An investigation of the nature of parameterization for the Hough transform

摘要

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.