A short introduction to the Radon and Hough transforms and how they relate to each other

Extraction of primitives, such as lines, edges and curves, is often a key step in an image analysis procedure. The most popular technique for curve detection is based on the Hough transform. The original formulation of the Hough transform is inherently discrete. It is therefore difficult to assess which properties are inherent to the transform-based technique and which are due to its discrete nature. As other authors have pointed out before, the Hough transform is closely related to the Radon transform, in fact equivalent, if one is not too pedantic about the original formulations of the two transforms. With this report we hope to once again stress this relationship. The Radon transform formalism has two advantages over the Hough formalism. It has a well-founded mathematical basis and, in our opinion, is more intuitive as well.