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1 42 11 Vol. 42, No ACTA AUTOMATICA SINICA November, , 2 2 1,,,.,,. SVC2004 SUSIG.,,. DOI,,,,,.., 2016, 42(11): /j.aas.2016.c Online Handwriting Matching Algorithm Based on Stroke Features ZOU Jie 1, 2 SUN Bao-Lin 2 YU Jun 1 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. Online handwriting verification, handwriting matching, stroke difference measurement, dynamic program- Key words ming Citation Zou Jie, Sun Bao-Lin, Yu Jun. Online handwriting matching algorithm based on stroke features. Acta Automatica Sinica, 2016, 42(11): ,., Manuscript received September 6, 2015; accepted June 22, 2016 ( , ), (WK ), (2014CFA055), (T201631), (A1501) Supported by National Natural Science Foundation of China ( , ), the Fundamental Research Funds for the Central Universities (WK ), the Key Project Natural Science Foundation of Hubei Province (2014CFA055), Hubei Province High School Outstanding Young Science and Technology Innovation Team Project (T201631), and the Open Project Program of the State Key Laboratory of CAD and CG of Zhejiang University (A1501) Recommended by Associate Editor SANG Nong Department of Automation, University of Science and Technology of China, Hefei Department of Computer Science and Technology, Wuhan Technology and Business University, Wuhan ,, DNA,,, [1 2].,. [3 4],.. [5].,. [5 6].,.,.

2 11 : 1745 (Dynamic time warping, DTW) [7 8] (Hidden Markov model, HMM) [8 9].. : 1).,,,. 2).,,,, [10].,,... [11] [12].,. : 1) [13]. DTW,. 2) [13].,.. 3) [14].. 4). [15 16]. 5).,, [17],,,,. 6) [18].,,., : 1) [19]. HMM.,,.. 2), DTW [19]., ; DTW ;,,. 3),., ;,, [20 24] [12, 23] [23 24] [22, 25] ;, ;,,. : [13] (Quadratic fitting criterion equation) [26] [27] (Thin-plate spline) (Warping energy) [28].,. : 1),, ( ), ; 2),, ;,,,.,,., : 1) ; 2)., : 1),.,. 2),,.,..,.,., ( ), ( )., [29 30] [31] [32].,,.,.

3 , SVC2004 [33] SUSIG [34], [12, 20 25, 30],. 1 :,,,., [35]., D.,., D. 1.1 : 1. Brault [18], , D. 2 ( ),.,. : (1) [a] [j] ( 1 : 1, 1 : 2, 2 : 1,, 1 : 4, 4 : 1 ),, P,. (1) d mer(i 1,i),j (i 1) i j, mer(x, y) x y,, 1 Fig. 1 Examples of handwriting segmented by perceptually important points 2 Fig. 2 Inconsistent segmentation caused by over and less curving strokes D ij = min [ min D i 1,j 1 + d i,j [a] D i 2,j 1 + d mer(i 1,i),j [b] D i 1,j 2 + d i,mer(j 1,j) [c] D i 3,j 1 + d mer(i 2,i),j [d] D i 1,j 3 + d i,mer(j 2,j) [e] D i 2,j 2 + d, min mer(i 1,i),mer(j 1,j) [f] D i 3,j 2 + d mer(i 2,i),mer(j 1,j) [g] D i 2,j 3 + d mer(i 1,i),mer(j 2,j) [h] D i 4,j 1 + d mer(i 3,i),j [i] D i 1,j 4 ] + d i,mer(j 3,j) [j] D i 1,j [k], [l] D i,j 1 d i,j d mer(i 1,i),j d i,mer(j 1,j) d mer(i 2,i),j d i,mer(j 2,j) d mer(i 1,i),mer(j 1,j) d mer(i 2,i),mer(j 1,j) d mer(i 1,i),mer(j 2,j) d mer(i 3,i),j d i,mer(j 3,j) < P, i j w (1)

