Image description with generalized pseudo-Zernike moments

Ting Xia; Hongqing Zhu; Huazhong Shu; Pascal Haigron; Limin Luo

doi:10.1364/JOSAA.24.000050

Journal of the Optical Society of America A
Vol. 24,
Issue 1,
pp. 50-59
(2007)
•https://doi.org/10.1364/JOSAA.24.000050

Image description with generalized pseudo-Zernike moments

Ting Xia, Hongqing Zhu, Huazhong Shu, Pascal Haigron, and Limin Luo

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Ting Xia, Hongqing Zhu, Huazhong Shu, Pascal Haigron, and Limin Luo, "Image description with generalized pseudo-Zernike moments," J. Opt. Soc. Am. A 24, 50-59 (2007)

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Abstract

A new set, to our knowledge, of orthogonal moment functions for describing images is proposed. It is based on the generalized pseudo-Zernike polynomials that are orthogonal on the unit circle. The generalized pseudo-Zernike polynomials are scaled to ensure numerical stability, and some properties are discussed. The performance of the proposed moments is analyzed in terms of image reconstruction capability and invariant character recognition accuracy. Experimental results demonstrate the superiority of generalized pseudo-Zernike moments compared with pseudo-Zernike and Chebyshev–Fourier moments in both noise-free and noisy conditions.

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Value of p $(q = 10)$	$α = 0$	$α = 10$	$α = 20$	$α = 30$	$α = 40$
10	—	—	—	—	—
11	0.956563	0.666563	0.511562	0.415312	0.349063
12	0.864688	0.575938	0.435937	0.350937	0.294063
	0.975313	0.738438	0.586562	0.485312	0.413438
13	0.772813	0.508125	0.382812	0.307813	0.257188
	0.910313	0.654375	0.510937	0.419063	0.355312
	0.983438	0.783438	0.638125	0.53625	0.461875
14	0.690313	0.45375	0.341562	0.274688	0.229688
	0.836563	0.587813	0.455937	0.372188	0.315000
	0.93375	0.706563	0.565313	0.470625	0.402813
	0.987188	0.815625	0.677813	0.577187	0.501563

	Recognition Accuracy (%) under Different Salt-and-Pepper Noises
Parameter α for GPZMs	Noise Free	5%	9%	10%	15%	18%
0	93.3333	60.8333	48.3333	41.6667	41.6667	36.6667
2	93.3333	86.6667	55.83333	50.8333	31.6667	30.8333
4	93.3333	59.1667	25.83333	23.3333	20.0000	20.0000
6	96.6667	55.0000	29.1667	25.0000	20.0000	20.0000
8	96.6667	59.1667	25.0000	24.1667	20.0000	20.0000
10	96.6667	94.1667	81.6667	66.6667	33.3333	30.0000
12	96.6667	85.8333	57.5000	48.3333	38.3333	36.6667
14	93.3333	75.8333	32.5000	30.8333	22.5000	20.0000
16	96.6667	81.6667	45.0000	37.5000	25.0000	20.8333
18	100	85.0000	69.1667	59.1667	42.5000	27.5000
20	100	86.6667	79.1667	67.5000	55.0000	45.0000
22	96.6667	88.3333	80.8333	71.6667	60.8000	50.8333
24	96.6667	91.6667	87.5000	75.0000	67.5000	58.3333
26	96.6667	91.6667	90.8333	79.1667	71.6667	60.8333
28	96.6667	90.8333	91.6667	78.3333	70.0000	62.5000
30	93.3333	85.0000	84.1667	74.1667	70.0000	59.1667
CHFMs	100	60	40	60	40	40

	Recognition Accuracy (%) under Different $σ^{2}$ Gaussian White Noises
Parameter α for GPZMs	Noise Free	0.01	0.03	0.05	0.10
0	100	83.7963	62.0370	44.4444	22.2222
2	100	99.0741	90.2778	77.7778	46.7593
4	100	96.7593	52.3148	31.4815	21.7593
6	100	94.9074	30.0926	6.94444	0
8	100	93.0556	32.8704	17.5926	12.5
10	100	99.5370	57.4074	33.7963	13.8889
12	100	100	74.5370	43.5185	23.1481
14	100	100	87.0370	66.2037	43.0556
16	100	100	95.8333	62.5000	46.2963
18	100	100	96.7593	84.2593	67.5926
20	100	100	98.1481	93.5185	65.2778
22	100	100	99.5370	96.7593	68.0556
24	100	100	100	96.2963	70.3704
26	100	100	100	97.2222	73.1481
28	100	100	100	98.6111	77.7778
30	100	100	100	98.6111	81.4815
CHFMs	100	100	77.7778	55.5556	22.2222

Value of p $(q = 10)$	$α = 0$	$α = 10$	$α = 20$	$α = 30$	$α = 40$
10	—	—	—	—	—
11	0.956563	0.666563	0.511562	0.415312	0.349063
12	0.864688	0.575938	0.435937	0.350937	0.294063
	0.975313	0.738438	0.586562	0.485312	0.413438
13	0.772813	0.508125	0.382812	0.307813	0.257188
	0.910313	0.654375	0.510937	0.419063	0.355312
	0.983438	0.783438	0.638125	0.53625	0.461875
14	0.690313	0.45375	0.341562	0.274688	0.229688
	0.836563	0.587813	0.455937	0.372188	0.315000
	0.93375	0.706563	0.565313	0.470625	0.402813
	0.987188	0.815625	0.677813	0.577187	0.501563

	Recognition Accuracy (%) under Different Salt-and-Pepper Noises
Parameter α for GPZMs	Noise Free	5%	9%	10%	15%	18%
0	93.3333	60.8333	48.3333	41.6667	41.6667	36.6667
2	93.3333	86.6667	55.83333	50.8333	31.6667	30.8333
4	93.3333	59.1667	25.83333	23.3333	20.0000	20.0000
6	96.6667	55.0000	29.1667	25.0000	20.0000	20.0000
8	96.6667	59.1667	25.0000	24.1667	20.0000	20.0000
10	96.6667	94.1667	81.6667	66.6667	33.3333	30.0000
12	96.6667	85.8333	57.5000	48.3333	38.3333	36.6667
14	93.3333	75.8333	32.5000	30.8333	22.5000	20.0000
16	96.6667	81.6667	45.0000	37.5000	25.0000	20.8333
18	100	85.0000	69.1667	59.1667	42.5000	27.5000
20	100	86.6667	79.1667	67.5000	55.0000	45.0000
22	96.6667	88.3333	80.8333	71.6667	60.8000	50.8333
24	96.6667	91.6667	87.5000	75.0000	67.5000	58.3333
26	96.6667	91.6667	90.8333	79.1667	71.6667	60.8333
28	96.6667	90.8333	91.6667	78.3333	70.0000	62.5000
30	93.3333	85.0000	84.1667	74.1667	70.0000	59.1667
CHFMs	100	60	40	60	40	40

Abstract

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Journal of the Optical Society of America A