活动标架在对象识别中的应用

Applications of moving frame in object recognition

基于Fels-Olver等变活动标架理论,借助构造活动标架的经典方法,得到了平面上欧几里得曲线的不变量和微分不变量,即曲率和曲率关于弧长参数的导数(包括关于弧长参数的所有高阶导数).由这些欧几里得微分不变量可以构造出曲线的欧几里得签名曲线,而签名曲线在刚性运动下是不变的.在计算机视觉中,签名曲线可以广泛地用于对象识别、视觉跟踪和对称检测.此外,在Cartan等价理论是签名曲线的基础理论支撑下,结合微分不变量在对象识别方面的抗噪优势,对签名曲线进行数值逼近,并用此方法给出若干欧几里得曲线的微分不变签名曲线.所给实例显示了基于曲线的微分不变量方法在计算机视图领域中的有效性.

It was presented that invariant, dierential invariants of Euclidean curves in plane, namely, curva- ture and its derivatives （ include higher order derivatives ） with respect to the arc length, were obtained by the- classical method of construction of moving frames, armed with Fels-Olver equivariant moving frame theory de- veloped by Mark Fels and Peter J. Olver. The Euclidean signature curves of curves were constructed in terms of Euclidean differential invariants. The signature ognition, visual tracking and symmetry detection. curves were generally applied to the problems of object rec- Moreover, Cartan＇s equivalence theorem .was afundamental theorem in signature curves. Based on the joint invariants, noise resistant was numerically approximated for signature curves, and some examples were used to indicate the efficiencies of the differential invariant method while dealing with computer vision problems.