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function [drak,gray,brig] = Fuzzy_Knowledge(Intensity)

  if(Intensity <= 0.27) drak = double(1); 
  elseif(Intensity >= 0.5) drak = double(0);
  else drak = (0.5 - double(Intensity))/(0.22);
  end    
  if(Intensity >= 0.72) brig = double(1); 
  elseif(Intensity <= 0.5) brig = double(0);   
  else brig = double((double(Intensity) - 0.5)/0.22);
  end
  if(Intensity >= 0.72) gray = double(0); 
  elseif(Intensity <= 0.27) gray = double(0);
  elseif(Intensity <= 0.5) gray = double((double(Intensity) - 0.27)/0.22);
  else gray = double((0.72 - double(Intensity))/0.22);
  end
end

close all;
clear all;
clc;

%% ---------Using Fuzzy for intensity transfromations---------------
f = imread('einstein_orig.tif');
f = mat2gray(f,[0 255]);

[M,N]=size(f);
g = zeros (M,N);

 for x = 1:1:M
     for y = 1:1:N
         [drak,gray,brig] = Fuzzy_Knowledge(f(x,y));
         g(x,y) = ((drak * 0) + (gray * 0.5) + (brig * 1))/(drak + gray + brig); 
     end
 end
figure();
subplot(1,2,1);
imshow(f,[0 1]);
xlabel('a).Original Image');

subplot(1,2,2);
imshow(g,[0 1]);
xlabel('b).Result of fuzzy');

figure();
subplot(1,2,1);
h = imhist(f)/(M*N);
bar(0:1/255:1,h);
axis([0 1 0 .2]),grid;
xlabel('c).The Histogram of a');

subplot(1,2,2);
h = imhist(g)/(M*N);
bar(0:1/255:1,h);
axis([0 1 0 .2]),grid;
xlabel('d).The Histogram of b');

%%
test = 0:1/255:1;
 for x = 1:1:256
         [drak(x),gray(x),brig(x)] = Fuzzy_Knowledge(test(x));
 end

figure();
subplot(1,2,1);
plot(test,drak,test,gray,test,brig); 
axis([0,1,0,1]),grid;
axis square;
legend('drak','gray','brig');
xlabel('a).Input memberchip functions for fuzzy');


subplot(1,2,2);
x1 = [0,0];y1 = [0,1];
x2 = [0.5,0.5];y2 = [0,1];
x3 = [1,1];y3 = [0,1];
plot(x1,y1,x2,y2,x3,y3); 
axis([-0.1,1.1,0,1.2]),grid;
axis square;
legend('drak','gray','brig');
xlabel('b).Output memberchip functions for fuzzy');

function [W1,W2,W3,W4,B] = Fuzzy_Knowledge_Filters(Intensity)

for x = 1:1:3
   for y = 1:1:3
       if((Intensity(x,y) <= 0.2) &&(Intensity(x,y) >= -0.2))
           Intensity(x,y) = exp(-20*Intensity(x,y).*Intensity(x,y));
       else Intensity(x,y) = 0;
       end
   end
end

W1 = min(Intensity(1,2),Intensity(2,3));
W2 = min(Intensity(2,3),Intensity(3,2));
W3 = min(Intensity(3,2),Intensity(2,1));
W4 = min(Intensity(2,1),Intensity(1,2));
B = min(min(1-W1,1-W2),min(1-W3,1-W4));
end

%% ---------Using Fuzzy for Spatial Filters---------------
close all;
clear all;
clc;

f = imread('headCT_Vandy.tif');
f = mat2gray(f,[0 255]);

[M,N]=size(f);
f_Ex = zeros(M+2,N+2);

for x = 1:1:M
    for y = 1:1:N
        f_Ex(x+1,y+1) = f(x,y);
    end
end

z = zeros (3,3);
g = zeros (M+2,N+2);
for x = 2:1:M+1
    for y = 2:1:N+1
        z(1,1) = f_Ex(x-1,y-1) - f_Ex(x,y);
        z(1,2) = f_Ex(x-1,y) - f_Ex(x,y);
        z(1,3) = f_Ex(x-1,y+1) - f_Ex(x,y);
        z(2,1) = f_Ex(x,y-1) - f_Ex(x,y);
        z(2,2) = f_Ex(x,y) - f_Ex(x,y);
        z(2,3) = f_Ex(x,y+1) - f_Ex(x,y);
        z(3,1) = f_Ex(x+1,y-1) - f_Ex(x,y);
        z(3,2) = f_Ex(x+1,y) - f_Ex(x,y);
        z(3,3) = f_Ex(x+1,y+1) - f_Ex(x,y);
        [W1,W2,W3,W4,B] = Fuzzy_Knowledge_Filters(z);
        V1 = 0.8 * W1 + 0.2;
        V2 = 0.8 * W2 + 0.2;
        V3 = 0.8 * W3 + 0.2;
        V4 = 0.8 * W4 + 0.2;
        V5 = 0.8 - (0.8 * B);
        g(x,y) = ((W1*V1) + (W2*V2) + (W3*V3) + (W4*V4) + (B*V5))/(W1+W2+W3+W4+B); 
    end
end

figure();
subplot(1,2,1);
imshow(f,[0 1]);
xlabel('a).Original Image');

subplot(1,2,2);
imshow(g,[0 1]);
xlabel('b).Result of fuzzy');


%%
figure();
subplot(1,2,1);
x=-0.2:1/255:0.2;
y=1/sqrt(2*pi)*exp(-20*x.*x);
y = y/max(y);
x = -1:1/255:1;
y = [zeros(1,204) y zeros(1,204)];
plot(x,y); 
axis([-1,1,0,1]),grid;
axis square;
xlabel('a).Input memberchip functions for fuzzy');

subplot(1,2,2);
x1 = [0,0.2,1];y1 = [0,0,1];
x2 = [0,0.8,1];y2 = [1,0,0];
plot(x1,y1,x2,y2); 
axis([0,1,0,1]),grid;
axis square;
legend('WH','BL');
xlabel('b).Output memberchip functions for fuzzy');