where Pma%e is the arithmetic mean of the pixel values in the image. The mean pixel value is usually somewhat greater than the sky pixel value because every object in the image that is brighter than the sky value raises the mean value. Median Pixel Value

The median is that pixel value for which MN/2 pixels in the image have greater values, and MN/2 pixels have lower values. In deep-sky images, the median pixel value is usually quite close to that of the sky. The median is useful because it is largely independent of low values that occur along the edges and extreme high values due to stars and other bright objects in the image. Standard Deviation

The standard deviation is a measure of the distribution of pixel values from the mean pixel value of the image; that is, how greatly the collection of pixels in the image stray from the mean pixel value. Given an image with dimensions M by TV pixels and a mean pixel value of Pimage, the standard deviation, a, is:

where Pi is the /th pixel in the collection of MN pixels.

Standard deviation is a more useful measure of the distribution of pixel values found in an image than is the range between the minimum and maximum, because it is not influenced by a small population of unusually low or high values, but by the properties of all pixels in the image. Low-Point and High-Point Pixel Values

The pixel values in an image are distributed between the minimum and maximum values. The minimum value is usually considerably less than that of the bulk of the pixels, and the maximum is often much greater than the bulk of the pixel values. If the pixel values are simply mapped into the range of grays available on a computer monitor, the image will appear dark and muddy. The low point and high point provide considerably more useful information.

The percent-point pixel value is the value that lies above some fraction of pixels in an image. The minimum and maximum are the extreme pixel percentiles—the minimum is the 0.00-point pixel value because none lie below the minimum. Likewise, the maximum is the 1.00-point pixel value because it is greater than that of all the pixels in the image. The 0.50-point pixel value has a value greater than half of the pixels in the image.

Percent-point pixel values are extremely valuable in displaying images because they allow the user to determine how many pixels will saturate to pure black or pure white on the display. If the black level (low point) in the display is set to 0.01, then 1% of the pixels in the image will be black. If the white level (high point) is set to 0.99, then 100%-99% = 1% of the pixels will saturate white.

For example, an image with a minimum pixel value of 0 and a maximum pixel value of 3545 may have a 0.01 low-point pixel value of 356 and a 0.99 highpoint pixel value of 510. Using these pixel values to display the image means that 2% of the pixels will be saturated either black or white (probably the dark corners of the image and the cores of the brightest stars), while the remaining 98% of the pixels will display in shades of gray.

• Tip: AIP4Win uses percent-point values to make the automatic brightness settings in the Image Display Control, and to select low- and high-point values for the Brightness Scaling Tool.

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