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frank

$ \bigcirc$Name


frank Generalized rank of a Fimage




$ \bigcirc$Command Synopsis


frank [-c] [-w w] [-g g] [-r rank] u



-c : normalize as a Cimage (into [0..256[)

-w w : weight: g = w*H + (1-w)*H-, default 0.5

-g g : output contrast change

-r rank : output rank Fimage = g(u)

u : input Fimage




$ \bigcirc$Function Summary


void frank (u , rank , g , w , c )

Fimage u , rank ;

Flist g ;

float *w ;

int *c ;




$ \bigcirc$Description


The repartition function of a Fimage u defined on the domain $ \Omega$ = {0..M - 1}×{0..N - 1} is the nondecreasing function

Hu(t) = $\displaystyle {\frac{{\vert\{(x,y) \in \Omega;u(x,y)\leq t\}\vert}}{{\vert\Omega\vert}}}$.

As well, its lower repartition may be defined by

H-u(t) = $\displaystyle {\frac{{\vert\{(x,y) \in \Omega;u(x,y)< t\}\vert}}{{\vert\Omega\vert}}}$.

This module computes an average repartition function

g(t) = w . Hu(t) + (1 - w)H-u(t),

usually with w = 0.5, but this weight may be changed with the -w option. If the -c option us selected, then g is multiplied by 256 (so that $ \lim_{\infty}^{}$g = 256 instead of $ \lim_{\infty}^{}$g = 1). This function g may serve as a contrast change to produce the rank image rank = g(u), performing the so-called histogram equalization of u, which is optimal in a general framework (see [Moi02] for more details).

If requested by the -g option, the function g is returned as the 2-Flist (ti, g(ti)), where (ti) is the (increasing) sorted sequence of all values taken by u.




$ \bigcirc$See Also


fvalues.




$ \bigcirc$Version 1.0


Last Modification date : Thu Apr 10 00:13:40 2003


$ \bigcirc$Author


Lionel Moisan






next up previous contents index
Next: fthre Up: Reference Previous: fquant   Contents   Index
mw 2004-05-05