file character). The file consists of a line for each input image. The lines must be in the same order as the input images and so an "@" list may be useful. The lines consist of whitespace separated offsets one for each dimension of the images. In the first example cited above the offset file might contain:
0 0 10 0 20 0
where we assume the second dimension has zero offsets.
The offsets need not have zero for one of the images. The offsets may include negative values or refer to some arbitrary common point. When the offsets are read by the program it will find the mininum value in each dimension and subtract it from all the other offsets in that dimension. The above example could also be specified as:
225 15 235 15 245 15
There may be cases where one doesn't want the mininum offsets reset to zero. If all the offsets are positive and the comment "# Absolute" appears in the offset file then the images will be combined with blank values between the first output pixel and the first overlapping input pixel. Continuing with the above example, the file
# Absolute 10 10 20 10 30 10
will have the first pixel of the first image in the 11th pixel of the output image. Note that there is no way to "pad" the other side of the output image.
SCALES AND WEIGHTS
In order to combine images with rejection of pixels based on deviations from some average or median they must be scaled to a common level. There are two types of scaling available, a multiplicative intensity scale and an additive zero point shift. The intensity scaling is defined by the scale parameter and the zero point shift by the zero parameter. These parameters may take the values "none" for no scaling, "mode", "median", or "mean" to scale by statistics of the image pixels, "exposure" (for intensity scaling only) to scale by the exposure time keyword in the image header, any other image header keyword specified by the keyword name prefixed by the character '!', and the name of a file containing the scale factors for the input image prefixed by the character '@'.
Examples of the possible parameter values are shown below where "myval" is the name of an image header keyword and "scales.dat" is a text file containing a list of scale factors.
scale = none No scaling zero = mean Intensity offset by the mean scale = exposure Scale by the exposure time zero = !myval Intensity offset by an image keyword scale = @scales.dat Scales specified in a file
The image statistics are computed by sampling a uniform grid of points with the smallest grid step that yields less than 10000 pixels; sampling is used to reduce the time needed to compute the statistics. If one wants to restrict the sampling to a region of the image the statsec parameter is used. This parameter has the following syntax:
[input|output|overlap] [image section]
The initial modifier defaults to "input" if absent. The modifiers are useful if the input images have offsets. In that case "input" specifies that the image section refers to each input image, "output" specifies that the image section refers to the output image coordinates, and "overlap" specifies the mutually overlapping region of the input images. In the latter case an image section is ignored.
The statistics are as indicated by their names. In particular, the mode is a true mode using a bin size which is a fraction of the range of the pixels and is not based on a relationship between the mode, median, and mean. Also masked pixels are excluded from the computations as well as during the rejection and combining operations.
The "exposure" option in the intensity scaling uses the value of the
image header keyword specified by the expname keyword. As implied
by the parameter name, this is typically the image exposure time since
intensity levels are linear with the exposure time in CCD detectors.
Note that the exposure keyword is also updated in the final image
as the weighted average of the input values. Thus, if one wants to
use a nonexposure time keyword and keep the exposure time updating
feature the image header keyword syntax is available; i.e. !
Scaling values may be defined as a list of values in a text file. The file
name is specified by the standard @file syntax. The list consists of one
value per line. The order of the list is assumed to be the same as the
order of the input images. It is a fatal error if the list is incomplete
and a warning if the list appears longer than the number of input images.
Because the scale and zero levels are adjusted only the relative
values are important.
If both an intensity scaling and zero point shift are selected the
multiplicative scaling is done first. Use of both makes sense
if the intensity scaling is the exposure time to correct for
different exposure times and then the zero point shift allows for
sky brightness changes.
The image statistics and scale factors are recorded in the log file
unless they are all equal, which is equivalent to no scaling. The
intensity scale factors are normalized to a unit mean and the zero
point shifts are adjust to a zero mean. When scale factors or
zero point shifts are specifed by the user in an @file or
by an image header keyword no normalization is done.
Scaling affects not only the mean values between images but also the
relative pixel uncertainties. For example scaling an image by a
factor of 0.5 will reduce the effective noise sigma of the image
at each pixel by the square root of 0.5. Changes in the zero
point also changes the noise sigma if the image noise characteristics
are Poissonian. In the various rejection algorithms based on
identifying a noise sigma and clipping large deviations relative to
the scaled median or mean, one may need to account for the scaling induced
changes in the image noise characteristics.
