Finding Poly-Curves of Straight Line and Ellipse Segments in Images

Simplification of given polygons has attracted many researchers. Especially, finding circular and elliptical structures in images is relevant in many applications. Given pixel chains from edge detection, this paper proposes a method to segment them into straight line and ellipse segments. We propose an adaption of Douglas-Peucker’s polygon simplification algorithm using circle segments instead of straight line segments and partition the sequence of points instead the sequence of edges. It is robust and decreases the complexity of given polygons better than the original algorithm. In a second step, we further simplify the poly-curve by merging neighbouring segments to straight line and ellipse segments. Merging is based on the evaluation of variation of entropy for proposed geometric models, which turns out as a combination of hypothesis testing and model selection. We demonstrate the results of circlePeucker as well as merging on several images of scenes with significant circular structures and compare them with the method of Patraucean et al. (2012).