Three Dimensional Hough Space

Question

Im searching for radius and the center coordinates of circle in a image. have already tried 2D Hough transform. but my circle radius is also a unknown. Im still a beginner to Computer vision so need guild lines and help for implementing three dimensional hough space.

Answer 1

You implement it just like 2D Hough space, but with an additional parameter. Pseudo code would look like this:

for each (x,y) in image
     for each test_radius in [min_radius .. max_radius]
         for each point (tx,ty) in the circle with radius test_radius around (x,y)
             HoughSpace(tx,ty,test_radius) += image(x,y)

Answer 2

Thiton gives you the correct approach to formalize the problem. But then, you will run in other problems inherent to the hough transform:

• how do you visualize the parameter space? You may implement something with a library like VTK, but 3D visualization of data is always a difficult topic. The visualization is important for debugging your detection algorithm and is one of the nice thing with 2D hough transform

• the local maximum detection is non trivial. The new dimension will mean that your parameter space will be more sparse. You will have more tuning to do in this area

If you are looking for a circle detection algorithm, you may have better options than the hough transform (google "Fast Circle Detection Using Gradient Pair Vectors" looks good to me)