In those algorithms it is possible to eliminate the "sigma correction"
while still using scaling. The reasons this might be desirable are 1) if
the scalings are similar the corrections in computing the mean or median
are important but the sigma corrections may not be important and 2) the
image statistics may not be Poissonian, either inherently or because the
images have been processed in some way that changes the statistics. In the
first case because computing square roots and making corrections to every
pixel during the iterative rejection operation may be a significant
computational speed limit the parameter sigscale selects how
dissimilar the scalings must be to require the sigma corrections. This
parameter is a fractional deviation which, since the scale factors are
normalized to unity, is the actual minimum deviation in the scale factors.
For the zero point shifts the shifts are normalized by the mean shift
before adjusting the shifts to a zero mean. To always use sigma scaling
corrections the parameter is set to zero and to eliminate the correction in
all cases it is set to a very large number.
If the final combining operation is "average" then the images may be
weighted during the averaging. The weights are specified in the
same way as the scale factors. In addition
the NCOMBINE keyword, if present, will be used in the weights.
The weights, scaled to a unit sum, are printed in the log output.
The weights are only used for the final weighted average and sigma image
output. They are not used to form averages in the various rejection
algorithms.
PIXEL MASKS
A pixel mask is a type of IRAF file having the extension ".pl" which
identifies an integer value with each pixel of the images to which it is
applied. The integer values may denote regions, a weight, a good or bad
flag, or some other type of integer or integer bit flag. In the common
case where many values are the same this file is compacted to be small and
efficient to use. It is also most compact and efficient if the majority of
the pixels have a zero mask value so frequently zero is the value for good
pixels. Note that these files, while not stored as a strict pixel array,
may be treated as images in programs. This means they may be created by
programs such as mkpattern, edited by imedit, examined by
imexamine, operated upon by imarith, graphed by implot,
and displayed by display.
At the time of introducing this task, generic tools for creating
pixel masks have yet to be written. There are two ways to create a
mask in V2.10. First if a regular integer image can be created
then it can be converted to pixel list format with imcopy:
by specifically using the .pl extension on output. Other programs that
can create integer images (such mkpattern or ccdred.badpiximage)
can create the pixel list file directly by simply using the ".pl"
extension in the output image name.
To use pixel masks with imcombine one must associate a pixel
mask file with an image by entering the pixel list file name in the
image header under the keyword BPM (bad pixel mask). This can be
done with hedit. Note that the same pixel mask may be associated
with more than one image as might be the case if the mask represents
defects in the detector used to obtain the images.
If a pixel mask is associated with an image the mask is used when the
masktype parameter is set to a value other than "none". Note that
when it is set to "none" mask information is not used even if it exists for
the image. The values of masktype which apply masks are "goodvalue",
"badvalue", "goodbits", and "badbits". They are used in conjunction with
the maskvalue parameter. When the mask type is "goodvalue" the
pixels with mask values matching the specified value are included in
combining and all others are rejected. Similarly, for a mask type of
"badvalue" the pixels with mask values matching the specified value are
rejected and all others are accepted. The bit types are useful for
selecting a combination of attributes in a mask consisting of bit flags.
The mask value is still an integer but is interpreted by bitwise comparison
with the values in the mask file.
If a mask operation is specified and an image has no mask image associated
with it then the mask values are taken as all zeros. In those cases be
careful that zero is an accepted value otherwise the entire image will be
rejected.
In the case of combining the higher dimensions of an image into a
lower dimensional image, the "project" option, the same pixel mask
is applied to all of the data being combined; i.e. the same 2D
pixel mask is applied to every plane of a 3D image. This is because
a higher dimensional image is treated as a collection of lower
dimensional images having the same header and hence the same
bad pixel mask. It would be tempting to use a bad pixel mask with
the same dimension as the image being projected but this is not
currently how the task works.
THRESHOLD REJECTION
In addition to rejecting masked pixels, pixels in the unscaled input
images which are below or above the thresholds given by the parameters
lthreshold and hthreshold are rejected. Values of INDEF
mean that no threshold value is applied. Threshold rejection may be used
to exclude very bad pixel values or as an alternative way of masking
images. In the latter case one can use a task like imedit
or imreplace to set parts of the images to be excluded to some
very low or high magic value.
REJECTION ALGORITHMS
The reject parameter selects a type of rejection operation to
be applied to pixels not masked or thresholded. If no rejection
operation is desired the value "none" is specified.
MINMAX
.in 4
A specified fraction of the highest and lowest pixels are rejected.
