Decomposition of the Hough Transform: Curve Detection with Efficient Error Propagation

This paper describes techniques to perform fast and accurate curve detection using a variant of the Hough transform. We show that the Hough transform can be decomposed into small subproblems that examine only a subset of the parameter space. Each subproblem considers only those curves that pass through some small subset of the data points. This property allows the e cient implementation of the Hough transform with respect to both time and space, and allows the careful propagation of the e ects of localization error in the detection process. The use of randomization yields an O(n) worst-case computational complexity for this method, where n is the number of data points, if we are only required to nd curves that are signi cant with respect to the complexity of the data. In addition, this method requires little memory and can be easily parallelized.