Demo of Hough Transform for straight lines

David Young

Contents

Read in the chessboard image

This assumes that the Sussex vision library is in your Matlab path.

The image is read, converted to gray-level and then displayed in a new figure.

im = teachimage();
f1 = figure; imshow(im);

Find edges

We use the Canny edge detector, from the Matlab Image Processing Toolbox. The thresholds (0.1 and 0.2) and the smoothing constant (2) have been tweaked by trial and error to work well for this image. Note that the smoothing has to remove the high spatial frequency texture in the background.

After finding the edges, we display the binary edge map in a new figure.

e = edge(im, , [0.1 0.2], 2);
figure; imshow(e);

Perform the Hough transform

We call the Matlab toolbox hough function to perform the tranform. Use the Matlab command helpwin hough to get more details, and see the lecture slides for more information on the principles behind the process.

In the display of the accumulator array, the theta axis runs vertically, and the rho axis runs horizontally. The two roughly horizontal rows of bright dots correspond to the two sets of lines at different angles on the chessboard.

The default settings for the bin sizes mean that for this input image, there are more bins in the rho direction than in the theta direction. This can easily be changed, but the defaults work well in this case.

[h, theta, rho] = hough(e);
figure; imshow(sqrt(h'), []);

Find the peaks in the transform

We use the toolbox function to locate the peak positions. Again, the parameters have been tweaked to suit this specific image. The maximum number of peaks to find is 21, and peaks must not be closer together than 27 bins in rho and 11 bins in theta.

p = houghpeaks(h, 21, , 0, , [27 11]);

Plot the lines on the image

We first convert the angles used from degrees to radians (because normal Matlab functions use radians - hough is peculiar in returning degrees). We switch back to the figure containing the original image for drawing.

We then use a loop to plot each line. (It would be possible, but fiddly, to vectorise this code.) line_box is another local function that just returns the coordinates of the points where the line intersects the boundaries of the image, to simplify plotting.

The results are good but not perfect - but that's to be expected, given that there are many objects and textures in the image.

theta = (pi/180)*theta;
figure(f1);           

[nr, nc] = size(im);
hold                
 pr = p'           
    r = rho(pr(1));   
    t = theta(pr(2)); 
    l = line_box(1, nc, 1, nr, r, t);   
 ~isempty(l)
        plot(l([1 3]), l([2,4]), , , 1);


hold 

Experimenting yourself

You can experiment with this demonstration yourself, by downloading this html document and using Matlab's grabcode function to extract the original M-file. You can then edit it to change the parameters or to try, perhaps, the toolbox houghlines function.

This document may be accessible from outside Sussex University, but to use functions from the local library you need to be a student or member of staff of the University.

Copyright University of Sussex, 2006

Published with MATLAB? 7.1