4 11 : 1747 ( ) ( ). d ij i j. 3 ( ), 1.,, (1) [k] [l],, D ij i j, 1 i N, 1 j M, N M. Fig. 3 3 Inconsistent segmentation caused by superfluous and loss strokes,,., : P,. (1) P. P., 4.,,, D ij,,. (1) [k] [l],. 4 Fig. 4 j ( ) i ( ) Jumping the jth stroke of testing handwriting (left) and jumping the ith stroke of template (right) handwriting 5., 2 : 1 1 : 2, 5 D ij,, 4. Fig : 1 ( ) 1 : 2 ( ) 2 : 1 (left) and 1 : 2 (right) merging rule,,.,, [24]. (1) w, w = β N, N. 3. (1), i = 1, j = 1, D, D 00 = D NM,,. 1.2,.., [29 30] [31] [31]. : 1),. 2),. 3).,. 6,. 1) D s = S A S B min(s A, S B ) (2) S A = (A MaxX A MinX )(A MaxY A MinY ) (3) S B = (B MaxX B MinX )(B MaxY B MinY ) (4), A MaxX, A MaxY, A MinX, A MinY, B MinY, B MinX, B MaxX, B MaxY X Y. 2) D g = G A G B (5)

5 , G A G B.., S1 d DTW S1 S2 [35] Fig. 6 Two handwriting examples of Chinese character nine 3) D α = α A α B (6), 0 α A 180, 0 α B 180 X [29]. 4),.. 1. [36] [29] [29],. [36]., max(width, height) 100, width height. 6 7., S1, S2. Fig. 7 7 Two normalized compound strokes in Chinese character nine D 2 D 3 d 2 8 Fig. 8 Fig. 9 9, D 2 D 3 d 2 Two compound strokes segmented by angle maximum points D 2, D 3, and d 2 DTW Point-to-point corresponding calculated by the classical DTW 4.,. 9,, S1 d 2 S2 D 2., DTW,.. 1. q S2 S1 d 2, D 2 S2 q, q D 2 T, S2 D 2 S1 d d 3 S1 S2 D 3, S1 d 3 T, D 3 d T = η L,, L S1, η., 10.

6 11 : Fig Revised segmentation point corresponding, (7). D t = k l i L V i U i (7) i=1, V i = d i d i+1, U i = D i D i+1 S1 S2 i, {d 1,, d k, d k+1 }, {D 1,, D k, D k+1 } S1 S2, l i S1 i, L, k. 11. Fig Stroke approximated by vectors consisting of adjacent segmentation points (8) D x = D s µ s σ s + D g µ g σ g + D α µ α σ α + D t µ t σ t (8), µ, σ. SVC , SUSIG, SVC2004 SUSIG, [12, 20 25, 30],. SVC2004 SUSIG ,,, 10., ,. : 20, 1, 19..,. P ath a = {(t 1 a, s 1 a), (t 2 a, s 2 a),, (t n a, s n a)} P ath b = {(t 1 b, s 1 b), (t 2 b, s 2 b),, (t m b, s m b )} (9),, t i a, t i a, t j b, tj b i j, 1 i n, 1 j m, n, m P ath a, P ath b. (t j a, s j a ) = arg min 1 x n (Len(tx a, t j b ) + Len(sx a, s j b )) (10) P ath a (t j b, sj b ), 1 j n, Len(, ). (t j a, s j a ) t j a t j b 1 s j a s j b 1 (11) (11) (12). Len(t j a, t j b ) 3 Len(t j a, t j b ) Len(t j 1 a, t j b ) 0.1 Len(s j a, s j b ) 3 Len(s j a, s j b ) 0.1 (12) Len(sa j 1, s j b )