The fraction is specified as the number of high and low pixels, the
nhigh and nlow parameters, when data from all the input images
are used. If pixels have been rejected by offseting, masking, or
thresholding then a matching fraction of the remaining pixels, truncated
to an integer, are used. Thus,
where n is the number of pixels surviving offseting, masking, and
thresholding, nimages is the number of input images, nlow and nhigh
are task parameters and nl and nh are the final number of low and
high pixels rejected by the algorithm. The factor of 0.001 is to
adjust for rounding of the ratio.
As an example with 10 input images and specifying one low and two high
pixels to be rejected the fractions to be rejected are nlow=0.1 and nhigh=0.2
and the number rejected as a function of n is:
.in -4
CCDCLIP
.in 4
If the images are obtained using a CCD with known read out noise, gain, and
sensitivity noise parameters and they have been processed to preserve the
relation between data values and photons or electrons then the noise
characteristics of the images are well defined. In this model the sigma in
data values at a pixel with true value , as approximated by the median
or average with the lowest and highest value excluded, is given by:
where rn is the read out noise in electrons, g is the gain in
electrons per data value, s is a sensitivity noise given as a fraction,
and ** is the exponentiation operator. Often the sensitivity noise,
due to uncertainties in the pixel sensitivities (for example from the
flat field), is not known in which case a value of zero can be used.
See the task stsdas.wfpc.noisemodel for a way to determine
these vaues (though that task expresses the read out noise in data
numbers and the sensitivity noise parameter as a percentage).
The read out noise is specified by the rdnoise parameter. The value
may be a numeric value to be applied to all the input images or a image
header keyword containing the value for each image. Similarly, the
parameter gain specifies the gain as either a value or image header
keyword and the parameter snoise specifies the sensitivity
noise parameter as either a value or image header keyword.
The algorithm operates on each output pixel independently. It starts by
taking the median or unweighted average (excluding the minimum and maximum)
of the unrejected pixels provided there are at least two input pixels. The
expected sigma is computed from the CCD noise parameters and pixels more
that lsigma times this sigma below or hsigma times this sigma
above the median or average are rejected. The process is then iterated
until no further pixels are rejected. If the average is used as the
estimator of the true value then after the first round of rejections the
highest and lowest values are no longer excluded. Note that it is possible
to reject all pixels if the average is used and is sufficiently skewed by
bad pixels such as cosmic rays.
If there are different CCD noise parameters for the input images
(as might occur using the image header keyword specification) then
the sigmas are computed for each pixel from each image using the
same estimated true value.
If the images are scaled and shifted and the sigscale threshold
is exceeded then a sigma is computed for each pixel based on the
image scale parameters; i.e. the median or average is scaled to that of the
original image before computing the sigma and residuals.
After rejection the number of retained pixels is checked against the
nkeep parameter. If there are fewer pixels retained than specified
by this parameter the pixels with the smallest residuals in absolute
value are added back. If there is more than one pixel with the same
absolute residual (for example the two pixels about an average
or median of two will have the same residuals) they are all added
back even if this means more than nkeep pixels are retained.
Note that the nkeep parameter only applies to the pixels used
by the clipping rejection algorithm and does not apply to threshold
or bad pixel mask rejection.
This is the best clipping algorithm to use if the CCD noise parameters are
adequately known. The parameters affecting this algorithm are reject
to select this algorithm, mclip to select the median or average for
the center of the clipping, nkeep to limit the number of pixels
rejected, the CCD noise parameters rdnoise, gain and snoise,
lsigma and hsigma to select the clipping thresholds,
and sigscale to set the threshold for making corrections to the sigma
calculation for different image scale factors.
.in -4
CRREJECT
.in 4
This algorithm is identical to "ccdclip" except that only pixels above
the average are rejected based on the hsigma parameter. This
is appropriate for rejecting cosmic ray events and works even with
two images.
.in -4
SIGCLIP
.in 4
The sigma clipping algorithm computes at each output pixel the median or
average excluding the high and low values and the sigma about this
estimate. There must be at least three input pixels, though for this method
to work well there should be at least 10 pixels. Values deviating by more
than the specified sigma threshold factors are rejected. These steps are
repeated, except that after the first time the average includes all values,
until no further pixels are rejected or there are fewer than three pixels.
After rejection the number of retained pixels is checked against the
nkeep parameter. If there are fewer pixels retained than specified
by this parameter the pixels with the smallest residuals in absolute
value are added back. If there is more than one pixel with the same
absolute residual (for example the two pixels about an average
or median of two will have the same residuals) they are all added
back even if this means more than nkeep pixels are retained.
