This means that the number of points in / that have gray levels z
x
,...
9
z
kl
_
x
is at most q
x
. Evidently, all of these points should be given gray level z
x
in
the transformed picture /'. In addition, if there are fewer than q
x
of these
points,
some of the points of/that have gray level z
k{
should also be given
gray level z
x
in /'. (One can choose these points randomly, or one can make
their choice depend on the gray levels of their neighboring points—e.g.,
use points having low average neighborhood gray levels first.)
Next, let
Σ
Pi ^ ?i +
a
2 < Σ Pi
i
=
1
i
=
1
This tells us which points of/should be given gray
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