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

Answer 1

The link to the referenced paper does not work, but if you used the standard hough transform than the four intersection points will be expressed in cartesian coordinates. In fact, the four lines detected with the hough tranform will be expressed using the "normal parametrization":

rho = x cos(theta) + y sin(theta)

so you will have four pairs (rho_i, theta_i) that identifies your four lines. After checking for orthogonality (for example just by comparing the angles theta_i) you solve four equation system each of the form:

rho_j = x cos(theta_j) + y sin(theta_j)
rho_k = x cos(theta_k) + y sin(theta_k)

where x and y are the unknowns that represents the cartesian coordinates of the intersection point.