Tightening: Morphological simplification
Given a two- or three-dimensional set S of arbitrary topology and a radius r, we show how to construct an r-tightening of S, which is a set whose boundary has mean curvature with magnitude less than or equal to 1/r and which only differs from S in a morphologically-defined tolerance zone we call themortar. The mortar consists of the thin or highly curved parts of S and its complements, such as corners, gaps, and small connected components, while the boundary of a tightening consists of components of locally minimal lenght (in 2D) or area (in 3D) that lie in the mortar. Tightenings are defined independently of shape representation, and it may be possible to find them using a variety of algorithms. We describe how to approximately compute tightenings for two-dimensional sets represented as binary images and for three-dimensional sets represented as triangle meshes using constrained, level-set curvature flow.
simplification topology mathematical morphology