image processing - Rectangle detection with Hough transform

Question

I'm trying to implement rectangle detection using the Hough transform, based on this paper.

I programmed it using Matlab, but after the detection of parallel pair lines and orthogonal pairs, I must detect the intersection of these pairs. My question is about the quality of the two line intersection in Hough space.

I found the intersection points by solving four equation systems. Do these intersection points lie in cartesian or polar coordinate space?

Answer 1

For those of you wondering about the paper, it's:

Rectangle Detection based on a Windowed Hough Transform by Cláudio Rosito Jung and Rodrigo Schramm.

Now according to the paper, the intersection points are expressed as polar coordinates, obviously you implementation may be different (the only way to tell is to show us your code).

Assuming you are being consistent with his notation, your peaks should be expressed as:

You must then perform peak paring given by equation (3) in section 4.3 or

where represents the angular threshold corresponding to parallel lines and is the normalized threshold corresponding to lines of similar length.