function?imagBW?=?kittlerMet（imag）
%?KITTLERMET?binarizes?a?gray?scale?image?‘imag‘?into?a?binary?image
%?Input:
%???imag:?the?gray?scale?image?with?black?foreground（0）?and?white
%???background（255）.
%?Output:
%???imagBW:?the?binary?image?of?the?gray?scale?image?‘imag‘?with?kittler‘s
%???minimum?error?thresholding?algorithm.

%?Reference:
%???J.?Kittler?and?J.?Illingworth.?Minimum?Error?Thresholding.?Pattern
%???Recognition.?1986.?19（1）:41-47

MAXD?=?100000;
imag?=?imag（::1）;
[counts?x]?=?imhist（imag）;??%?counts?are?the?histogram.?x?is?the?intensity?level.
GradeI?=?length（x）;???%?the?resolusion?of?the?intensity.?i.e.?256?for?uint8.
J_t?=?zeros（GradeI?1）;??%?criterion?function
prob?=?counts?./?sum（counts）;??%?Probability?distribution
meanT?=?x‘?*?prob;??%?Total?mean?level?of?the?picture
%?Initialization
w0?=?prob（1）;???%?Probability?of?the?first?class
miuK?=?0;???%?First-order?cumulative?moments?of?the?histogram?up?to?the?kth?level.
J_t（1）?=?MAXD;?
n?=?GradeI-1;
for?i?=?1?:?n
????w0?=?w0?+?prob（i+1）;
????miuK?=?miuK?+?i?*?prob（i+1）;??%?first-order?cumulative?moment
????if?（w0??1-eps）
????????J_t（i+1）?=?MAXD;????%?T?=?i
????else
????????miu1?=?miuK?/?w0;
????????miu2?=?（meanT-miuK）?/?（1-w0）;
????????var1?=?（（（0?:?i）‘-miu1）.^2）‘?*?prob（1?:?i+1）;
????????var1?=?var1?/?w0;??%?variance
????????var2?=?（（（i+1?:?n）‘-miu2）.^2）‘?*?prob（i+2?:?n+1）;
????????var2?=?var2?/?（1-w0）;
????????if?var1?>?eps?&&?var2?>?eps???%?in?case?of?var1=0?or?var2?=0
????????????J_t（i+1）?=?1+w0?*?log（var1）+（1-w0）?*?log（var2）-2*w0*log（w0）-2*（1-w0）*log（1-w0）;
????????else
????????????J_t（i+1）?=?MAXD;
????????end
????end
end
minJ?=?min（J_t）;
index?=?find（J_t?==?minJ）;
th?=?mean（index）;
th?=?（th-1）/n
imagBW?=?im2bw（imag?th）;

%?figure?imshow（imagBW）?title（‘kittler?binary‘）;

?屬性????????????大小?????日期????時(shí)間???名稱
-----------?---------??----------?-----??----

?????文件???????1845??2010-05-04?16:48??二值化\kittlerMet.m

?????文件????????423??2010-05-05?14:18??二值化\main.m

?????文件???????2606??2010-05-04?16:48??二值化\niblack.m

?????文件???????1642??2010-05-04?16:48??二值化\otsu.m

?????目錄??????????0??2010-05-13?14:50??二值化

-----------?---------??----------?-----??----

?????????????????6516????????????????????5