中文摘要：

Hough变换因其固有的鲁棒性在众多视觉问题中得到了广泛应用.文中探讨了当Hough变换的参数空间均匀离散化后,如果要求不同的直线对应不同的计数器,则对应的离散参数空间所需的最少计数器个数的问题.以Hough变换的标准参数（ρ,θ）空间为例进行探讨,相关方法完全可以推广到Hough变换的其他参数化形式.文中的结果从一个侧面揭示了图像均匀噪声在Hough变换参数空间分布的固有的不均匀性现象,这种不均匀性必然导致Hough变换在直线检测时直线位置和朝向的依赖性对噪声的不同敏感程度,该结果对从事Hough变换研究的相关人员具有一定的参考作用.

英文摘要：

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.