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Figure 1
(Color online) Examples of ancient Chinese seals. (a) Ancient personal seal; (b) different forms of the character łqłq yinrqrq (seal) in seal fonts.
Figure 2
(Color online) Graph-matching-based character recognition for Chinese seal images.
Figure 3
(Color online) Graph construction process.
Figure 4
(Color online) Examples of graph construction result for Chinese seal character. (a) Missing turning points detected by polygonal approximation; (b) original character image; (c) skeleton extraction result; (d) skeleton pruning result; (e) graph model (endpoints, branch points, and new turning points calculated via polygonal approximation are represented by red, green, and blue, respectively).
Figure 5
(Color online) Shape context feature distribution of seal character graph.
Figure 6
(Color online) An example of seal character matching. (a) Two seal character graphs; (b) two graphs' incidence matrices ${\boldsymbol~S}$ and ${\boldsymbol~T}$, where non-zero elements in each column of ${\boldsymbol~S}$ and ${\boldsymbol~T}$ indicate the start and terminal nodes in the corresponding directed edge, respectively; (c) node affinity matrix ${\boldsymbol~K}_v$ and edge affinity matrix ${\boldsymbol~K}_e$; (d) node correspondence matrix ${\boldsymbol~X}$ and edge correspondence matrix ${\boldsymbol~Y}$.
Figure 7
(Color online) Character sample examples.
Figure 8
(Color online) Comparison of matching for samples from the same and different categories.
Resize the input image ${\boldsymbol~I}$ to a normalized image ${\boldsymbol~I}^{\rm~re}$ in fixed size $100\times100$; |
Obtain the binary image with Otsu's algorithm: ${\boldsymbol~I}^{\rm~bw}~=~{\rm~Otsu}(~{\boldsymbol~I}^{\rm~re}~)$; |
Extract the skeleton image ${\boldsymbol~I}^{\rm~sk}$ from ${\boldsymbol~I}^{\rm~bw}$; |
Find ${\boldsymbol~V}_{\rm~branch}$ and ${\boldsymbol~V}_{\rm~end}$ with ( |
Find the path $\psi_{i~\rightarrow~j}$ for $v_i$ to the first branch point $v_j\in~{\boldsymbol~V}_{\rm~branch}$ in the skeleton images; |
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Delete $v_i$ and $\psi_{i~\rightarrow~j}$ from ${\boldsymbol~V}_{\rm~end}$ and ${\boldsymbol~I}_{\rm~sk}$ respectively; |
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Let ${\boldsymbol~V}~=~\{{\boldsymbol~V}_{\rm~branch};{\boldsymbol~V}_{\rm~end}\}$; |
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${\boldsymbol~E}=\{{\boldsymbol~E};(i,j)\}$; |
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$n={\rm~size}({\boldsymbol~V})$; |
Find candidate key point $\hat{p}$ with ( |
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Calculate the path point angle $\theta(\hat{p})$ with ( |
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${\boldsymbol~V}~=\{~{\boldsymbol~V};v_{n+1}=\hat{p}~\}$; |
${\boldsymbol~E}=\{{\boldsymbol~E};(i,n+1);(n+1,j)\}$; |
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The graph model is integrated with ${\boldsymbol~V}$ and ${\boldsymbol~E}$: ${\boldsymbol~G}=[{\boldsymbol~V},~{\boldsymbol~E}]$; |
Return ${\boldsymbol~G}$. |
Step | Parameter | Value |
