I'm studying Hough Transform. I have fully understood the HT for detecting lines and successfully implemented it. I have more problems with the circle detection HT. Given a circle, if the radius is known i have to work in a 2d parameter space (each point in the image space becomes a circle in the parameter space; the intersection of all the circles gives me the center of the image circle).If the radius is not known the parameter space becomes 3d.What i don't understand is why if i know the direction of the edges, even if my radius is unknown the parameter space lowers to 2d.
Circle Hough Transform. Improvement by knowing edge direction
image processing;computer vision