An Effective Approach for Noise Robust and Rotation Invariant Handwritten Character Recognition Using Zernike Moments Features and Optimal Similarity Measure

Figures & data

Figure 1. Sample images of three DBs (a) MNIST (Roman numerals), (b) Gurumukhi characters (GurChar), and (c) Gurumukhi numerals (GurNum).

Figure 2. (a) Recognition rate (%) versus moment order for MNIST DB using inner unit disk mapping. (b) Recognition rate (%) versus moment order for MNIST DB using outer unit disk mapping.

Figure 3. (a) Recognition rate (%) versus moment order for GurChar DB using inner unit disk mapping. (b) Recognition rate (%) versus moment order for GurChar DB using outer unit disk mapping.

Figure 4. (a) Recognition rate (%) versus moment order for GurNum DB using inner unit disk mapping. (b) Recognition rate (%) versus moment order for GurNum DB using outer unit disk mapping.

Table 1. Recognition rates (%) for three DBs for inner and outer unit disk mappings.

	MNIST		GurChar		GurNum
Method	Inner	Outer	Inner	Outer	Inner	Outer
ZM_MAG	81.00	75.24	59.14	69.11	86.53	91.07
ZM_MAG_PHASE (Li, Lee, and Pun 2009)	73.00	66.96	37.66	47.54	71.87	84.53
ZM_COMPLEX (Singh, Walia, and Mittal 2011)	80.22	75.32	55.83	68.49	85.33	92.13
ZM_SVM	86.92	84.50	64.74	78.46	88.53	95.47
ZM_OPT (Revaud, Lavoue, and Baskurt 2009)	94.18	90.76	85.34	87.57	97.33	98.67

Table 2a. Recognition rates (%) for rotated Roman numerals (MNIST DB) using inner unit disk mapping.

Method	Angle of rotation
	0°	10°	20°	30°	40°	45°	50°	60°	70°	80°	90°
ZM_MAG	81.00	80.34	80.08	80.04	79.84	79.56	80.28	80.32	79.96	79.70	81.00
ZM_MAG_PHASE (Li, Lee, and Pun 2009)	73.00	72.12	72.9	73.04	73.14	73.36	72.58	72.76	72.68	72.52	73.00
ZM_COMPLEX (Singh, Walia, and Mittal 2011)	80.22	79.72	79.1	79.80	79.32	79.18	79.78	79.90	79.26	78.96	80.22
ZM_SVM	86.92	86.52	86.38	86.34	86.52	85.82	86.48	86.40	86.34	86.06	86.92
ZM_OPT (Revaud, Lavoue, and Baskurt 2009)	94.18	93.96	93.98	94.20	93.92	93.80	93.84	93.88	94.02	94.00	94.18

Table 2b. Recognition rates (%) for rotated Roman numerals (MNIST DB) using outer unit disk mapping.

Method	Angle of rotation
	0°	10°	20°	30°	40°	45°	50°	60°	70°	80°	90°
ZM_MAG	75.24	74.44	74.54	73.94	74.34	73.62	73.86	74.40	74.52	74.44	75.24
ZM_MAG_PHASE (Li, Lee, and Pun 2009)	66.96	66.60	66.98	67.28	66.30	66.54	66.14	66.68	66.14	66.92	66.96
ZM_COMPLEX (Singh, Walia, and Mittal 2011)	75.32	74.40	74.78	73.84	74.62	73.26	74.02	74.80	74.44	74.34	75.32
ZM_SVM	84.50	84.04	84.02	84.00	83.98	82.68	83.68	83.86	84.20	83.84	84.50
ZM_OPT (Revaud, Lavoue, and Baskurt 2009)	90.76	89.98	90.46	89.98	90.40	90.14	89.78	89.90	90.58	90.50	90.76

Table 3a. Recognition rates (%) for rotated Gurumukhi characters (GurChar DB) using inner unit disk mapping.

Method	Angle of rotation
	0°	10°	20°	30°	40°	45°	50°	60°	70°	80°	90°
ZM_MAG	59.14	57.49	57.69	58.20	57.14	57.51	58.03	57.34	57.34	57.46	59.14
ZM_MAG_PHASE (Li, Lee, and Pun 2009)	37.66	35.94	37.37	36.91	36.60	37.26	36.60	38.03	36.94	37.06	37.66
ZM_COMPLEX (Singh, Walia, and Mittal 2011)	55.83	54.31	54.09	53.69	53.66	54.20	53.43	53.86	54.03	53.86	55.83
ZM_SVM	64.74	64.06	63.49	63.11	63.83	63.91	64.09	63.97	63.69	63.71	64.74
ZM_OPT (Revaud, Lavoue, and Baskurt 2009)	85.34	85.06	85.20	85.60	85.09	85.31	85.00	85.20	85.11	85.17	85.34

Table 3b. Recognition rates (%) for rotated Gurumukhi characters (GurChar DB) using outer unit disk mapping.

