This part gives the algorithm of Canny edge detector. The outputs are six subfigures shown in the same figure:
* Subfigure 1: The initial "lena"
* Subfigure 2: Edge detection along X-axis direction
* Subfigure 3: Edge detection along Y-axis direction
* Subfigure 4: The Norm of the image gradient
* Subfigure 5: The Norm of the gradient after thresholding
* Subfigure 6: The edges detected by thinning
The matlab codes:
%%%%%%%%%%%%% The main.m file %%%%%%%%%%%%%%%
clear;
% The algorithm parameters:
% 1. Parameters of edge detecting filters:
% X-axis direction filter:
Nx1=10;Sigmax1=1;Nx2=10;Sigmax2=1;Theta1=pi/2;
% Y-axis direction filter:
Ny1=10;Sigmay1=1;Ny2=10;Sigmay2=1;Theta2=0;
% 2. The thresholding parameter alfa:
alfa=0.1;
% Get the initial image lena.gif
[x,map]=gifread('lena.gif');
w=ind2gray(x,map);
figure(1);colormap(gray);
subplot(3,2,1);
imagesc(w,200);
title('Image: lena.gif');
% X-axis direction edge detection
subplot(3,2,2);
filterx=d2dgauss(Nx1,Sigmax1,Nx2,Sigmax2,Theta1);
Ix= conv2(w,filterx,'same');
imagesc(Ix);
title('Ix');
% Y-axis direction edge detection
subplot(3,2,3)
filtery=d2dgauss(Ny1,Sigmay1,Ny2,Sigmay2,Theta2);
Iy=conv2(w,filtery,'same');
imagesc(Iy);
title('Iy');
% Norm of the gradient (Combining the X and Y directional derivatives)
subplot(3,2,4);
NVI=sqrt(Ix.*Ix.*Iy);
imagesc(NVI);
title('Norm of Gradient');
% Thresholding
I_max=max(max(NVI));
I_min=min(min(NVI));
level=alfa*(I_max-I_min)_min;
subplot(3,2,5);
Ibw=max(NVI,level.*ones(size(NVI)));
imagesc(Ibw);
title('After Thresholding');
% Thinning (Using interpolation to find the pixels where the norms of
% gradient are local maximum.)
subplot(3,2,6);
[n,m]=size(Ibw);
for i=2:n-1,
for j=2:m-1,
if Ibw(i,j) > level,
X=[-1,0,;-1,0,;-1,0,];
Y=[-1,-1,-1;0,0,0;,,];
Z=[Ibw(i-1,j-1),Ibw(i-1,j),Ibw(i-1,j);
Ibw(i,j-1),Ibw(i,j),Ibw(i,j);
Ibw(i,j-1),Ibw(i,j),Ibw(i,j)];
XI=[Ix(i,j)/NVI(i,j), -Ix(i,j)/NVI(i,j)];
YI=[Iy(i,j)/NVI(i,j), -Iy(i,j)/NVI(i,j)];
ZI=interp2(X,Y,Z,XI,YI);
if Ibw(i,j) >= ZI(1) & Ibw(i,j) >= ZI(2)
I_temp(i,j)=I_max;
else
I_temp(i,j)=I_min;
end
else
I_temp(i,j)=I_min;
end
end
end
imagesc(I_temp);
title('After Thinning');
colormap(gray);
%%%%%%%%%%%%%% End of the main.m file %%%%%%%%%%%%%%%
%%%%%%% The functions used in the main.m file %%%%%%%
% Function "d2dgauss.m":
% This function returns a 2D edge detector (first order derivative
% of 2D Gaussian function) with size n1*n2; theta is the angle that
% the detector rotated counter clockwise; and sigma1 and sigma2 are the
% standard deviation of the gaussian functions.
function h = d2dgauss(n1,sigma1,n2,sigma2,theta)
r=[cos(theta) -sin(theta);
sin(theta) cos(theta)];
for i = 1 : n2
for j = 1 : n1
u = r * [j-(n1)/2 i-(n2)/2]';
h(i,j) = gauss(u(1),sigma1)*dgauss(u(2),sigma2);
end
end
h = h / sqrt(sum(sum(abs(h).*abs(h))));
% Function "gauss.m":
function y = gauss(x,std)
y = exp(-x^2/(2*std^2)) / (std*sqrt(2*pi));
% Function "dgauss.m"(first order derivative of gauss function):
function y = dgauss(x,std)
y = -x * gauss(x,std) / std^2;
%%%%%%%%%%%%%% end of the functions %%%%%%%%%%%%%