An investigation of the nature of parametrization for the Hough transform

A novel parametrization method for the Hough transform is reported. Instead of the conventional non-parametric form, the parametric form is used and copies of the transformed shape are plotted on two dimensional slices of the Hough space. It is shown that the corresponding parametrization has uniform precision with respect to translation, and cancels out the quantization uncertainty due to image digitization. A problem of the Hough transform is discovered which is due to non-uniform discretized voting. It is shown that the above class of parametrizations avoids the problem. Finally, a particular solution of the parametrization scheme is described which is called the Fourier parametrization. It is shown that the parametrization has uniform precision with respect to the affine transformation