Skeleton pruning | Length threshold $l_{\rm~max}$ | 10 |
Polygon approximation | Angle threshold $\theta_{\rm~min}$ | $2.36$ |
Distance threshold $d_{\rm~min}$ | 5 | |
Shape feature | Step length | 20 |
Orientation difference | $0.52$ | |
Affinity matrix calculating | Spatial scale factor $\sigma_d$ | 35 |
Orientation scale factor $\sigma_\theta$ | 25 |
Initialize ${\boldsymbol~X}$ to be a doubly stochastic matrix; |
Factorize ${\boldsymbol~K}_e={\boldsymbol~U}{\boldsymbol~V}^{\rm~T}$; |
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Update ${\boldsymbol~X}leftarrow{{\boldsymbol~X}_0}$; |
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Optimize ( |
Update ${\boldsymbol~X}$ $\leftarrow$ ${\boldsymbol~X}^*$; |
Calculate $J_{\rm~gm}({\boldsymbol~X})={\rm~tr}({\boldsymbol~K}_v^{\rm~T}{\boldsymbol~X})+{\rm~tr}({\boldsymbol~K}_e^{\rm~T}({\boldsymbol~S}_1^{\rm~T}{\boldsymbol~X}{\boldsymbol~S}_2\circ~{\boldsymbol~T}_1^{\rm~T}{\boldsymbol~X}{\boldsymbol~T}_2))$; |
Return ${\boldsymbol~X}$, ${\boldsymbol~J}$. |
Top 1 | Top 3 | Top 5 | |
Accuracy (%) | 83.42 | 88.52 | 91.33 |
Category | 不 | 个 | 之 | 书 | 二 | 人 | 佛 | 刘 | 北 | 千 | 午 | 南 | 印 | 启 | 堂 |
Test/train | 4/3 | 3/3 | 17/17 | 5/5 | 4/4 | 8/7 | 3/2 | 7/7 | 3/2 | 25/24 | 3/2 | 3/2 | 19/19 | 6/5 | 7/7 |
SVM | 0 | 0 | 14 | 0 | 3 | 1 | 0 | 1 | 0 | 12 | 2 | 0 | 4 | 1 | 0 |
CNN | 2 | 0 | 10 | 0 | 4 | 0 | 6 | 0 | 17 | 1 | 1 | 16 | 2 | 4 | |
MPSC | 2 | 0 | 11 | 1 | 4 | 4 | 1 | 5 | 0 | 14 | 1 | 1 | 14 | 0 | 0 |
SRC | 2 | 0 | 11 | 1 | 4 | 4 | 1 | 5 | 0 | 15 | 1 | 1 | 14 | 0 | 0 |
GMCSCR | 0 | 4 | 4 | 0 | |||||||||||
Category | 墨 | 士 | 大 | 天 | 好 | 季 | 宁 | 家 | 寿 | 居 | 山 | 己 | 巳 | 年 | 庐 |
Test/train | 3/2 | 5/5 | 32/32 | 3/3 | 3/2 | 3/2 | 7/6 | 3/3 | 5/4 | 6/5 | 3/2 | 3/2 | 3/2 | 3/3 | 3/2 |
SVM | 0 | 2 | 9 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
CNN | 0 | 3 | 26 | 0 | 0 | 0 | 0 | 0 | 3 | 3 | 2 | 1 | 0 | 0 | 0 |
MPSC | 1 | 2 | 30 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ||
SRC | 1 | 3 | 30 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | ||
GMCSCR | 4 | 2 | 0 | ||||||||||||
Category | 张 | 心 | 戊 | 成 | 我 | 摩 | 斧 | 海 | 爰 | 王 | 生 | 画 | 真 | 石 | 私 |
Test/train | 26/25 | 3/3 | 3/2 | 5/5 | 4/3 | 3/3 | 8/7 | 21/21 | 22/22 | 6/5 | 3/3 | 6/5 | 3/2 | 3/3 | 5/5 |
SVM | 3 | 0 | 0 | 0 | 0 | 0 | 2 | 7 | 5 | 0 | 0 | 0 | 0 | 0 | |
CNN | 19 | 0 | 0 | 1 | 1 | 0 | 3 | 19 | 15 | 1 | 0 | 2 | 1 | 0 | 3 |
MPSC | 20 | 0 | 0 | 1 | 1 | 1 | 4 | 12 | 14 | 3 | 0 | 1 | 0 | 0 | |
SRC | 20 | 0 | 0 | 1 | 1 | 1 | 4 | 12 | 14 | 3 | 0 | 1 | 0 | 0 | |
GMCSCR | 1 | 2 | 3 | ||||||||||||
Category | ?m | 粟 | 翁 | 老 | 腐 | 花 | 藏 | 蜀 | 西 | 贤 | 进 | ? | 长 | 风 | Overall |
Test/train | 3/2 | 13/13 | 7/6 | 7/7 | 3/2 | 3/2 | 3/2 | 3/3 | 4/3 | 5/5 | 3/2 | 3/3 | 7/6 | 5/5 | Accuracy (%) |
SVM | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 18.37 |
CNN | 0 | 9 | 3 | 1 | 0 | 0 | 1 | 1 | 1 | 2 | 0 | 1 | 2 | 2 | 49.23 |
MPSC | 0 | 9 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 2 | 1 | 1 | 1 | 1 | 46.17 |
SRC | 0 | 9 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 3 | 0 | 2 | 1 | 1 | 47.45 |
GMCSCR | 0 | 1 | 1 | 2 | $\mathbf{83.42}$ |