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

I am not a mathematician. I am willing to stand corrected...
From Hough 2) ... any line on the xy plane can be described as p = x cos theta + y sin theta. In this representation, p is the normal distance and theta is the normal angle of a straight line, ... In practical applications, the angles theta and distances p are quantized, and we obtain an array C(p, theta).
from CRC standard math tables Analytic Geometry, Polar Coordinates in a Plane section ... Such an ordered pair of numbers (r, theta) are called polar coordinates of the point p. Straight lines: let p = distance of line from O, w = counterclockwise angle from OX to the perpendicular through O to the line. Normal form: r cos(theta - w) = p. From this I conclude that the points lie in polar coordinate space.