Note that the nkeep parameter only applies to the pixels used
by the clipping rejection algorithm and does not apply to threshold
or bad pixel mask rejection.
The parameters affecting this algorithm are reject to select
this algorithm, mclip to select the median or average for the
center of the clipping, nkeep to limit the number of pixels
rejected, lsigma and hsigma to select the
clipping thresholds, and sigscale to set the threshold for
making corrections to the sigma calculation for different image scale
factors.
.in -4
AVSIGCLIP
.in 4
The averaged sigma clipping algorithm assumes that the sigma about the
median or mean (average excluding the low and high values) is proportional
to the square root of the median or mean at each point. This is
described by the equation:
where the estimated signal is the mean or median (hopefully excluding
any bad pixels) and the gain is the estimated proportionality
constant having units of photons/data number.
This noise model is valid for images whose values are proportional to the
number of photons recorded. In effect this algorithm estimates a
detector gain for each line with no read out noise component when
information about the detector noise parameters are not known or
available. The gain proportionality factor is computed
independently for each output line by averaging the square of the residuals
(at points having three or more input values) scaled by the median or
mean. In theory the proportionality should be the same for all rows but
because of the estimating process will vary somewhat.
Once the proportionality factor is determined, deviant pixels exceeding the
specified thresholds are rejected at each point by estimating the sigma
from the median or mean. If any values are rejected the median or mean
(this time not excluding the extreme values) is recomputed and further
values rejected. This is repeated until there are no further pixels
rejected or the number of remaining input values falls below three. Note
that the proportionality factor is not recomputed after rejections.
If the images are scaled differently and the sigma scaling correction
threshold is exceeded then a correction is made in the sigma
calculations for these differences, again under the assumption that
the noise in an image scales as the square root of the mean intensity.
After rejection the number of retained pixels is checked against the
nkeep parameter. If there are fewer pixels retained than specified
by this parameter the pixels with the smallest residuals in absolute
value are added back. If there is more than one pixel with the same
absolute residual (for example the two pixels about an average
or median of two will have the same residuals) they are all added
back even if this means more than nkeep pixels are retained.
Note that the nkeep parameter only applies to the pixels used
by the clipping rejection algorithm and does not apply to threshold
or bad pixel mask rejection.
This algorithm works well for even a few input images. It works better if
the median is used though this is slower than using the average. Note that
if the images have a known read out noise and gain (the proportionality
factor above) then the "ccdclip" algorithm is superior. The two algorithms
are related in that the average sigma proportionality factor is an estimate
of the gain.
The parameters affecting this algorithm are reject to select
this algorithm, mclip to select the median or average for the
center of the clipping, nkeep to limit the number of pixels
rejected, lsigma and hsigma to select the
clipping thresholds, and sigscale to set the threshold for
making corrections to the sigma calculation for different image scale
factors.
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PCLIP
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The percentile clipping algorithm is similar to sigma clipping using the
median as the center of the distribution except that, instead of computing
the sigma of the pixels from the CCD noise parameters or from the data
values, the width of the distribution is characterized by the difference
between the median value and a specified "percentile" pixel value. This
width is then multipled by the scale factors lsigma and hsigma
to define the clipping thresholds above and below the median. The clipping
is not iterated.
The pixel values at each output point are ordered in magnitude and the
median is determined. In the case of an even number of pixels the average
of the two middle values is used as the median value and the lower or upper
of the two is the median pixel when counting from the median pixel to
selecting the percentile pixel. The parameter pclip selects the
percentile pixel as the number (if the absolute value is greater
than unity) or fraction of the pixels from the median in the ordered set.
The direction of the percentile pixel from the median is set by the sign of
the pclip parameter with a negative value signifying pixels with
values less than the median. Fractional values are internally converted to
the appropriate number of pixels for the number of input images. A minimum
of one pixel and a maximum corresponding to the extreme pixels from the
median are enforced. The value used is reported in the log output. Note
that the same percentile pixel is used even if pixels have been rejected by
offseting, masking, or thresholding; for example, if the 3nd pixel below
the median is specified then the 3rd pixel will be used whether there are
10 pixels or 5 pixels remaining after the preliminary steps.
