Hough Transformation in  "Hesse´scher Normalenform"

Mathmatical background

Normally a straight line is described as an equation like Y=aX+b where a is the slope and b is the y-axis section.

Another possibility is to represent a straight line with to components. Let r be the distance from the origin and

Θ the angel relative to the normal:

Then the equation of the line is r = x*cosΘ + y*sinΘ

So the Hough representation of a point (x,y) in the image space is a sinusoidal function because Θ ranges from 0 to 360 degree and every point

(Θ,r) in the Hough space is a possible line in the original image.