function?[IDXsep]?=?otsu（In）

%OTSU?Global?image?thresholding/segmentation?using?Otsu‘s?method.
%???IDX?=?OTSU（IN）?segments?the?image?I?into?N?classes?of?Otsu‘s
%???N-thresholding?method.?OTSU?returns?an?array?IDX?containing?the?cluster
%???indices?（from?1?to?N）?of?each?point.?Zero?values?are?assigned?to
%???non-finite?（NaN?or?Inf）?pixels.
%
%???IDX?=?OTSU（I）?uses?two?classes?（N=2?default?value）.
%
%???[IDXsep]?=?OTSU（...）?also?returns?the?value?（sep）?of?the?separability
%???criterion?within?the?range?[0?1].?Zero?is?obtained?only?with?data
%???having?less?than?N?values?whereas?one?（optimal?value）?is?obtained?only
%???with?N-valued?arrays.
%
%???Notes:
%???-----
%???It?should?be?noticed?that?the?thresholds?generally?become?less?credible
%???as?the?number?of?classes?（N）?to?be?separated?increases?（see?Otsu‘s
%???paper?for?more?details）.
%
%???If?I?is?an?RGB?image?a?Karhunen-Loeve?transform?is?first?performed?on
%???the?three?RGB?channels.?The?segmentation?is?then?carried?out?on?the
%???image?component?that?contains?most?of?the?energy.
%
%???Example:
%???-------
%???load?clown
%???subplot（221）
%???X?=?ind2rgb（Xmap）;
%???imshow（X）
%???title（‘Original‘‘FontWeight‘‘bold‘）
%???for?n?=?2:4
%?????IDX?=?otsu（Xn）;
%?????subplot（22n）
%?????imagesc（IDX）?axis?image?off
%?????title（[‘n?=?‘?int2str（n）]‘FontWeight‘‘bold‘）
%???end
%???colormap（gray）
%
%???Reference:
%???---------
%???Otsu?N?A?Threshold?Selection?Method?from?Gray-Level?Histograms
%???IEEE?Trans.?Syst.?Man?Cybern.?9:62-66;1979
%
%???See?also?GRAYTHRESH?IM2BW
%
%???--?Damien?Garcia?--?2007/08?revised?2010/03
%???Visit?my?%???href=“matlab:web（‘http://www.biomecardio.com/matlab/otsu.html‘）“>website?for?more?details?about?OTSU

error（nargchk（12nargin））

%?Check?if?is?the?input?is?an?RGB?image
isRGB?=?isrgb（I）;

assert（isRGB?|?ndims（I）==2...
????‘The?input?must?be?a?2-D?array?or?an?RGB?image.‘）

%%?Checking?n?（number?of?classes）
if?nargin==1
????n?=?2;
elseif?n==1;
????IDX?=?NaN（size（I））;
????sep?=?0;
????return
elseif?n~=abs（round（n））?||?n==0
????error（‘MATLAB:otsu:WrongNValue‘...
????????‘n?must?be?a?strictly?positive?integer!‘）
elseif?n>255
????n?=?255;
????warning（‘MATLAB:otsu:TooHighN‘...
????????‘n?is?too?high.?n?value?has?been?changed?to?255.‘）
end

I?=?single（I）;

%%?Perform?a?KLT?if?isRGB?and?keep?the?component?of?highest?energy
if?isRGB
????sizI?=?size（I）;
????I?=?reshape（I[]3）;
????[VD]?=?eig（cov（I））;
????[tmpc]?=?max（diag（D））;
????I?=?reshape（I*V（:c）sizI（1:2））;?%?component?with?the?highest?energy
end

%%?Convert?to?256?levels
I?=?I-min（I（:））;
I?=?round（I/max（I（:））*255）;

%%?Probability?distribution
unI?=?sort（unique（I））;
nbins?=?min（length（unI）256）;
if?nbins==n
????IDX?=?ones（size（I））;
????for?i?=?1:n?IDX（I==unI（i））?=?i;?end
????sep?=?1;
????return
elseif?nbins????IDX?=?NaN（si