Recursive computation of minimum-length polygons

摘要

The relative convex hull, or the minimum-perimeter polygon (MPP) of a simple polygon A, contained in a second polygon B, is a unique polygon in the set of nested polygons between A and B. The computation of the minimum-length polygon (MLP), as a special case for isothetic polygons A and B, is useful for various applications in image analysis and robotics. The paper discusses the first recursive approach to compute the relative convex hull for the general case of simple polygons A and B, following an earlier publication by the author, and it derives a (methodologically more simple) algorithm to compute the MLP for the special case of isothetic polygons. The recursive algorithm for the isothetic case allows us to create rooted trees for digitized measurable sets S⊂R2. Those trees are useful for the characterization of digital convexity.