In digital geometry we study the properties of discrete representations of geometrical sets; in general, a discrete representation consists of a set of digital points on a rectangular grid. In this paper we consider discrete representations that can be specified by linear inequalities. For example, a digital straight line, and more generally, a digital hyperplane can be specified by an expression that involves two inequalities. First, we describe an elimination method to solve systems of inequalities; it is based on a theorem on convex sets due to Helly. Next, we discuss how this method can be used to derive properties of digital sets. Finally, we illustrate this approach for digital curves. In particular, we show how the chord property for digital straight lines can be extended to digital curves of arbitrary order.
Peter Veelaert, Peter Veelaert,
"Elimination theory for systems of linear inequalities applied to problems in digital geometry", Proc. SPIE 1832, Vision Geometry, (9 April 1993); doi: 10.1117/12.142183; https://doi.org/10.1117/12.142183