Counting Gaps in Binary Pictures

摘要

An important concept in combinatorial image analysis is that of gap. In this paper we derive a simple formula for the number of gaps in a 2D binary picture. Our approach is based on introducing the notions of free vertex and free edge and studying their properties from point of view of combinatorial topology. The number of gaps characterizes the topological structure of a binary picture and is of potential interest in property-based image analysis.