Theoretical analysis of hough transform optimal cell size: Segmentation of nearby lines

Hough Transform (HT) is commonly used to solve the line extraction problem. Although images are discretized at the onset, the Hough domain is continuous and in practice it has to be partitioned into cells. It has been suggested that the optimality of the size (resolution) of those cells would depend on the amount noise in the image. In this paper, we study the effect of discretization on the success of line detection where there are nearby lines and develop a theoretical foundation for the optimality of the Hough domain discretization for segmentation purposes. Experiments with real images show that our results are useful in practice for line detection applications.