Deriving stopping rules for the probabilistic Hough transform by sequential analysis

In probabilistic Hough transforms computation is accelerated by polling instead of voting. A small part of the data set is selected at random and used as input to the algorithm. Most probabilistic Hough algorithms use a fixed poll size. It has been experimentally demonstrated that adaptive termination of voting can lead to improved performance in terms of the error rate versus average poll size tradeoff. However, the lack of a solid theoretical foundation made general performance evaluation and optimal design of adaptive stopping rules nearly impossible. In this paper we suggest two novel adaptive stopping rules in the framework of the statistical theory of sequential hypothesis testing. The performance of the suggested stopping rules is verified using real images. It is shown that the extension suggested in this paper to Wald's one sided alternative sequential test (1947) performs better than previously available adaptive (or fixed) stopping rules.