Hough Transform

The Image Processing Toolbox™ supports functions that enable you to use the Hough transform to detect lines in an image.

The hough function implements the Standard Hough Transform (SHT). The Hough transform is designed to detect lines, using the parametric representation of a line:

rho = x*cos(theta) + y*sin(theta)

The variable rho is the distance from the origin to the line along a vector perpendicular to the line. theta is the angle between the x-axis and this vector. The hough function generates a parameter space matrix whose rows and columns correspond to these rho and theta values, respectively.

After you compute the Hough transform, you can use the houghpeaks function to find peak values in the parameter space. These peaks represent potential lines in the input image.

After you identify the peaks in the Hough transform, you can use the houghlines function to find the endpoints of the line segments corresponding to peaks in the Hough transform. This function automatically fills in small gaps in the line segments.

I = imread('circuit.tif');
rotI = imrotate(I,33,'crop');
imshow(rotI)

BW = edge(rotI,'canny');
imshow(BW);

[H,theta,rho] = hough(BW);

figure
imshow(imadjust(rescale(H)),[],...
       'XData',theta,...
       'YData',rho,...
       'InitialMagnification','fit');
xlabel('\theta (degrees)')
ylabel('\rho')
axis on
axis normal 
hold on
colormap(gca,hot)

P = houghpeaks(H,5,'threshold',ceil(0.3*max(H(:))));

x = theta(P(:,2));
y = rho(P(:,1));
plot(x,y,'s','color','black');

lines = houghlines(BW,theta,rho,P,'FillGap',5,'MinLength',7);

figure, imshow(rotI), hold on
max_len = 0;
for k = 1:length(lines)
   xy = [lines(k).point1; lines(k).point2];
   plot(xy(:,1),xy(:,2),'LineWidth',2,'Color','green');

   % Plot beginnings and ends of lines
   plot(xy(1,1),xy(1,2),'x','LineWidth',2,'Color','yellow');
   plot(xy(2,1),xy(2,2),'x','LineWidth',2,'Color','red');

   % Determine the endpoints of the longest line segment
   len = norm(lines(k).point1 - lines(k).point2);
   if ( len > max_len)
      max_len = len;
      xy_long = xy;
   end
end
% highlight the longest line segment
plot(xy_long(:,1),xy_long(:,2),'LineWidth',2,'Color','red');