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摘要: 针对现有在线笔迹匹配算法鲁棒性不强的问题，本文提出将合并规则和跳跃规则引入到动态规划的迭代过程，以跳跃规则应对书写中的多、漏笔现象，以合并规则应对因多种书写不一致造成的分割点多提取、漏提取现象.在累计差异矩阵计算中，提出以笔画特征，特别是笔画形状信息来度量笔画间的差异.在SVC2004和SUSIG签名数据库上与现有主要在线笔迹匹配算法进行比较.实验结果表明，本文方法能较好应对多种局部书写和分割的不一致，从而获得更准确、鲁棒的笔画对应关系.Abstract: To solve the robustness problem of online handwriting matching, a novel method is proposed in which the jumping and merging rules are introduced to the iterative step of dynamic programming. Specifically, jumping rules are used to deal with the superfluous and loss strokes while merging rules are used to deal with inconsistent handwriting segmentation caused by jerk, hesitating, compound-strokes, etc. In calculation of the cumulative difference matrix, a new measurement is proposed in which stroke shape information is applied to measuring stroke differences. The matching results calculated by the proposed method are compared to those of the existing main methods on SVC2004 and SUSIG public signatures databases. It is shown that the new method can obtain better accuracy and more robust stroke correspondence with respect to various local writings and segmentation inconsistency.
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图 1 按视觉关键点得到的笔迹分割结果示例
Fig. 1 Examples of handwriting segmented by perceptually important points
图 2 因弯曲程度不够造成的笔迹分割不一致
Fig. 2 Inconsistent segmentation caused by over and\\ less curving strokes
图 3 因多笔造成的笔迹分割不一致
Fig. 3 Inconsistent segmentation caused by superfluous and loss strokes
图 4 跳过测试笔迹的第j段笔画(左)和跳过模板笔迹的第i段笔画(右)
Fig. 4 Jumping the jth stroke of testing handwriting(left) and jumping the ith stroke of template (right) handwriting
图 7 两段归一化后"九"字的横竖弯笔画
Fig. 7 Two normalized compound strokes in Chinese character"nine"
图 8 笔画分割结果,D2、D3、d2为角度极大值点
Fig. 8 Two compound strokes segmented by angle maximum points D2,D3,and d2
图 9 采用经典DTW得到的点点对应关系
Fig. 9 Point-to-point corresponding calculated by the classical DTW
图 11 以相邻分割点构成的向量近似表示笔画
Fig. 11 Stroke approximated by vectors consisting of adjacent segmentation points
图 12 由人工给出的四组笔迹分割点的理想对应关系
Fig. 12 Four group of ideal segmentation point corresponding
图 13 本文方法和已有笔画差异度量方法在匹配结果上的比较 (第1栏和第2栏给出了本文方法的匹配结果示例,第3栏和第4栏给出了相同笔迹在已有方法上的匹配结果示例)
Fig. 13 Comparison of matching results based on stroke difference measurement between the proposed (the 1 and 2 columns)and existing methods (the 3 and 4 columns)
图 14 本文方法与现有方法在SVC2004上匹配结果示例
Fig. 14 Examples of matching result obtained by the proposed and the existing methods on SVC2004
图 15 本文方法与现有方法在SUSIG上匹配结果示例
Fig. 15 Examples of matching result obtained by the proposed and the existing methods on SUSIG
表 1 $\beta$ 取值对平均匹配错误率(%)的影响
Table 1 Average matching error rate (%) for various values of $\beta$
β 平均匹配错误率 0.075 9.53 0.10 8.93 0.125 8.23 0.15 7.92 0.175 7.91 0.20 7.96 0.225 8.32 0.25 8.53 
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表 2 $\eta$ 取值对平均匹配错误率 (%) 的影响
Table 2 Average matching error rate (%) for various values of $\eta$
η 平均匹配错误率 0.05 8.26 0.075 8.07 0.10 7.91 0.125 7.99 0.15 8.03 1.175 8.57
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表 3 $\alpha$ 取值对平均匹配错误率(%)的影响
Table 3 Average matching error rate (%) for various values of $\alpha$
α 平均匹配错误率 –0.5 12.13 0 11.26 0.5 10.54 1 9.56 1.5 8.33 2 7.06 2.5 7.31 3 7.91 3.5 8.42 4 8.79
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表 4 不同合并规则对匹配错误率 (%) 的影响
Table 4 Average matching error rate (%) for different merging rule combination schemes
组合方案 合并规则序号集合 平均匹配错误率 方案 1 [a] 11.21 方案 2 [a] ~ [c] 8.33 方案 3 [a] ~ [e] 7.12 方案 4 [a] ~ [f ] 6.04 方案 5 [a] ~ [h] 6.52 方案 6 [a] ~ [j] 7.31
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表 5 本文笔画差异度量方法与已有方法比较
Table 5 Comparison of the proposed stroke difference measurement method and the existing method
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表 6 SVC2004的签名分组表
Table 6 SVC2004 signature group table
组号 签名组序号 1 3, 4, 6, 13, 15, 16, 27, 29, 31, 40 2 2, 5, 9, 11, 12, 14, 17, 18, 28, 30 3 1, 8, 19, 20, 22, 24, 25, 32, 36, 38 4 7, 10, 21, 23, 26, 33, 34, 35, 37, 39
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表 7 SUSIG的签名分组表
Table 7 SUSIG signature group table
组号 签名组序号 1 9, 11, 13, 14, 16, 18, 19, 20, 23, 24, 25, 28, 36, 37, 46, 53, 54, 65, 69, 88, 105, 106, 113 2 1, 2, 4, 8, 10, 22, 39, 44, 55, 56, 67, 70, 71, 73, 80, 82, 84, 85, 90, 92, 93, 108, 109, 114 3 3, 21, 26, 38, 40, 53, 59, 61, 64, 66, 74, 76, 77, 83, 86, 89, 91, 94, 97, 99, 100, 101, 103, 111 4 15, 29, 32, 34, 42, 57, 58, 60, 62, 63, 64, 72, 75, 78, 79, 81, 87, 95, 96, 98, 107, 110, 115
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表 8 在SVC2004和SUSIG上,本文方法与已有方法在4组笔迹上平均匹配错误率 (%) 比较
Table 8 Average matching error rate (%) comparison on four group signatures between our method and existing methods on SVC2004 and SUSIG
第 1 组 第 2 组 第 3 组 第 4 组 SVC2004 SUSIG SVC2004 SUSIG SVC2004 SUSIG SVC2004 SUSIG Cpalka et al.[30] 8.96 10.17 15.76 16.56 18.85 20.96 23.42 26.85 Barkoula et al.[25] 10.12 11.85 15.73 16.98 19.31 21.21 23.27 26.23 Mohammadi et al.[21] 9.54 10.32 16.53 17.34 20.14 24.44 25.21 29.45 Wang et al.[12] 8.72 9.97 16.23 17.85 20.81 20.64 24.83 23.80 Lee et al.[23] 8.14 9.07 15.13 17.57 19.62 25.17 27.04 28.12 Quan et al.[20] 19.14 20.18 26.31 26.21 31.25 30.47 35.21 34.19 Li et al.[22] 12.34 13.97 20.14 19.39 18.93 25.32 25.31 29.93 Hao et al.[24] 9.31 13.83 17.01 17.63 17.48 20.85 23.18 26.21 本文方法 4.56 5.48 5.14 6.52 5.57 7.41 8.89 10.32
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