Digital Line Recognition, Convex Hull, Thickness, a Unified and Logarithmic Technique

Abstract

The recognition of discrete primitives as digital straight segments (DSS) is a deeply studied problem in digital geometry (see a review in [6]). One characterization of the DSS is purely geometrical: all the points must lie between two lines whose distance (relative to the infinite norm) is less than 1. A common approach used to solve this question is to compute the convex hull of the given points. Recent papers explain how to update the minimum distance when a point is inserted during an online (incremental) recognition in O(log n) time in the general case [2] or in O(1) time with assumption [2, 4]. Nevertheless, for other cases like insertions mixed with deletions or the union of two DSS, we have no optimal method to compute the resulting width. Thus, we propose a unified, simple and optimal approach applicable for any configuration. Moreover, our function is called independently from the convex hull processing. This allows to reuse any existing library without any modification. Thereby, we offer an efficient tool that opens a new horizon for the applications.