7 1750 自 r =1 c m 动化 (13) 其中, c 表示 P atha 中正确匹配个数. 图 12 列出了 4 组由人工给出分割点的理想对应关系示例, 图中用星号表示分割点, 星号旁边的数字表示该分割点在关键点序列中的序号. 两个序号相同的分割点相对应. 学 42 卷报他阈值的预设值与第 2.1 节所述相同. 不同 η 取值在 SVC2004 库 40 组签名上得到的平均匹配错误率如表 2 所示. 表 1 β 取值对平均匹配错误率 (%) 的影响 Table 1 Average matching error rate (%) for various values of β β 2.1 窗口宽度阈值选取实验本节讨论式 (1) 中窗口宽度阈值 w 的选取对匹配结果的影响. 设 w = β N, 其中, N 表示模板笔迹被分割的笔画数. 其他阈值预设为: 采用式 (1) 列出的所有 10 种合并规则; T = 0.1 L; P = u + 3 σ; 其中, L 表示模板笔画的长度, u, σ 含义如第 2.3 节所述. 不同 β 取值在 SVC2004 库 40 组签名上得到的平均匹配错误率如表 1 所示. 从表 1 可以看出, 过小和过大的 β 取值, 匹配错误率较高. 因为过小的窗口宽度使本应正确的匹配笔画被排除在窗口以外; 而过大的窗口则引入了过多的错误匹配笔画. 当 0.15 β 0.20 时, β 的取值对匹配结果影响不大, 因为尽管多笔少笔普遍存在, 但从以笔画作为笔迹构成单位来看, 多数人笔迹具有较好的书写一致性, 没有出现严重的少笔多笔问题. 因此相对较松的窗口阈值即可将正确的笔画包含进来. 平均匹配错误率表 2 η 取值对平均匹配错误率 (%) 的影响 Table 2 Average matching error rate (%) for various values of η η 平均匹配错误率距离阈值选取实验本节讨论距离阈值 T = η L 选取对匹配结果的影响. 基于第 2.1 节的实验结果, 设 β = 0.175, 其图 12 Fig. 12 由人工给出的四组笔迹分割点的理想对应关系 Four group of ideal segmentation point corresponding

8 11 : ,,. DTW.,,,., η = 0.10,. 2.3 (1) P. P = u + ασ,, u, σ, α., F Tablet [37] 34, 30, 1 020, 10 10, 680., α, (1) 10, SVC α (%) Table 3 Average matching error rate (%) for various α values of α , α,.,. α,. α,.,, (1),.,. 2.4 (1) 10.,, (1) [k] [l]. 3,,, SVC Table 4 4 (%) Average matching error rate (%) for different merging rule combination schemes 1 [a] [a] [c] [a] [e] [a] [f] [a] [h] [a] [j] ,.,.,,.,,,.,.,., 4,. 2.5, 1.2 [29 32], SVC ,. :,. 13,, 1 2, , 2 4

9 ,,.. 13,,. A.,,,. B F.,,. 2.6 SVC2004 SUSIG,,,. SVC2004 SUSIG, , (Windows 7.0, Matlab 2007b, 4 GB, GHz CPU) [12, 20 25, 30].,, 8. 8,, , 1 2, 3 4 Table 5 5 Comparison of the proposed stroke difference measurement method and the existing method [29 30] [31] [32] (%) ( 1 2, 3 4 ) 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)

