The Hough Transform (HT) method has long been recognized as a promising detection technique for images containing noisy, missing, and extraneous data. However, its performance depends very much on the way the transformed space, Hough space (HS), is quantized. Van Veen and Groen (1981) derived formulae specifying the effect of peak spreading in Hough space H (, ) for a line segment when neither oversampling nor undersampling occurs. But since then, no further investigations on other parametric curves were mentioned. In this paper, starting from the point of view of uncertainty incurred in the parameter sampling and quantization, we study its effect on the formation of peaks in the Hough space. In addition, relations between sampling intervals and quantizing intervals for line segments and circles are derived which can serve as a guideline to achieve optimal quantization. For line segments, we arrive at the same result as in (Van Veen and Groen, 1981). Moreover, our approach can also be applied to other parametric curves.