Shape recognition of planar curves is a fundamental problem of pattern recognition. But it has not been well resolved by now. It is difficult to value the shape difference between two curves. This paper gives a mathematical definition to that two open planar curves have the same shape based on curvature representation

therefore

a new kind of shape distance is proposed. It is concluded that the problem of computing the shape distance between two open planar curves can be changed to the problem of a functional extremum

and the differential equation is given

which can be used to figure out the shape distance. However

it is very difficult to solve that equation. Since there is no better means at hand

a rude method of fragmentation matching is used in experiments. It is also presented in this paper how to implement the algorithm step by step

especially how to represent an open planar curve in the discrete case. A constant momentum based Gaussian filtering is applied to reduce the noise sensitivity of curvature based representation. The experimental results show that this kind of shape distance is effective.