10 11 : 1753 Table 6 6 SVC2004 SVC2004 signature group table 1 3, 4, 6, 13, 15, 16, 27, 29, 31, , 5, 9, 11, 12, 14, 17, 18, 28, , 8, 19, 20, 22, 24, 25, 32, 36, , 10, 21, 23, 26, 33, 34, 35, 37, : 1), (A, T ) (E, D, J, R, U, W ) (I) (G, P ) (K); 2), (B) (C, F, L, Q, S) (H, M, N) (O, V ).,, , SVC2004 SUSIG,. : 1) +,,., X Y [12, 20 25, 30],, [22]. ( ), ( ),, (, 15 P U ).,,.,. [12, 23], 7 SUSIG Table 7 SUSIG signature group table 1 9, 11, 13, 14, 16, 18, 19, 20, 23, 24, 25, 28, 36, 37, 46, 53, 54, 65, 69, 88, 105, 106, , 2, 4, 8, 10, 22, 39, 44, 55, 56, 67, 70, 71, 73, 80, 82, 84, 85, 90, 92, 93, 108, 109, , 21, 26, 38, 40, 53, 59, 61, 64, 66, 74, 76, 77, 83, 86, 89, 91, 94, 97, 99, 100, 101, 103, , 29, 32, 34, 42, 57, 58, 60, 62, 63, 64, 72, 75, 78, 79, 81, 87, 95, 96, 98, 107, 110, SVC2004 SUSIG, 4 (%) Table 8 Average matching error rate (%) comparison on four group signatures between our method and existing methods on SVC2004 and SUSIG SVC2004 SUSIG SVC2004 SUSIG SVC2004 SUSIG SVC2004 SUSIG Cpa lka et al. [30] Barkoula et al. [25] Mohammadi et al. [21] Wang et al. [12] Lee et al. [23] Quan et al. [20] Li et al. [22] Hao et al. [24]

11 Fig SVC2004 Examples of matching result obtained by the proposed and the existing methods on SVC2004 (X, Y ) [12, 21, 30] [21, 30] [25] [12].,,. 2.5,. ( 13 A, B, C, D, E, F )., : a) ; b), ; c). 2),,. ( ) [22 24], X, Y, X, Y [22 24]. ( C, F, H, N, O, V ).,,, ( ).,., (1), ( ) , (1), P,..,

12 11 期邹杰等: 基于笔画特征的在线笔迹匹配算法图 15 Fig 本文方法与现有方法在 SUSIG 上匹配结果示例 Examples of matching result obtained by the proposed and the existing methods on SUSIG 与该多笔对应的笔画, 因此导致匹配错误. 进一步, 该错误被传导到后继匹配而导致连锁反应, 例如图 14 中箭头 A B 所示. 相似的因多笔引起的匹配错误如图 14 中箭头 C 所示, 本来应该合并模板笔迹 (图 14 第 2 行第 3 列) 中的第段与测试笔迹 (图 14 第 2 行第 4 列) 中的第段相匹配 (这里的数字表示图中关键点的序号), 然而由于现有算法没有引入合并规则, 从而致使匹配错误; 与之相反, 在本文方法中, 由于引入了多种合并规则并且新的笔画差异度量方法计算的差异值在所有合并规则中最小, 从而使得期望的合理匹配被寻优方法选中, 最终输出正确的匹配结果. 因快速运笔导致的分割点漏提取例子如图 15 第 3 行第 1 列和第 2 列所示. 图中第 1 列第 10 段笔画由于快速书写, 本应提取的两个关键点被漏提取. 但是由于本文方法引入了合并规则并且根据正确合并规则 (第 3 行第 1 列中的第 10 段笔画与第 2 列中的由 3 个子段组成的第 10 段笔画相匹配) 得到的差异值在所有合并规则中最小, 因而输出正确的匹配结果. 与此相反, 从图 15 第 3 行第 3 列和第 4 列给出的已有方法的匹配结果可以看出, 由于同样的原因, 已有方法未能输出正确匹配结果. 由于本文引入的合并规则跳跃规则和有效的笔画差异度量方法, 在面对因小碎笔 (图 14 和图 15 中箭头 H, M, N 所示) 和简化笔 (图 15 中箭头 O, V 所示) 导致的分割不一致问题时, 本文方法均输出了正确的匹配结果 (本文方法的匹配结果如图 14 和图 15 中相同行的第 1 行和第 2 行所示). 本文方法得到正确匹配的原因与前述多笔分割点漏提取的相同. 2.7 本文方法存在的问题及不足本文方法存在以下不足及有待解决的问题: 1) 如图 16 第 1 行所示, 若笔迹中包含如 ABAB 这样特征相似的笔画组, 如笔迹军字中的横折横折运笔, 且横笔画出现在两个笔迹中的次数不一致时, 可能出现匹配错误. 图 16 第 1 行中两个签名匹配错误的原因在于测试笔迹中第 1 个横折画与其他位置处的横折画在长度和形状上更一致. 2) 本

