The efficient sampling interval+ of the scanning parameter in the hough transform

It is well known that in the Hough transform, the sampling interval of the scanning parameter influences the vote distribution around the peak in parameter space. Decreasing the sampling interval to improve the precision of parameters increases the computation cost, and this often becomes a major problem in applications using Hough transform. A standard that guarantees the practical precision of parameters is required for the sampling interval. In this paper, we first define two types of noise: the transformation noise, caused by the Hough transform, and the quantization noise, caused by the quantization of the image. We investigate their distribution. A condition is derived that the transformation noise must satisfy under the assumption that sufficient image resolution must be retained, and we introduce a method for deriving the upper bound of the sampling interval.