function func_ant_colony_image_edge_detection % % % This is a demo program of image edge detection using ant colony, based on % the paper, "An Ant Colony Optimization Algorithm For Image Edge % Detection," IEEE Congress on Evolutionary Computation (CEC), pp. 751-756, Hongkong, % Jun. 2008. % % % % Input: % gray image with a square size % % Output: % four edge map images, which are obtained by the method using four functions, % respectively. % % image loading filename = 'camera128'; img = double(imread([filename '.bmp']))./255; [nrow, ncol] = size(img); %visiblity function initialization, see equation (4) for nMethod = 1:4; %Four kernel functions used in the paper, see equations (7)-(10) %E: exponential; F: flat; G: gaussian; S:Sine; T:Turkey; W:Wave fprintf('Welcome to demo program of image edge detection using ant colony.\nPlease wait......\n'); v = zeros(size(img)); v_norm = 0; for rr =1:nrow for cc=1:ncol %defination of clique temp1 = [rr-2 cc-1; rr-2 cc+1; rr-1 cc-2; rr-1 cc-1; rr-1 cc; rr-1 cc+1; rr-1 cc+2; rr cc-1]; temp2 = [rr+2 cc+1; rr+2 cc-1; rr+1 cc+2; rr+1 cc+1; rr+1 cc; rr+1 cc-1; rr+1 cc-2; rr cc+1]; temp0 = find(temp1(:,1)>=1 & temp1(:,1)<=nrow & temp1(:,2)>=1 & temp1(:,2)<=ncol & temp2(:,1)>=1 & temp2(:,1)<=nrow & temp2(:,2)>=1 & temp2(:,2)<=ncol); temp11 = temp1(temp0, :); temp22 = temp2(temp0, :); temp00 = zeros(size(temp11,1)); for kk = 1:size(temp11,1) temp00(kk) = abs(img(temp11(kk,1), temp11(kk,2))-img(temp22(kk,1), temp22(kk,2))); end if size(temp11,1) == 0 v(rr, cc) = 0; v_norm = v_norm + v(rr, cc); else lambda = 10; switch nMethod case 1%'F' temp00 = lambda .* temp00; case 2%'Q' temp00 = lambda .* temp00.^2; case 3%'S' temp00 = sin(pi .* temp00./2./lambda); case 4%'W' temp00 = sin(pi.*temp00./lambda).*pi.*temp00./lambda; end v(rr, cc) = sum(sum(temp00.^2)); v_norm = v_norm + v(rr, cc); end end end v = v./v_norm; %do normalization v = v.*100; % pheromone function initialization p = 0.0001 .* ones(size(img)); %paramete setting, see Section IV in CEC paper alpha = 1; %equation (4) beta = 0.1; %equation (4) rho = 0.1; %equation (11) phi = 0.05; %equation (12), i.e., (9) in IEEE-CIM-06 ant_total_num = round(sqrt(nrow*ncol)); ant_pos_idx = zeros(ant_total_num, 2); % record the location of ant % initialize the positions of ants rand('state', sum(clock)); temp = rand(ant_total_num, 2); ant_pos_idx(:,1) = round(1 + (nrow-1) * temp(:,1)); %row index ant_pos_idx(:,2) = round(1 + (ncol-1) * temp(:,2)); %column index search_clique_mode = '8'; %Figure 1 % define the memory length, the positions in ant's memory are % non-admissible positions for the next movement if nrow*ncol == 128*128 A = 40; memory_length = round(rand(1).*(1.15*A-0.85*A)+0.85*A); % memory length elseif nrow*ncol == 256*256 A = 30; memory_length = round(rand(1).*(1.15*A-0.85*A)+0.85*A); % memory length elseif nrow*ncol == 512*512 A = 20; memory_length = round(rand(1).*(1.15*A-0.85*A)+0.85*A); % memory length end % record the positions in ant's memory, convert 2D position-index (row, col) into % 1D position-index ant_memory = zeros(ant_total_num, memory_length); % System setup if nrow*ncol == 128*128 total_step_num = 300; % the numbe of iterations? elseif nrow*ncol == 256*256 total_step_num = 900; elseif nrow*ncol == 512*512 total_step_num = 1500; end total_iteration_num = 3; for iteration_idx = 1: total_iteration_num %record the positions where ant have reached in the last 'memory_length' iterations delta_p = zeros(nrow, ncol); for step_idx = 1: total_step_num delta_p_current = zeros(nrow, ncol); for ant_idx = 1:ant_total_num ant_current_row_idx = ant_pos_idx(ant_idx,1); ant_current_col_idx = ant_pos_idx(ant_idx,2); % find the neighborhood of current position if search_clique_mode == '4' rr = ant_current_row_idx; cc = ant_current_col_idx; ant_search_range_temp = [rr-1 cc; rr cc+1; rr+1 cc; rr cc-1]; elseif search_clique_mode == '8' rr = ant_current_row_idx; cc = ant_current_col_idx; ant_search_range_temp = [rr-1 cc-1; rr-1 cc; rr-1 cc+1; rr cc-1; rr cc+1; rr+1 cc-1; rr+1 cc; rr+1 cc+1]; end %remove the positions our of the image's range temp = find(ant_search_range_temp(:,1)>=1 & ant_search_range_temp(:,1)<=nrow & ant_search_range_temp(:,2)>=1 & ant_search_range_temp(:,2)<=ncol); ant_search_range = ant_search_range_temp(temp, :); %calculate the transit prob. to the neighborhood of current %position ant_transit_prob_v = zeros(size(ant_search_range,1),1); ant_transit_prob_p = zeros(size(ant_search_range,1),1); for kk = 1:size(ant_search_range,1) temp = (ant_search_range(kk,1)-1)*ncol + ant_search_range(kk,2); if length(find(ant_memory(ant_idx,:)==temp))==0 %not in ant's memory ant_transit_prob_v(kk) = v(ant_search_range(kk,1), ant_search_range(kk,2)); ant_transit_prob_p(kk) = p(ant_search_range(kk,1), ant_search_range(kk,2)); else %in ant's memory ant_transit_prob_v(kk) = 0; ant_transit_prob_p(kk) = 0; end end % if all neighborhood are in memory, then the permissible search range is RE-calculated. if (sum(sum(ant_transit_prob_v))==0) | (sum(sum(ant_transit_prob_p))==0) for kk = 1:size(ant_search_range,1) temp = (ant_search_range(kk,1)-1)*ncol + ant_search_range(kk,2); ant_transit_prob_v(kk) = v(ant_search_range(kk,1), ant_search_range(kk,2)); ant_transit_prob_p(kk) = p(ant_search_range(kk,1), ant_search_range(kk,2)); end end ant_transit_prob = (ant_transit_prob_v.^alpha) .* (ant_transit_prob_p.^beta) ./ (sum(sum((ant_transit_prob_v.^alpha) .* (ant_transit_prob_p.^beta)))); % generate a random number to determine the next position. rand('state', sum(100*clock)); temp = find(cumsum(ant_transit_prob)>=rand(1), 1); ant_next_row_idx = ant_search_range(temp,1); ant_next_col_idx = ant_search_range(temp,2); if length(ant_next_row_idx) == 0 ant_next_row_idx = ant_current_row_idx; ant_next_col_idx = ant_current_col_idx; end ant_pos_idx(ant_idx,1) = ant_next_row_idx; ant_pos_idx(ant_idx,2) = ant_next_col_idx; %record the delta_p_current delta_p_current(ant_pos_idx(ant_idx,1), ant_pos_idx(ant_idx,2)) = 1; % record the new position into ant's memory if step_idx <= memory_length ant_memory(ant_idx,step_idx) = (ant_pos_idx(ant_idx,1)-1)*ncol + ant_pos_idx(ant_idx,2); elseif step_idx > memory_length ant_memory(ant_idx,:) = circshift(ant_memory(ant_idx,:),[0 -1]); ant_memory(ant_idx,end) = (ant_pos_idx(ant_idx,1)-1)*ncol + ant_pos_idx(ant_idx,2); end %update the pheromone function (10) in IEEE-CIM-06 p = ((1-rho).*p + rho.*delta_p_current.*v).*delta_p_current + p.*(abs(1-delta_p_current)); end % end of ant_idx % update the pheromone function see equation (9) in IEEE-CIM-06 delta_p = (delta_p + (delta_p_current>0))>0; p = (1-phi).*p; %equation (9) in IEEE-CIM-06 end % end of step_idx end % end of iteration_idx % generate edge map matrix % It uses pheromone function to determine edge? T = func_seperate_two_class(p); %eq. (13)-(21), Calculate the threshold to seperate the edge map into two class fprintf('Done!\n'); imwrite(uint8(abs((p>=T).*255-255)), gray(256), [filename '_edge_aco_' num2str(nMethod) '.bmp'], 'bmp'); end % end of nMethod %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Inner Function %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function level = func_seperate_two_class(I) % ISODATA Compute global image threshold using iterative isodata method. % LEVEL = ISODATA(I) computes a global threshold (LEVEL) that can be % used to convert an intensity image to a binary image with IM2BW. LEVEL % is a normalized intensity value that lies in the range [0, 1]. % This iterative technique for choosing a threshold was developed by Ridler and Calvard . % The histogram is initially segmented into two parts using a starting threshold value such as 0 = 2B-1, % half the maximum dynamic range. % The sample mean (mf,0) of the gray values associated with the foreground pixels and the sample mean (mb,0) % of the gray values associated with the background pixels are computed. A new threshold value 1 is now computed % as the average of these two sample means. The process is repeated, based upon the new threshold, % until the threshold value does not change any more. % % Reference :T.W. Ridler, S. Calvard, Picture thresholding using an iterative selection method, % IEEE Trans. System, Man and Cybernetics, SMC-8 (1978) 630-632. % Convert all N-D arrays into a single column. Convert to uint8 for % fastest histogram computation. I = I(:); % STEP 1: Compute mean intensity of image from histogram, set T=mean(I) [counts, N]=hist(I,256); i=1; mu=cumsum(counts); T(i)=(sum(N.*counts))/mu(end); % STEP 2: compute Mean above T (MAT) and Mean below T (MBT) using T from % step 1 mu2=cumsum(counts(N<=T(i))); MBT=sum(N(N<=T(i)).*counts(N<=T(i)))/mu2(end); mu3=cumsum(counts(N>T(i))); MAT=sum(N(N>T(i)).*counts(N>T(i)))/mu3(end); i=i+1; T(i)=(MAT+MBT)/2; % STEP 3 to n: repeat step 2 if T(i)~=T(i-1) Threshold=T(i); while abs(T(i)-T(i-1))>=1 mu2=cumsum(counts(N<=T(i))); MBT=sum(N(N<=T(i)).*counts(N<=T(i)))/mu2(end); mu3=cumsum(counts(N>T(i))); MAT=sum(N(N>T(i)).*counts(N>T(i)))/mu3(end); i=i+1; T(i)=(MAT+MBT)/2; Threshold=T(i); end % Normalize the threshold to the range [i, 1]. level = Threshold;