中文摘要：

通过物体的对称性,人们可以推断物体的结构并估计它的形状,从而恢复被遮挡或丢失部分的信息。针对二维点集,提出了一种新的求解信息完整和不完整点集对称轴的方法。首先根据凸壳算法求出点集的凸壳,对于信息完整点集,点集的对称轴必是凸壳的对称轴,因此可以借助求解凸壳的对称轴来求解点集的对称轴;对于信息不完整点集,当遗失的点为凸壳内部点时,点集的对称轴也必为凸壳对称轴,当凸壳上的点有遗失时,则可通过求凸壳边的中垂线,以及长度相等两邻边组成角的角平分线来确定点集的对称轴。该方法解决了现有算法只能求解封闭和信息完整图形的对称轴的不足,实验结果表明该方法是高效、可行的。

英文摘要：

Based on the symmetry of an object,people can infer its structure and estimate its pose even if some parts of object are lost or occluded.This paper presented a new algorithm for detecting the symmetry axes of 2D point set.Firstly,convex hull of 2D point set can be obtained by convex hull algorithm.Secondly,for complete point set,its symmetry axes can be found through seeking the symmetry axes of convex hull.Thirdly,for incomplete point set,if the missing points are located inside the convex hull,point set＇s symmetry axes must be the symmetry axes of its convex hull;if the missing points include those points on the convex hull,perpendicular bisectors of convex hull＇s edges or angle bisectors of convex hull may be the symmetry axes of the point set.The method proposed in this paper can search the symmetry axes of object even though some points are lost or occluded.The experimental results demonstrate that the method has higher efficiency and better applicability.