After rejection the number of retained pixels is checked against the
nkeep parameter. If there are fewer pixels retained than specified
by this parameter the pixels with the smallest residuals in absolute
value are added back. If there is more than one pixel with the same
absolute residual (for example the two pixels about an average
or median of two will have the same residuals) they are all added
back even if this means more than nkeep pixels are retained.
Note that the nkeep parameter only applies to the pixels used
by the clipping rejection algorithm and does not apply to threshold
or bad pixel mask rejection.
Some examples help clarify the definition of the percentile pixel. In the
examples assume 10 pixels. The median is then the average of the
5th and 6th pixels. A pclip value of 2 selects the 2nd pixel
above the median (6th) pixel which is the 8th pixel. A pclip
value of -0.5 selects the point halfway between the median and the
lowest pixel. In this case there are 4 pixels below the median,
half of that is 2 pixels which makes the percentile pixel the 3rd pixel.
The percentile clipping algorithm is most useful for clipping small
excursions, such as the wings of bright objects when combining
disregistered observations for a sky flat field, that are missed when using
the pixel values to compute a sigma. It is not as powerful, however, as
using the CCD noise parameters (provided they are accurately known) to clip
about the median.
The parameters affecting this algorithm are reject to select this
algorithm, pclip to select the percentile pixel, nkeep to limit
the number of pixels rejected, and lsigma and hsigma to select
the clipping thresholds.
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GROW REJECTION
Neighbors of pixels rejected by the rejection algorithms along image lines
may also be rejected. The number of neighbors to be rejected on either
side is specified by the grow parameter. The rejection only
applies to neighbors along each image line. This is because the
task operates independently on each image line and does not have the
ability to go back to previous lines or maintain a list of rejected
pixels to later lines.
This rejection step is also checked against the nkeep parameter
and only as many pixels as would not violate this parameter are
rejected. Unlike it's application in the rejection algorithms at
this stage there is no checking on the magnitude of the residuals
and the pixels retained which would otherwise be rejected are randomly
selected.
COMBINING
After all the steps of offsetting the input images, masking pixels,
threshold rejection, scaling, and applying a rejection algorithms the
remaining pixels are combined and output. The pixels may be combined
by computing the median or by computing a weighted average.
SIGMA OUTPUT
In addition to the combined image and optional sigma image may be
produced. The sigma computed is the standard deviation, corrected for a
finite population by a factor of n/(n-1), of the unrejected input pixel
values about the output combined pixel values.
1. To average and median images without any other features:
2. To reject cosmic rays:
3. To make a grid for display purposes with 21 64x64 images:
4. To apply a mask image with good pixels marked with a zero value and
bad pixels marked with a value of one:
5. To scale image by the exposure time and then adjust for varying
sky brightness and make a weighted average:
TIME REQUIREMENTS
The following times were obtain with a Sun 4/470. The tests combine
1000x200 images consisting of Poisson noise and cosmic rays generated
with the artdata package. The times, especially the total time,
are approximate and depend on user loads.
REVISIONS
Though this task is essentially not limited by the physical
limits of the host (number of open files, amount of memory) there is a
software limit in the IRAF virtual operating system of about 120 separate
images which may be combined. To combine more images one may combine smaller
groups and then combine those or one may stack the images into a higher
dimensional image using imstack and use the project option.
ccdred.combine onedspec.scombine,
wpfc.noisemodel,
cl> imcopy template plfile.pl
nl = n * nlow/nimages + 0.001
nh = n * nhigh/nimages + 0.001
n 0 1 2 3 4 5 6 7 8 9 10
nl 0 0 0 0 0 0 0 0 0 0 1
nh 0 0 0 0 0 1 1 1 1 1 2
sigma = ((rn / g) ** 2 + / g + (s * ) ** 2) ** 1/2
sigma(column,line) = sqrt (gain(line) * signal(column,line))
EXAMPLES
cl> imcombine obj* avg combine=average reject=none
cl> imcombine obj* med combine=median reject=none
cl> imcombine obs1,obs2 Obs reject=crreject rdnoise=5.1, gain=4.3
cl> imcombine @list grid offset="grid 5 65 5 65"
cl> hedit ims* bpm badpix.pl add+ ver-
cl> imcombine ims* final combine=median masktype=goodval
cl> imcombine obj* avsig combine=average reject=avsig
>>> scale=exp zero=mode weight=exp expname=exptime
TIME REQUIREMENTS
IMAGES: Number of images (1000x200) and datatype (R=real, S=short)
COMBINE: Combine option
REJECT: Rejection option with grow = 0
minmax: nlow = 1, nhigh = 1
ccdclip: lsigma = 3., hsigma = 3, sigscale = 0.
sigclip: lsigma = 3., hsigma = 3, sigscale = 0.
avsigclip: lsigma = 3., hsigma = 3, sigscale = 0.
pclip: lsigma = 3., hsigma = 3, pclip = -0.5
/a: mclip = no (clip about the average)
/m: mclip = yes (clip about the median)
O M T S: Features used (Y=yes, N=no)
O: offset = "grid 5 10 2 10"
M: masktype = goodval, maskval = 0
Pixel mask has 2 bad lines and 20 bad columns
T: lthreshold = INDEF, hthreshold = 1100.
