标记曲线在目标识别中的应用

摘要

It introduces a method of construction of differential signature on arbitrary manifold. This method has applied to object-recog-nition successfully by team of Olver. E Cartan's original work involved the general theory of signature curves. He indicated that the trans-formation group acting on curves equivalence if and only if their signature curves equivalence. It will detect some geometric object sym-metrically by construction of numerically differential invariants and mathematical modeling. The simulation experiments show that the al-gorithm can detect the symmetry axis of target object,and the accuracy of detection depends on the local properties of geometric object. In addition,this method produces some certain errors with regard to the geometrical objects which possess the high curvature transforma-tion. It will reveal the advantage of application of symmetry detection by signature curves and will make the theory of moving frame wide-ly applying on computer vision.%　　文章介绍了任意流形空间上的微分不变标记曲线的构造和应用，该方法已经成功得被 Olver 团队应用到了图像目标识别中. E. Cartan 在他早期工作中提出标记曲线一般化理论，他指出在给定变换群下作用的曲线等价当且仅当他们的标记曲线等价.文中将沿着 Olver 团队在近似数值微分不变量构造的工作对不同标记曲线数值化过程进行研究，利用标记曲线通过数学建模对几何对象进行对称检测，仿真实验结果表明该算法能够检测出目标对称轴，检测的准确性取决于几何对象的局部性质.可以看出标记曲线在这方面的应用有着非常明显的优势，从而能够使活动标架理论在计算机视觉中得以广泛的应用.