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摘要: 研究了在小波多尺度分解情况下, 采用分形维数描述车牌字符特征, 并在分区情况下计算出典型车牌字符的分段分形维数。发现小波变换能获取丰富的车牌字符特征, 采用分段分形维数描述车牌解决了单一维数描述车牌字符时, 有些字符维数相差太小, 导致阈值难以选取的问题。结果表明, 小波分形方法是研究车牌字符识别的有效的新方法。Abstract: Fractal dimension of some typical vehicle license characters were calculated in the condition of three zoning to vehicle license. It is found that prolific property of vehicle license can be obtained through wavelet transform, multi-fractal dimension is a good tool to solve the problem that threshold is hard to decide when too close between some characters using single fractal dimension. Simulation results show that the method is feasible to recognize vehicle license characters.
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表 1 离散滤波器的离散系数
Table 1. Discrete coefficients of discrete filters
n -3 -2 -1 H 0.125 G K 0.007 813 0.054 685 0.171 875 n 0 1 2 3 H 0.375 0.375 0.125 G -2.0 2.0 K -0.171 875 -0.054 685 -0.007 813 0 
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表 2 汉字模板分段分形维数
Table 2. Multiscale fractal dimension of Chinese characters template
字符 H1 H2 H3 字符 H1 H2 H3 苏 0.5156 0.5187 0.7461 宁 0.3043 0.5384 0.7196 鄂 0.5667 0.4203 0.9904 津 0.1220 0.7705 0.5984 沪 0.3803 0.6125 0.8465 吉 0.3760 0.6429 0.7718 琼 0.5802 0.4214 0.8012 蒙 0.3808 0.8509 0.5033 辽 0.2916 0.4513 0.7693 黑 0.3420 0.5986 0.6743 桂 0.6349 0.4803 0.7081 海 0.3768 0.5946 0.8951 晋 0.3971 0.7559 0.7399 甘 0.3710 0.8260 0.3833 川 0.3497 0.5321 0.7240 台 0.5480 0.4129 0.7131 浙 0.4647 0.5795 0.7060 皖 0.4483 0.6142 0.7938 滇 0.5225 0.5805 0.6750 疆 0.5287 0.7784 0.5139 赣 0.6531 0.6518 0.5989 粤 0.6221 0.5701 0.7784
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表 3 字母模板分段分形维数
Table 3. Multiscale fractal dimension of letter template
字符 H1 H2 H3 字符 H1 H2 H3 A 0.476 3 0.344 8 0.619 0 N 0.782 8 0.016 3 0.748 4 B 0.076 2 0.474 9 0.874 5 O 0.3350 0.4008 0.6075 C 0.382 6 0.297 1 0.573 1 P 0.4090 0.2858 0.5572 D 0.022 8 0.455 9 0.758 9 Q 0.2701 0.5154 0.4281 E 0.404 6 0.291 9 0.747 1 R 0.5131 0.2644 0.5185 F -0.294 7 0.550 7 0.727 3 S 0.3458 0.4496 0.5617 G 0.337 9 0.442 2 0.630 5 T 0.3176 0.4816 0.5748 H 0.302 7 0.394 2 1.002 8 U 0.3847 0.3705 0.5585 I -0.828 5 0.626 9 0.622 3 V 0.4199 0.3976 0.6158 J 0.442 3 0.332 6 0.374 6 W 0.4484 0.4847 0.7105 K 0.040 6 0.499 7 0.676 0 X 0.4233 0.3526 0.5589 L 0.122 3 0.406 7 0.885 2 Y 0.3482 0.4036 0.6003 M 0.314 1 0.291 2 1.110 4 Z 0.3615 0.4625 0.6040
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表 4 数字模板分段分形维数
Table 4. Multiscale fractal dimension of number template
字符 H1 H2 H3 字符 H1 H2 H3 0 0.3810 0.2544 0.8158 5 0.3932 0.2626 0.7231 1 0.1368 0.4235 0.5663 6 0.4295 0.5402 0.4121 2 0.4020 0.4878 0.4324 7 0.4743 0.3124 0.6525 3 0.3790 0.3373 0.7071 8 0.4054 0.4491 0.6426 4 0.3595 0.4390 0.4368 9 0.3430 0.6030 0.4103
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表 5 易混淆的字符分段分形维数
Table 5. Multiscale fractal dimension of undistinguishable characters template
字符 H1 H2 H3 字符 H1 H2 H3 D 0.0228 0.4559 0.7589 8 0.4054 0.4491 0.6426 O 0.3350 0.4008 0.6075 B 0.0762 0.4749 0.8745 黔 0.5406 0.7208 0.7660 7 0.4743 0.3124 0.6525 陕 0.3983 0.6111 0.8561 1 0.1368 0.4235 0.5663 1 0.1368 0.4235 0.5663 A 0.4763 0.3448 0.6190 I -0.8285 0.6269 0.6223 4 0.3595 0.4390 0.4368
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表 6 汉字12维数据信息
Table 6. 12-D data information of Chinese characters template
字符 ha1 ha2 ha3 hh1 hh2 hh3 hv1 hv2 hv3 hd1 hd2 hd3 鲁 0.8398 0.8442 0.7569 0.4681 0.6423 0.9245 0.3288 0.2924 0.6736 0.3560 0.0856 0.5124 川 0.8070 0.8261 0.7747 0.0581 0.3429 0.2841 0.3097 0.5192 0.7392 0.1926 0.1262 -0.0320 浙 0.8463 0.8534 0.7954 0.2826 0.5571 0.7339 0.3419 0.4818 0.7110 0.3149 0.2243 0.3822 滇 0.8465 0.8528 0.7932 0.5379 0.4264 0.8310 0.2411 0.5537 0.5795 0.4134 0.2143 0.6437 赣 0.8153 0.7902 0.7570 0.5975 0.7312 0.5345 0.5290 0.3998 0.4970 0.3826 0.2882 0.6075 辽 0.7630 0.8076 0.7862 0.3509 0.3919 0.5294 0.0774 0.2978 0.6285 0.2929 0.1869 0.3699 桂 0.7764 0.8131 0.7458 0.5457 0.5470 0.5947 0.6035 0.1711 0.6826 0.3332 0.1059 0.4763 鄂 0.7925 0.8415 0.7412 0.4589 0.5822 0.6590 0.4895 0.1480 0.8091 0.4222 0.1941 0.4353 沪 0.7837 0.7871 0.6930 0.0835 0.5466 0.5730 0.3620 0.4554 0.7767 0.2976 0.3233 0.2615
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