Method	Angle of rotation
	0°	10°	20°	30°	40°	45°	50°	60°	70°	80°	90°
ZM_MAG	69.11	68.94	69.37	68.71	68.97	68.83	68.77	69.06	69.63	68.94	69.11
ZM_MAG_PHASE (Li, Lee, and Pun 2009)	47.54	47.20	47.49	46.77	46.14	47.03	46.74	47.80	47.09	48.43	47.54
ZM_COMPLEX (Singh, Walia, and Mittal 2011)	68.49	69.09	68.49	68.26	67.94	68.40	67.89	68.60	68.31	68.71	68.49
ZM_SVM	78.46	77.80	77.71	77.66	77.40	77.14	77.31	77.63	77.83	77.26	78.46
ZM_OPT (Revaud, Lavoue, and Baskurt 2009)	87.57	87.23	87.14	87.40	87.43	86.91	87.09	87.20	87.46	87.37	87.57

Table 4a. Recognition rates (%) for rotated Gurumukhi numerals (GurNum DB) using inner unit disk mapping.

Method	Angle of rotation
	0°	10°	20°	30°	40°	45°	50°	60°	70°	80°	90°
ZM_MAG	86.53	87.20	86.93	87.47	86.13	86.40	86.80	87.07	86.67	86.93	86.53
ZM_MAG_PHASE (Li, Lee, and Pun 2009)	71.87	69.07	69.60	71.47	71.20	71.20	71.47	69.20	70.53	71.07	71.87
ZM_COMPLEX (Singh, Walia, and Mittal 2011)	85.33	83.87	84.67	84.53	83.73	83.33	83.60	84.27	83.47	84.00	85.33
ZM_SVM	88.53	87.20	87.60	87.20	87.60	87.87	88.13	87.07	86.93	87.07	88.53
ZM_OPT (Revaud, Lavoue, and Baskurt 2009)	97.33	97.20	97.33	97.33	97.07	97.47	97.07	97.47	97.07	97.20	97.33

Table 4b. Recognition rates (%) for rotated Gurumukhi numerals (GurNum DB) using outer unit disk mapping.

Method	Angle of rotation
	0°	10°	20°	30°	40°	45°	50°	60°	70°	80°	90°
ZM_MAG	91.07	90.80	91.20	90.80	90.27	91.07	90.27	91.33	91.47	90.00	91.07
ZM_MAG_PHASE (Li, Lee, and Pun 2009)	84.53	83.20	84.93	82.13	84.53	81.47	80.93	84.27	83.73	83.33	84.53
ZM_COMPLEX (Singh, Walia, and Mittal 2011)	92.13	92.00	92.27	91.60	92.13	92.13	92.53	90.93	91.60	92.00	92.13
ZM_SVM	95.47	95.07	94.80	94.67	94.67	94.93	95.07	95.87	95.07	95.07	95.47
ZM_OPT (Revaud, Lavoue, and Baskurt 2009)	98.67	98.53	98.80	98.80	98.93	98.67	98.40	98.67	98.53	98.53	98.67

Table 5a. Recognition rates (%) for MNIST Roman numerals DB at different noise densities.

	Inner unit disk						Outer unit disk
Method	Noise-free (0%)	Noise density					Noise-free (0%)	Noise density
		5%	10%	15%	20%	25%		5%	10%	15%	20%	25%
ZM_MAG	81.00	77.50	73.52	66.70	59.54	51.52	75.24	72.20	65.08	56.02	43.46	35.42
ZM_MAG_PHASE (Li, Lee, and Pun 2009)	73.00	65.22	58.94	51.06	45.24	39.98	66.96	47.14	38.94	32.38	28.78	24.78
ZM_COMPLEX (Singh, Walia, and Mittal 2011)	80.22	76.54	71.24	64.46	55.04	47.98	75.32	70.96	64.56	57.50	49.00	39.78
ZM_SVM	86.92	83.10	75.98	65.74	59.16	53.56	84.50	76.20	63.88	56.18	49.54	42.40
ZM_OPT (Revaud, Lavoue, and Baskurt 2009)	94.18	93.70	92.72	92.02	90.78	87.74	90.76	89.34	87.84	82.60	74.70	66.42

Table 5b. Recognition rates (%) for Gurumukhi characters DB at different noise densities.

