Introduction

The Hough Transform is known as the popular and powerful technique for finding multiple lines in a binary image, and has been used in various applications. Though the principle of the Hough Transform is rather simple and seems easy to use, we cannot bring out precise results without paying enough attention to the arrangement of the parameter space used in the Hough Transform. This document gives a brief explanation on the parameter errors in the Hough Transform and shows that there exists the upper bound of the sampling interval. This document is intended for helping readers designing the Hough Transform appropriate for their systems as well.

The detail of the theoretical analysis on the errors in the Hough Transform can be found in the following paper.

• H. Goto and H. Aso, ``The Efficient Sampling Interval of the Scanning Parameter in the Hough Transform,'' Systems and Computers in Japan, Vol.29, No.11, pp.9-19, 1998, Scripta Technica, Inc.

I omit the introduction of the Hough Transform for line detection here, because there are a lot of websites and books about the transformation. For example:

• Generalized Hough Transform (in XFormics)
• V.F. Leavers, ``Shape Detection in Computer Vision Using the Hough Transform,'' Springer-Verlag.