13 P. :,. 16 2,,,.,,,. 16 Fig. 16 Examples of remaining shortcomings of 3 our method,,,.,,,. SVC2004 SUSIG,., DTW,,. References 1 Mohammed R A, Nabi R M, Mahmood S M R, Nabi R M. State-of-the-art in handwritten signature verification system. In: Proceedings of the 2015 International Conference on Computational Science and Computational Intelligence. Las Vegas, NV: IEEE, Yu J, Wang Z F. A video, text, and speech-driven realistic 3-D virtual head for human-machine interface. IEEE Transactions on Cybernetics, 2015, 45(5): Li Xin, Ding Xiao-Qing, Peng Liang-Rui. A microstructure feature based text-independent method of writer identification for multilingual handwritings. Acta Automatica Sinica, 2009, 35(9): (,,.., 2009, 35(9): ) 4 Chen Xiao-Su, Wu Zhen-Hua, Xiao Dao-Ju. Off-line Chinese signature verification based on segmentation and HMM. Acta Automatica Sinica, 2007, 32(2): (,,. HMM., 2007, 32(2): ) 5 Liu Y S, Yang Z H, Yang L H. Online signature verification based on DCT and sparse representation. IEEE Transactions on Cybernetics, 2015, 45(11): Parodi M, Gómez J C. Legendre polynomials based feature extraction for online signature verification. Consistency analysis of feature combinations. Pattern Recognition, 2014, 47(1): Nautsch A, Rathgeb C, Busch C. Bridging gaps: an application of feature warping to online signature verification. In: Proceedings of the 2014 International Carnahan Conference on Security Technology (ICCST). Rome, Italy: IEEE, Jiao Hui-Min, Wang Dang-Xiao, Zhang Yu-Ru, Fang Lei. Signature verification using handwriting friction force. Acta Automatica Sinica, 2011, 37(7): (,,,.., 2011, 37(7): ) 9 Pirlo G, Cuccovillo V, Impedovo D, Mignone P. On-line signature verification by multi-domain classification. In: Proceedings of the 14th International Conference on Frontiers in Handwriting Recognition (ICFHR). Heraklion, Greece: IEEE, Wang Zi-He. Identification of Practicing Imitating Handwriting [Master dissertation], Southwest University of Political Science and Law, China, (. [ ],,, 2010.) 11 Ansari A Q, Kour J. Uniform segmentation in online signature verification. In: Proceedings of the 2015 Annual IEEE India Conference. New Delhi, India: IEEE, Wang K Y, Wang Y H, Zhang Z X. On-line signature verification using segment-to-segment graph matching. In: Proceedings of the 2011 International Conference on Document Analysis and Recognition. Beijing, China: IEEE, Wirotius M, Ramel J Y, Vincent N. Selection of points for on-line signature comparison. In: Proceedings of the 9th International Workshop on Frontiers in Handwriting Recognition (IWFHR). Tokyo, Japan: IEEE, Cai Hong-Bin, Shi Ze-Sheng, Fan Xiao-Feng, Huang Hao, Yin She-Guang. A handwritten signature verification method based on wavelet transform to pick up inflection points. Journal of Image and Graphics, 2003, 8(3): (,,,,.., 2003, 8(3): )

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,,.,, : 1),,,,, 2),,,,, 3),,,,,,,,,, [6].,,, ( ),, [9], : 1), 2),,,,, 3),,, 2.,, [10].,,,,,,,,, [11]. 2.1,, [12],, ;, ; Fig. 1 1 Granular hier 36 7 Vol. 36, No. 7 2010 7 ACTA AUTOMATICA SINICA July, 2010 1, 2 1, 2, 3 1, 2,,,,,,, DOI,,, 10.3724/SP.J.1004.2010.00923 Distributed Simulation System Hierarchical Design Model Based on Quotient Space