The \verb+fvar+ module returns the variance 
\index{variance!of an image}
\index{standart deviation!of an image}
of the $m\times n$ gray level the image $A$, estimated by
$$var = \frac 1N
\sum_{1\leq x \leq m, \,1 \leq y \leq n} \big(A(x,y)-M\big)^2,$$
where
$$M = \frac 1{m \cdot n} 
\sum_{1\leq x \leq m, \,1 \leq y \leq n} A(x,y).$$
The normalization factor $N$ has the default value $N=m \cdot n-1$
(which yields an unbiased estimate), but the true empirical variance
(obtained with $N=m \cdot n$) can be computed instead by setting the 
\verb+-e+ option.
If the option \verb+-s+ is specified, then the square root function
is applied to the result, so that a standart deviation is estimated.
Note that the result is zero if the domain of $A$ does not contain at least
2 pixels.
