Reversibly visible polygons and polygonal approximation in two dimensional space

Abstract

A digitized picture in a 2D array of points is often desired to be approximated by polygonal lines, with the smallest number of sides under the given error tolerance E. To approximate the polygonal line of such data, we introduce two new terms called "windows in the edges" and "reversibly visible polygons". We also present linear time algorithms that find minimax polygons, windows in the edges and the reversibly visible polygons. Based on these algorithms we finally produce a general polygonal line that lies in the reversibly visible polygon and approximates the polygonal line of the given data.