Quaternion fast and accurate polar harmonic Fourier moments for color image analysis and&#x00A0;object recognition

Siyu Yang; Ansheng Deng

doi:10.1364/JOSAA.514567

Journal of the Optical Society of America A
Vol. 41,
Issue 5,
pp. 852-862
(2024)
•https://doi.org/10.1364/JOSAA.514567

Quaternion fast and accurate polar harmonic Fourier moments for color image analysis and object recognition

Siyu Yang and Ansheng Deng

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Siyu Yang and Ansheng Deng, "Quaternion fast and accurate polar harmonic Fourier moments for color image analysis and object recognition," J. Opt. Soc. Am. A 41, 852-862 (2024)

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Abstract

Image moments, as a kind of global feature descriptor of images, have become a valuable tool for pattern recognition and image analysis. However, traditional methods are mainly used to deal with grayscale images. In this paper, we apply quaternions to fast and accurate polar harmonic Fourier moments, proposing a kind of quaternion fast and accurate polar harmonic Fourier moment (QFAPHFM) capable of handling color images. Furthermore, this paper provides a detailed analysis of the invariance of QFAPHFMs under rotation, scaling, and translation transformations. The experimental results show that QFAPHFMs exhibit excellent performance in both image reconstruction and object recognition tasks. QFAPHFMs achieve accurate image reconstruction under noiseless and noisy conditions, and demonstrate excellent recognition performance in the color-based object recognition tasks.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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	Decomposition Time (s)		Reconstruction Time (s)
Order	QPHFMs	QFAPHFMs	QPHFMs	QFAPHFMs
5	0.1055	0.1051	0.2146	0.2314
20	0.9426	0.7169	1.2043	0.5677
40	4.2463	3.7433	4.4319	3.9769
60	6.3791	5.5641	8.5137	6.5676
80	12.9422	8.7292	13.6418	9.4267

Number of Moments	$σ^{2}$	QFAPHFMs	QZMs	QOFMMs	QCHFMs	QRHFMs	QPHFMs
7	0	100.00	95.31	100.00	100.00	100.00	100.00
	0.05	93.75	80.69	78.14	78.52	79.25	75.63
	0.10	78.66	55.43	53.41	56.47	52.67	58.88
	0.15	62.71	40.36	33.12	38.94	37.46	35.23
	0.20	50.95	28.49	30.44	31.67	31.93	33.26
	0.25	45.19	29.74	27.82	29.61	31.71	31.34
15	0	100.00	95.27	100.00	100.00	100.00	100.00
	0.05	97.81	91.26	87.27	90.43	85.59	81.69
	0.10	82.57	70.94	74.95	74.74	66.93	68.33
	0.15	66.46	56.13	59.42	49.50	55.12	53.14
	0.20	57.16	40.69	44.83	37.19	41.75	48.78
	0.25	53.61	39.98	41.17	35.83	39.46	46.85
30	0	100.00	98.84	100.00	100.00	100.00	100.00
	0.05	99.34	93.13	90.71	88.85	92.46	85.43
	0.10	88.55	77.49	79.23	75.33	81.55	73.47
	0.15	81.39	65.34	67.97	62.49	66.48	64.52
	0.20	81.39	65.34	67.97	62.49	66.48	64.52
	0.25	68.16	47.17	46.24	43.84	45.35	49.68

Number of Moments	$σ^{2}$	QFAPHFMs	QZMs	QOFMMs	QCHFMs	QRHFMs	QPHFMs
7	0	100.00	100.00	100.00	100.00	100.00	100.00
	0.05	93.75	80.69	78.14	78.52	79.25	75.63
	0.10	78.66	55.43	53.41	56.47	52.67	58.88
	0.15	62.71	40.36	33.12	38.94	37.46	35.23
	0.20	50.95	28.49	30.44	31.67	31.93	33.26
	0.25	45.19	29.74	27.82	29.61	31.71	31.34
15	0	100.00	100.00	100.00	100.00	100.00	100.00
	0.05	97.81	91.26	83.27	90.43	86.59	80.69
	0.10	82.57	76.94	72.95	74.74	68.93	75.33
	0.15	66.46	55.13	57.42	59.50	58.12	63.14
	0.20	56.16	44.69	41.83	45.19	40.75	44.78
	0.25	53.61	39.98	39.17	42.83	38.46	40.85
30	0	100.00	100.00	100.00	100.00	100.00	100.00
	0.05	99.45	94.34	91.67	87.93	88.25	85.49
	0.10	90.37	87.48	85.73	79.76	81.61	78.84
	0.15	84.92	70.25	65.42	68.19	67.38	72.31
	0.20	73.59	58.64	55.86	60.86	63.14	68.28
	0.25	61.26	53.92	52.27	56.38	49.73	55.97

	Decomposition Time (s)		Reconstruction Time (s)
Order	QPHFMs	QFAPHFMs	QPHFMs	QFAPHFMs
5	0.1055	0.1051	0.2146	0.2314
20	0.9426	0.7169	1.2043	0.5677
40	4.2463	3.7433	4.4319	3.9769
60	6.3791	5.5641	8.5137	6.5676
80	12.9422	8.7292	13.6418	9.4267

Number of Moments	$σ^{2}$	QFAPHFMs	QZMs	QOFMMs	QCHFMs	QRHFMs	QPHFMs
7	0	100.00	95.31	100.00	100.00	100.00	100.00
	0.05	93.75	80.69	78.14	78.52	79.25	75.63
	0.10	78.66	55.43	53.41	56.47	52.67	58.88
	0.15	62.71	40.36	33.12	38.94	37.46	35.23
	0.20	50.95	28.49	30.44	31.67	31.93	33.26
	0.25	45.19	29.74	27.82	29.61	31.71	31.34
15	0	100.00	95.27	100.00	100.00	100.00	100.00
	0.05	97.81	91.26	87.27	90.43	85.59	81.69
	0.10	82.57	70.94	74.95	74.74	66.93	68.33
	0.15	66.46	56.13	59.42	49.50	55.12	53.14
	0.20	57.16	40.69	44.83	37.19	41.75	48.78
	0.25	53.61	39.98	41.17	35.83	39.46	46.85
30	0	100.00	98.84	100.00	100.00	100.00	100.00
	0.05	99.34	93.13	90.71	88.85	92.46	85.43
	0.10	88.55	77.49	79.23	75.33	81.55	73.47
	0.15	81.39	65.34	67.97	62.49	66.48	64.52
	0.20	81.39	65.34	67.97	62.49	66.48	64.52
	0.25	68.16	47.17	46.24	43.84	45.35	49.68

Abstract

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Journal of the Optical Society of America A