Connected distance-based rasterization of objects in arbitrary dimension

In this paper we investigate an approach for constructing a connected digitization of an object S⊆RnS⊆Rn by taking the integer points within an offset of S of a certain radius. We consider the cases when S is a curve, surface, and an arbitrary path-connected object. We determine the minimal value of the offset radius which guarantees connectivity of the digitization. We also derive conditions under which the offset digitization of a disconnected object is always connected.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► We consider the cases when the digitized set is a curve, surface, and an arbitrary pathconnected object. ► We determine the minimal value of the offset radius which guarantees connectedness of the digitization. ► We also derive conditions under which the offset digitization of a disconnected object is always connected.