Image Processing Toolbox

Using the Radon Transform to Detect Lines

The Radon transform is closely related to a common computer vision operation known as the Hough transform. You can use the radon function to implement a form of the Hough transform used to detect straight lines. The steps are:

1. Compute a binary edge image using the edge function.

• I = imread('ic.tif');
  BW = edge(I);
  imshow(I)
  figure, imshow(BW)
  
  
  

2. Compute the Radon transform of the edge image.

• theta = 0:179;
  [R,xp] = radon(BW,theta);
  figure, imagesc(theta, xp, R); colormap(hot);
  xlabel('\theta (degrees)'); ylabel('X\prime');
  title('R_{\theta} (X\prime)');
  colorbar
  
  
  

Figure 8-15: Radon Transform of an Edge Image

3. Find the locations of strong peaks in the Radon transform matrix. The locations of these peaks correspond to the location of straight lines in the original image.

In this example, the strongest peak in R corresponds to and . The line perpendicular to that angle and located at is shown below, superimposed in red on the original image. The Radon transform geometry is shown in black.

Figure 8-16: The Radon Transform Geometry and the Strongest Peak (Red)

Notice that the other strong lines parallel to the red line also appear as peaks at in the transform. Also, the lines perpendicular to this line appear as peaks at .

Radon Transform

The Inverse Radon Transform