imstatistics images
images
Images for which pixel statistics are to be computed.
fields = image,npix,mean,stddev,min,max
The statistical quantities to be computed and printed.
lower = INDEF
Use only pixels with values greater than or equal to this limit.
All pixels are above the default value of INDEF.
upper = INDEF
Use only pixels with values less than or equal to this limit.
All pixels are below the default value of INDEF.
binwidth = 0.1
The width of the histogram bins used for computing the midpoint (estimate
of the median) and the mode.
The units are in sigma.
format = yes
Label the output columns and print the result in fixed format. If format
is "no" no column labels are printed and the output is in free format.
The statistical quantities specified by the parameter fields are computed and printed for each image in the list specified by images. The results are printed in tabular form with the fields listed in the order they are specified in the fields parameter. The available fields are the following.
image - the image name
npix - the number of pixels used to do the statistics
mean - the mean of the pixel distribution
midpt - estimate of the median of the pixel distribution
mode - the mode of the pixel distribution
stddev - the standard deviation of the pixel distribution
skew - the skew of the pixel distribution
kurtosis - the kurtosis of the pixel distribution
min - the minimum pixel value
max - the maximum pixel value
The mean, standard deviation, skew, kurtosis, min and max are computed in a single pass through the image using the expressions listed below. Only the quantities selected by the fields parameter are actually computed.
mean = sum (x1,...,xN) / N
y = x - mean
variance = sum (y1 ** 2,...,yN ** 2) / (N-1)
stddev = sqrt (variance)
skew = sum ((y1 / stddev) ** 3,...,(yN / stddev) ** 3) / (N-1)
kurtosis = sum ((y1 / stddev) ** 4,...,(yN / stddev) ** 4) / (N-1) - 3
The midpoint and mode are computed in two passes through the image. In the first pass the standard deviation of the pixels is calculated and used with the binwidth parameter to compute the resolution of the data histogram. The midpoint is estimated by integrating the histogram and computing by interpolation the data value at which exactly half the pixels are below that data value and half are above it. The mode is computed by locating the maximum of the data histogram and fitting the peak by parabolic interpolation.
1. To find the number of pixels, mean, standard deviation and the minimum and maximum pixel value of a bias region in an image.
cl> imstat flat*[*,1]
# IMAGE NPIX MEAN STDDEV MIN MAX
flat1[*,1] 800 999.5 14.09 941. 1062.
flat2[*,1] 800 999.4 28.87 918. 1413.
The string "flat*" uses a wildcard to select all images beginning with the word flat. The string "[*,1]" is an image section selecting row 1.
2. Compute the mean, midpoint, mode and standard deviation of a pixel distribution.
cl> imstat m51 fields="image,mean,midpt,mode,stddev"
# IMAGE PIXELS MEAN MIDPT MODE STDDEV
M51 262144 108.3 88.75 49.4 131.3
When using a very large number of pixels the accumulation of the sums of the pixel values to the various powers may encounter roundoff error. This is significant when the true standard deviation is small compared to the mean.