N-Point Hough Transform Derived by Geometric Duality

We propose an extension of the three-point Randomized Hough transform. Our new Hough transform, which permits a continuous voting space without any cell-tessellation, uses both one-to-one mapping from an image plane to the parameter space and from the parameter space to the image plane. These transforms define a parameter from samples and a line from a parameter, respectively. Furthermore, we describe the classical Hough transform, the randomized Hough transform, the three-point randomized Hough transform and our new Hough transform in a generalized framework using geometric duality.