Spatial decomposition of the Hough transform

In the field of image processing, it is a common problem to search for edges within an image, typically using the Hough transform, and attempt to extract the end points of those edges. This paper discusses an improved technique for accomplishing this task. The idea is based on the observation of an additive property of the Hough transform. That is, the global Hough Transform can be obtained by the summation of local Hough transforms of disjoint sub-regions. The method discussed involves the recursive subdivision of the image into sub-images, each with their own parameter space, and organized in a quadtree structure, which allows for implicit storage of arbitrary parameter space manifolds. This method results in improved efficiency in finding endpoints of line segments and improved robustness and reliability in extracting lines in noisy situations, at a slightly increased cost of memory. The new algorithm is presented in detail, along with a discussion of time and space complexities. The paper is concluded with proposed future research in this direction.