S: scale = mode, zero = none, weight = mode
TIME: cpu time in seconds, total time in minutes and seconds
IMAGES COMBINE REJECT O M T S TIME
10R average none N N N N 1.3 0:08
10R average minmax N N N N 4.3 0:10
10R average pclip N N N N 17.9 0:32
10R average ccdclip/a N N N N 11.6 0:21
10R average crreject/a N N N N 11.4 0:21
10R average sigclip/a N N N N 13.6 0:29
10R average avsigclip/a N N N N 15.9 0:35
10R average ccdclip/m N N N N 16.9 0:32
10R average crreject/m N N N N 17.0 0:28
10R average sigclip/m N N N N 19.6 0:42
10R average avsigclip/m N N N N 20.6 0:43
10R median none N N N N 6.8 0:17
10R median minmax N N N N 7.8 0:15
10R median pclip N N N N 16.9 1:00
10R median ccdclip/a N N N N 18.0 0:34
10R median crreject/a N N N N 17.7 0:30
10R median sigclip/a N N N N 21.1 1:13
10R median avsigclip/a N N N N 23.1 0:41
10R median ccdclip/m N N N N 16.1 0:27
10R median crreject/m N N N N 16.0 0:27
10R median sigclip/m N N N N 18.1 0:29
10R median avsigclip/m N N N N 19.6 0:32
10R average none N N N Y 6.1 0:36
10R median none N N N Y 10.4 0:49
10R median pclip N N N Y 20.4 1:10
10R median ccdclip/m N N N Y 19.5 0:36
10R median avsigclip/m N N N Y 23.0 1:06
10R average none N Y N N 3.5 0:12
10R median none N Y N N 8.9 0:21
10R median pclip N Y N N 19.9 0:45
10R median ccdclip/m N Y N N 18.0 0:44
10R median avsigclip/m N Y N N 20.9 0:28
10R average none Y N N N 4.3 0:13
10R median none Y N N N 9.6 0:21
10R median pclip Y N N N 21.8 0:54
10R median ccdclip/m Y N N N 19.3 0:44
10R median avsigclip/m Y N N N 22.8 0:51
10R average none Y Y Y Y 10.8 0:22
10R median none Y Y Y Y 16.1 0:28
10R median pclip Y Y Y Y 27.4 0:42
10R median ccdclip/m Y Y Y Y 25.5 0:39
10R median avsigclip/m Y Y Y Y 28.9 0:44
10S average none N N N N 2.2 0:06
10S average minmax N N N N 4.6 0:12
10S average pclip N N N N 18.1 0:33
REVISIONS
IMCOMBINE V2.10.3
The input scalings from an @file or header keyword are now truely
mulitplicative or additive and they are not normalized. The output
pixel types now include unsigned short integer.
IMCOMBINE V2.10.2
The weighting was changed from using the square root of the exposure time
or image statistics to using the values directly. This corresponds
to variance weighting. Other options for specifying the scaling and
weighting factors were added; namely from a file or from a different
image header keyword. The nkeep parameter was added to allow
controlling the maximum number of pixels to be rejected by the clipping
algorithms. The snoise parameter was added to include a sensitivity
or scale noise component to the noise model. Errors will now delete
the output images.
IMCOMBINE V2.10
This task was greatly revised to provide many new features. These features
are:
o Bad pixel masks
o Combining offset and different size images
o Blank value for missing data
o Combining across the highest dimension (the project option)
o Separating threshold rejection, the rejection algorithms,
and the final combining statistic
o New CCDCLIP, CRREJECT, and PCLIP algorithms
o Rejection now may reject more than one pixel per output pixel
o Choice of a central median or average for clipping
o Choice of final combining operation
o Simultaneous multiplicative and zero point scaling
.le
LIMITATIONS
SEE ALSO
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