Geometric Constructions for Predicting Hough Transform Performance

Graphical techniques are presented for estimating Hough transform performance for detecting straight lines in noisy digital pictures. The methods show explicitly the influence of noise due, for example, to quantizing errors on the accuracy of estimating the underlying sets of collinear points. Exact bounds are obtained for sets of collinear points showing that under quite general conditions only the endpoints are of significance. Theorems governing grid size for the accumulator method are given.