Statistical properties of the Hough transform estimator in the presence of measurement errors

The Hough transform is a common computer vision algorithm used to detect shapes in a noisy image. Originally the Hough transform was proposed as a technique for detection of straight lines in images. In this paper we study the statistical properties of the Hough transform estimator in the presence of measurement errors. We consider the simple case of detection of one line parameterized in polar coordinates. We show that the estimator is consistent, and possesses a rate of convergence of the cube-root type. We derive its limiting distribution, and study its robustness properties. Numerical results are discussed as well. In particular, based on extensive experiments, we define a "rule of thumb" for the determination of the optimal width parameter of the template used in the algorithm.