Segmentation of Planar Curves into Straight-Line Segments and Elliptical Arcs

Abstract

This paper presents a procedure for segmenting planar curves, mainly the projected boundary contours of machined parts, into straight-line segments and elliptical arcs. The break points are divided into two types: corners and smooth joins. The corners are detected by first applying adaptive smoothing to the tangent orientation along the curve, then taking the derivative of the smoothed tangent orientation, and finally locating the high spikes on the derivative. The smooth joins are first roughly located by a dynamic focusing fitting technique and then refined by an adjustment algorithm. The dynamic focusing fitting technique holds one end of a curve segment (which is bounded by a pair of adjacent corners) fixed and scans it from the other end until it focuses on a component segment which fits either a straight line or an elliptical arc. This component segment is identified and the process is repeated in the same manner for the rest of the curve. In the refining stage, each smooth join is adjusted to the left or to the right, point by point, until the measurement of goodness of fit for the curve segment is optimized. Tests of the procedure were performed with the boundary curves of three real object images.