Parameter probability density analysis for the Hough transform

Abstract The Hough transform is a widely used technique in computer vision. An analysis of the probability density distributions in parameter space is an indispensable prerequisite for performing subsequent object detection because of unavoidable noise. Assuming that the input image is only uniform noise we systematically analyze the parameter density distributions for line detection and circle center detection when the Hough transform is carried out under different procedures. For the above two cases, we have found general results, which are independent of the shape and position of the image. Moreover, these general results convert the problem of determining the parameter density functions into a much easier one of calculating line or arc lengths.