This has the nice property that it's easy to calculate the distance between a given line ( point in hough space ) and the nearest point on the circle as a single square root.
On the down side, because the hough transform usually takes advantage of the distortion of euclidean distance for small \theta , the end result has an absolute maxima at ( 0, 0 ). This maxima is very predictable, so I'm going to try just dividing by a function which is an idealized model near the origin, but quickly approaches 1 instead of 0 in every direction.
Still, without further ado, some pictures:
|This image shows a single line: x + y = 10. In hough space this corresponds to the maxima at (5, 5). notice the nasty spurious point (0, 0).|
|x + y = 10, x + y = -10, and x + y = 20.|
|Just x + y = 10 and x + y = 20|
|x + y = 10, y - x = 10 and y = -7. This is a fairly unfavorable set of points. I think the top left maxima would be rather hard for a computer to locate.|
|The same three lines as above, but this time I picked sample points in the triangle. Much easier to locate all three maxima.|
Update: Quotienting out the central maxima works! This is the same triangle data set as above.