多维OTSU阈值分割方法，能够实现二维图像多阈值分割附matlab代码.zip

function [IDX,sep] = otsu(I,n) %OTSU Global image thresholding/segmentation using Otsu's method. % IDX = OTSU(I,N) segments the image I into N classes by means 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). % % [IDX,sep] = 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 R,G,B channels. The segmentation is then carried out on the % image component that contains most of the energy. % % Example: % ------- % load clown % subplot(221) % X = ind2rgb(X,map); % imshow(X) % title('Original','FontWeight','bold') % for n = 2:4 % IDX = otsu(X,n); % subplot(2,2,n) % imagesc(IDX), axis image off % title(['n = ' int2str(n)],'FontWeight','bold') % end % colormap(gray) % % Reference: % --------- % Otsu N, <a href="matlab:web('http://dx.doi.org/doi:10.1109/TSMC.1979.4310076')">A Threshold Selection Method from Gray-Level Histograms</a>, % IEEE Trans. Syst. Man Cybern. 9:62-66;1979 % % See also GRAYTHRESH, IM2BW % % -- Damien Garcia -- 2007/08, revised 2010/03 % Visit my <a % href="matlab:web('http://www.biomecardio.com/matlab/otsu.html')">website</a> for more details about OTSU error(nargchk(1,2,nargin)) % 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); [V,D] = eig(cov(I)); [tmp,c] = 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<n IDX = NaN(size(I)); sep = 0; return elseif nbins<256 [histo,pixval] = hist(I(:),unI); else [histo,pixval] = hist(I(:),256); end P = histo/sum(histo); clear unI %% Zeroth- and first-order cumulative moments w = cumsum(P); mu = cumsum((1:nbins).*P); %% Maximal sigmaB^2 and Segmented image if n==2 sigma2B =... (mu(end)*w(2:end-1)-mu(2:end-1)).^2./w(2:end-1)./(1-w(2:end-1)); [maxsig,k] = max(sigma2B); % segmented image IDX = ones(size(I)); IDX(I>pixval(k+1)) = 2; % separability criterion sep = maxsig/sum(((1:nbins)-mu(end)).^2.*P); elseif n==3 w0 = w; w2 = fliplr(cumsum(fliplr(P))); [w0,w2] = ndgrid(w0,w2); mu0 = mu./w; mu2 = fliplr(cumsum(fliplr((1:nbins).*P))./cumsum(fliplr(P))); [mu0,mu2] = ndgrid(mu0,mu2); w1 = 1-w0-w2; w1(w1<=0) = NaN; sigma2B =... w0.*(mu0-mu(end)).^2 + w2.*(mu2-mu(end)).^2 +... (w0.*(mu0-mu(end)) + w2.*(mu2-mu(end))).^2./w1; sigma2B(isnan(sigma2B)) = 0; % zeroing if k1 >= k2 [maxsig,k] = max(sigma2B(:)); [k1,k2] = ind2sub([nbins nbins],k); % segmented image IDX = ones(size(I))*3; IDX(I<=pixval(k1)) = 1; IDX(I>pixval(k1) & I<=pixval(k2)) = 2; % separability criterion sep = maxsig/sum(((1:nbins)-mu(end)).^2.*P); else k0 = linspace(0,1,n+1); k0 = k0(2:n); [k,y] = fminsearch(@sig_func,k0,optimset('TolX',1)); k = round(k*(nbins-1)+1); % segmented image IDX = ones(size(I))*n; IDX(I<=pixval(k(1))) = 1; for i = 1:n-2 IDX(I>pixval(k(i)) & I<=pixval(k(i+1))) = i+1; end % separability criterion sep = 1-y; end IDX(~isfinite(I)) = 0; %% Function to be minimized if n>=4 function y = sig_func(k) muT = sum((1:nbins).*P); sigma2T = sum(((1:nbins)-muT).^2.*P); k = round(k*(nbins-1)+1); k = sort(k); if any(k<1 | k>nbins), y = 1; return, end k = [0 k nbins]; sigma2B = 0; for j = 1:n wj = sum(P(k(j)+1:k(j+1))); if wj==0, y = 1; return, end muj = sum((k(j)+1:k(j+1)).*P(k(j)+1:k(j+1)))/wj; sigma2B = sigma2B + wj*(muj-muT)^2; end y = 1-sigma2B/sigma2T; % within the range [0 1] end end function isRGB = isrgb(A) % --- Do we have an RGB image? % RGB images can be only uint8, uint16, single, or double isRGB = ndims(A)==3 && (isfloat(A) || isa(A,'uint8') || isa(A,'uint16')); % ---- Adapted from the obsolete function ISRGB ---- if isRGB && isfloat(A) % At first, just test a small chunk to get a possible quick negative mm = size(A,1); nn = size(A,2); chunk = A(1:min(mm,10),1:min(nn,10),:); isRGB = (min(chunk(:))>=0 && max(chunk(:))<=1); % If the chunk is an RGB image, test the whole image if isRGB, isRGB = (min(A(:))>=0 && max(A(:))<=1); end end end