摘 要

签名验证是一种传统的身份判别法, 在银行业务、自动文档处理、电子商务等都发挥着至关重要的作用。在科学技术的发展十分快速的今天，计算机与网络的普及让人们生活与工作中的交流更加频繁、也更加方便。但是，他带来的安全问题也越来越突出。所以，如今社会中，如何准确地判断一个身份的真实性，保护信息安全是如今信息化社会必须面对的一个关键问题。与指纹、语音等识别比起来，他的成本十分低廉，且只需简单的采集设备就可以得到相对满意的结果。因此本文提出了基于Hausdorff距的在线手写签名认证方法研究，首先提取出签名曲线稳定的极值点，并在特征点两侧各取若干个点构成特征段，将特征段中各点曲率的Hausdorff距作匹配标准。Hausdorff距不强调特征段的匹配点对，点与点间的关系是模糊的，而曲率具有平移，旋转不变性，以及缩放的比例特性，对于曲线之间的匹配具有更好的鲁棒性，因而可以提高签名认证的识别率，更能辨别出真伪签名。本文选取20个已采集的真实签名为参考签名，通过这些真实签名相互间的匹配结果求均值可得出参考签名与测试签名间的一个阈值。经实验在距离的匹配中取一阈值。当距离小于此阈值时则接受此签名并认定为真实签名，若大于则拒绝，并认定为伪造签名。最终选择20个伪造签名进行了匹配对算法试验。对实验结果进行分析验证了算法对签名验证的有效性，分析离散曲线的相似性上比较适用。

关键字：签名验证；Hausdorff距；曲率；曲线匹配

Abstract

Signature verification is a traditional identity discrimination, in banking, automatic document processing, e-commerce and so plays a crucial role. With the rapid development of science and technology, the popularity of computer and network to make more frequent exchanges between people, but also more convenient, it brings security issues are also increasingly prominent. Therefore, how to accurately determine the authenticity of an identity and protect information security is a key issue in today's information-based society must face. It’s low cost and fingerprints, voice recognition and other than up, and you can simply capture device. Therefore, this article presents research line handwritten signature authentication method based on Hausdorff distance, first extract the signature curve stable extreme points, and on both sides of the feature points from each of a plurality of dots feature segments, each segment will feature Hausdorff Curvature from as matching criteria, Hausdorff distance does not emphasize a feature segment on match point, the relationship between the point and the point is ambiguous, and the curvature of the translation, rotation invariance, and the ratio of the zoom feature, for better matching between the curves robustness, which can improve the recognition rate of signature verification, better identify the authenticity of the signature. This article has been selected 20 authentic signatures collected for the reference signature, handwritten signature because the real inherent change, there is always a certain degree forgery similarity. The experiment in the match to take a distance from the threshold, when the distance is less than this threshold value is accepted as true signature of this signature, if more than rejecting, identified as forged signatures. Chose 20 forged signatures match, the experimental results were analyzed to verify the validity of the signature verification algorithm, but also for the similarity analysis of dispersion curves.

Keywords: Signature Verification；Hausdorff distance；Feature points；Curve matching

目录

摘要……………………………………………………………………………………………I

Abstract……………………………………………………………………………………………II

1．绪论 1

1.1研究背景 1

1.1.1目标匹配 1

1.1.2签名验证 1

1.2研究意义 2

1.3在线手写签名验证概述及发展现状 2

1.3.1在线手写签名验证的原理 2

1.3.2在线手写签名验证的发展现状及问题 4

1.4常用方法与本文采用方法 5

2签名的曲线表示与hausdorff距离 7

2.1曲线的表示 7

2.2Hausdorff 距离 8

2.2.1Hausdorff 距离的定义 8

2.2.2Hausdorff 距离的性质 9

小结 10

3基于 Hausdorff 距离和曲率的曲线匹配 11

3.1平面曲线的曲率表示及其不变性 11

3.1.1曲率 11

3.1.2利用曲率描述签名曲线 12

3.1.3曲率表示法的离散提取及编码 13

小结 14

4数学模型 15

4.1相似度的定义 15

4.2基于离散Hausdorff距离的判断签名曲线相似性的算法设计 15

5 数值实例 17

5.1 数据的采集与预处理 17

5.2实验结果分析 19

结束语 23

参考文献 24

致谢 25

1．绪论

1.1研究背景

1.1.1目标匹配

在模式识别领域中，目标匹配作为热门的研究问题,研究成果拥有广泛的应用前景^[4]。在基于内容的图像检索，目标分类，目标检测和人脸识别等领域中,目标匹配技术己成为整个系统核心的主要研究部分。

如今,目标匹配问题的重点表现在两方面: