Average

The average brightness of a region is defined as sample mean of the pixel brightnesses within that region. The average, of the brightness over the N pixels within a region is given by:

Alternatively, we can use a formulation based upon the (unnormalized) brightness histogram, ,with discrete brightness values a. This gives:

The average brightness is an estimate of the mean brightness, ,of the underlying brightness probability distribution.

Standard deviation

The unbiased estimate of the standard deviation, of the brightnesses within a region with N pixels is called the sample standard deviation and is given by:

Using the histogram formulation gives

The standard deviation , is an estimate of of the underlying brightness probability distribution.