Exercises

1. How could the Hough transform method be used to detect circles of radius 10 units? Show that pixels in (x,y) space would map to circles in this case if Eqn. 8 is used to define circles.
2. Suppose the Hough transform method is to be used to detect circles of arbitrary radius. What would pixels in (x,y) space now map to? How much less efficient would it be to search for arbitrary circles than circles of a fixed radius?
3. We can represent the equation of a circle parametrically by

   
   
   

   How you could implement a Hough Transform to detect circles using this form of equation? Comment on this methods relative merits / drawbacks.

4. How would you use the Hough transform to detect
   1. an ellipse
   2. a hexagon.
5. How would you use the Hough transform to detect three-dimensional shapes (in depth maps). In particular how would detect three-dimensional straight lines.
6. Write a C or PASCAL type procedure to detect straight lines only in an image using the Hough transform algorithm.
7. Draw some simple objects and work out their extended Gaussian images.
8. Give some examples of sets of objects that have the same extended Gaussian image (see Fig. 54).