	Inner unit disk						Outer unit disk
Method	Noise-free (0%)	Noise density					Noise-free (0%)	Noise density
		5%	10%	15%	20%	25%		5%	10%	15%	20%	25%
ZM_MAG	59.14	57.06	54.40	50.80	44.23	37.46	69.11	68.00	64.69	61.26	54.34	46.14
ZM_MAG_PHASE (Li, Lee, and Pun 2009)	37.66	36.74	35.26	33.03	32.00	28.14	47.54	45.71	44.91	43.83	40.34	38.40
ZM_COMPLEX (Singh, Walia, and Mittal 2011)	55.83	53.23	50.74	44.37	38.11	30.09	68.49	66.60	63.34	59.74	52.89	45.09
ZM_SVM	64.74	62.86	60.66	56.60	50.69	43.94	78.46	75.74	72.29	66.40	59.00	49.37
ZM_OPT (Revaud, Lavoue, and Baskurt 2009)	85.34	85.17	84.51	84.00	83.66	83.69	87.57	86.66	86.49	85.43	84.17	82.34

Table 5c. Recognition rates (%) for Gurumukhi numerals DB at different noise densities.

	Inner unit disk						Outer unit disk
Method	Noise-free (0%)	Noise density					Noise-free (0%)	Noise density
		5%	10%	15%	20%	25%		5%	10%	15%	20%	25%
ZM_MAG	86.53	85.60	84.13	82.53	79.20	74.93	91.07	91.07	91.07	88.93	87.07	83.60
ZM_MAG_PHASE (Li, Lee, and Pun 2009)	71.87	69.60	69.07	65.33	62.27	59.33	84.53	81.87	78.67	78.40	75.47	75.33
ZM_COMPLEX (Singh, Walia, and Mittal 2011)	85.33	83.60	81.20	80.13	73.20	69.07	92.13	91.73	90.27	89.87	86.53	82.00
ZM_SVM	88.53	86.53	86.00	84.93	81.33	77.47	95.47	95.20	93.20	92.40	89.60	84.80
ZM_OPT (Revaud, Lavoue, and Baskurt 2009)	97.33	97.20	97.20	97.06	96.93	96.93	98.67	98.40	98.40	98.40	98.40	98.13

Table 6. CPU elapse time (in sec) for training and testing on three DBs for p_max = 12. The quantities in parenthesis represent the average time taken for one image.

Training (feature extraction)			Testing (feature extraction & classification)
Data sets	Inner unit disk	Outer unit disk	Inner unit disk					Outer unit disk
			ZM_MAG	ZM_ MAG_PHASE	ZM_COMPLEX	ZM_ SVM	ZM_ OPT	ZM_MAG	ZM_ MAG_PHASE	ZM_COMPLEX	ZM_ SVM	ZM_ OPT
MNIST	1.09 (0.00022)	1.27 (0.00025)	17.88 (0.0036)	129.37 (0.026)	265.04 (0.053)	244.31 (0.049)	319.06 (0.064)	18.19 (0.004)	127.53 (0.026)	264.03 (0.053)	216.36 (0.043)	311.88 (0.062)
GUR CHAR	0.97 (0.00028)	1.12 (0.00032)	8.22 (0.0024)	64.55 (0.018)	131.03 (0.037)	214.36 (0.061)	166.17 (0.047)	8.37 (0.002)	64.25 (0.018)	130.78 (0.037)	191.02 (0.055)	160.44 (0.046)
GUR NUM	0.28 (0.00037)	0.31 (0.00041)	0.89 (0.0012)	3.78 (0.005)	6.41 (0.009)	17.26 (0.023)	8.10 (0.011)	0.95 (0.001)	3.82 (0.005)	6.44 (0.009)	15.35 (0.020)	7.78 (0.010)

Figure 5. Noise samples of three DBs at different noise densities. (a) MNIST Roman numerals, (b) Gurumukhi characters, and (c) Gurumukhi numerals.

Figure 6. Comparison of CPU elapse time taken by a naïve implementation of ZM_OPT and its proposed fast method.

Li, S., M.-C. Lee, and C. M. Pun. 2009. Complex Zernike moments features for shape based image retrieval. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 39 (1):227–37. doi:10.1109/TSMCA.2008.2007988.

 Web of Science ®Google Scholar

Singh, C., E. Walia, and N. Mittal. 2011. Rotation invariant complex Zernike moments features and their applications to human face and character recognition. IET Computer Vision 5 (5):255–66. doi:10.1049/iet-cvi.2010.0020.

 Web of Science ®Google Scholar

Revaud, J., G. Lavoue, and A. Baskurt. 2009. Improving Zernike moments comparison for optimal similarity and rotation angle retrieval. IEEE Transactions on Pattern Analysis and Machine Intelligence 31 (4):627–36. doi:10.1109/TPAMI.2008.115.

 PubMed Web of Science ®Google Scholar