Abstract: In this paper，a new algorithm of on-line handwriting signature verification is proposed.Our researches are mainly on the matching of special points of signature curves.The authors pick up the position coordinates of the special points in signature curves first，and then pick up the key characters vertices and rock bottom from the special points.The authors take the discrete Fréchet distance as the distance measurement and introduce a new curves similarity definition.The authors present a new mathematical model for the signature curves similarity judgment，which implies carrying on the translation and the stretching to the curves.Because the model solution is one kind of NP difficult problem，the authors propose one kind of new multinomial solution algorithm，and finally take online handwriting signature verification as example to confirm the mathematical model.The experimental result confirms the validity of this method in the signature verification，and it is also used to the discrete curves similarity judgment.

Key words: signature verification, discrete Fréchet distance, paired walk, Fréchet alignment

摘要： 提出了一种新的在线手写签名认证算法，着重研究签名曲线中的特殊点的匹配情况。该算法将签名曲线中特殊点的位置坐标提取出来，然后提取出特殊点中的关键特征至高点与至低点，并且用离散Fréchet距离作为距离的测度来对至高点与至低点进行研究，提出了一种新的关于曲线相似性的定义，并且在这种定义的基础上建立了一种新的判断签名曲线相似性的数学模型，此模型中隐含了对签名曲线的平移和伸缩变换。由于模型的求解是一种NP困难问题，针对这种情况，提出了一种新的多项式的求解算法，最后通过对实验结果的分析验证了此算法用于签名认证的有效性，且适用于判别离散曲线的相似性。

关键词: 签名认证, 离散Fréchet距离, 组合步, Fréchet排列