隐含多项式曲线对称性几何特征及其检测研究

Research on geometrical feature and detection of symmetry for implicit polynomial curves

隐含多项式曲线在物体描述和识别中具有许多优点并得到实际应用,因而物体的对称性检测问题可以转换成对隐含多项式曲线的对称性检测来研究。对隐含多项式曲线对称几何结构性质进行了探讨,提出隐含多项式曲线如果是对称的,则其充分必要条件是首二次因子积组成的椭圆图形是对称的,同时指出椭圆图形对称轴就是隐含多项式曲线的对称轴。算法较为简单和直观,实验结果证明算法的有效性和可操作性。

Object description and recognition based on implicit polynomial curves are applied well.Then,the symmetry detection of the object can be changed to study implicit polynomial curves.The feature of symmetry geometry structure is studied,and the conclusion is drawn that the necessary and sufficient condition of symmetry implicit polynomial curves is that the image of first decomposed conics of the implicit polynomials curve is symmetrical.In addition,the symmetry axis of the image also is that of implicit polynomial curves.The algorithm is simple and intuitional,and the validity and operation are proved by the experiment.