Question

Papers have been written describing how the Hough transform can be generalised to detect shapes like circles and parabolas. I’m new to computer vision though and find these papers pretty tough going. There is also code out there that does this detection but this is more than I want. I was wondering if anyone could briefly describe in bullet points or pseudo-code really simply how Hough Transforms are used to detect parabolas in images. That would be amazing. Or if anyone knows any basic explanations online that I haven’t come across than that would be good enough too :).

Thanks very much :).

Answer 1

Interesting question. This looks like a great resource. I included a summary (loosely quoted). Also see the source from Mathworks at the bottom of this answer – Matlab has houghlines and houghpeaks functions which will be useful for you. Hope it helps.

• Run edge detection algorithm, such as the Canny edge detector, on subject image
• Input edge/boundary points into Hough Transform (line detecting)
  • Generate a curve in polar space (radius, angle) for each point
    in Cartesian space (also called
    accumulator array)
  • Extract local maxima from the accumulator array, for example using a
    relative threshold
  • In other words, we take only those local maxima in the accumulator
    array whose values are equal to or
    greater than some fixed percentage of
    the global maximum value.
• De-Houghing into Cartesian space yields a set of line descriptions of the image subject

cs.jhu.edu:
http://www.cs.jhu.edu/~misha/Fall04/GHT1.pdf

Code from Mathworks: http://www.mathworks.com/help/toolbox/images/ref/hough.html