平面开曲线形状识别技术的研究

【作者】 张学；

【导师】 顾宝根；

【作者基本信息】 南京航空航天大学 ， 计算机应用技术， 2003， 硕士

【摘要】 本文主要研究平面开曲线的形状识别问题。本文提出了一种基于力学表示的变形匹配法。曲线可以看成是物体运动的轨迹，那么物体在运动过程中所受到的力就决定了曲线的形状，将两条曲线适当地变形之后，通过比较各自的形状形成的力学原因，就可以计算出它们的形状差异或形状距离，从而达到曲线形状识别的目的。这种方法为曲线的曲率赋予了明确的力学意义，从而使曲线在曲率表示下的形状识别技术得到了更为深入的研究。实验表明这种方法能够有效地解决开曲线的形状识别问题。本文在最后还证明了这样一个结论，两条平面开曲线的形状距离的计算问题可以转化为一个泛函的极值问题，于是通过解一个欧拉方程就可以求出两条开曲线的形状距离。更多还原

【Abstract】 This paper is primarily concerned with the shape recognition problem of open planar curves. A flabby-shape matching algorithm based on mechanical representation is proposed. A curve is regarded as the trace of a moving body, the force acting on which decides the shape of the curve. Through some necessary shape transformation, the shape distance or shape difference between two open curves can be valued by comparing their mechanical causation. Therefore, the purpose of recognizing open curves is reached. This method gives a mechanical meaning to the curvature of a curve, just because of that, more research can be done on the problem of curvature representation based curve recognition. Experiments shows it is an effective approach to recognizing open curves. At last, a better idea is presented: In fact, the problem of computing the shape distance between two open curves can be changed to the problem of a functional extremum, therefore, we can get the shape distance through solving an Euler equation.更多还原