A digitized picture in 2D array of points is often desired to be approximated by polygonal lines, with 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''. And we present linear time algorithms that find minimax polygons, windows in the edges and the reversibly polygons. Based on these algorithms we finally produce a general polygonal line that lies in the reversibly polygon and approximates the polygonal line of given data.Keywords; Polygonal line, approximation, windows in the edges, reversibly visible polygons.