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.

• 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。