An investigation of the nature of parameterization for the Hough transform

A novel parameterization 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 parameterization 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 parameterizations avoids the problem. Finally, a particular solution of the parameterization scheme is described which is called the Fourier parameterization. It is shown that the parameterization has uniform precision with respect to the affine transformation. (C) 1997 Pattern Recognition Society.