A Linear Time and Space Algorithm for Detecting Path Intersection

For discrete sets coded by the Freeman chain describing their contour, several linear algorithms have been designed for determining their shape properties. Most of them are based on the assumption that the boundary word forms a closed and non-intersecting discrete curve. In this article, we provide a linear time and space algorithm for deciding whether a path on a square lattice intersects itself. This work removes a drawback by determining efficiently whether a given path forms the contour of a discrete figure. This is achieved by using a radix tree structure over a quadtree, where nodes are the visited grid points, enriched with neighborhood links that are essential for obtaining linearity.