A Note on Minimum Discrete Hough Parameter Space

Hough transform is widely used in various vision problems due to its inherent robustness.This work is intended to investigate the minimum required accumulators under the condition that each parameter is equidistantly discredited and each different realizable line in a point grid should vote to a different accumulator.In particular,the normal line parameterization is investigated,and the result could be generalized to other parameterizations.Our results demonstrate that the uniform noise in the image space will result in non-uniform distribution in Hough space,and this non-uniformness will in turn inevitably produce the undesirable effect of the dependency of line detection performance on its location and orientation.Our results could be of reference to those people who are interested in Hough transform.