A Markov model for estimating camera pose using target changes

doi:10.11947/j.AGCS.2025.20230077

Abstract

Abstract:

Different from the joint solution of object-image point correspondences for camera pose estimation, we propose a Markov model for estimating camera pose using target changes, which considers the pose parameters as random variables based on the observation of object changes. The specific contributions are as follows. Firstly, using the least squares method to obtain the Markov regression model for solving the state transition matrix. Secondly, based on the priori information, determining the pose transition matrix based on the a priori information to construct a Markov model about the pose parameters. Lastly, a multi-temporal attitude matrix is embedded to correct the pose estimation bias, resulting in a robust Markov pose model. The experimental results show that the Markov model performs well under translation, rotation and composite variations of the observed target, and can realize the effective estimation of camera pose, which can overcome the deficiencies of the existing methods in the case of restricted feature points.

Key words: camera pose, Markov, least square, multi-temporal

CLC Number:

P232

Jiayin LIU, Jiatian LI, Guokun CHEN, Xiaohui A, Jingjing WEI, Hao HU. A Markov model for estimating camera pose using target changes[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(6): 1071-1081.

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变化方式	旋转向量	初始旋转向量	平移向量	初始平移向量
平移	r₁	（-1.990 4，1.571 4，0.663 6）	t₁	（308.390 3，-70.652 2，5 876.476 1）
平移	r₂	（-1.990 3，1.571 2，0.663 8）	t₂	（308.366 1，-70.645 4，5 876.003 5）
旋转	r₁	（-2.127 1，1.640 1，0.561 6）	t₁	（322.115 6，-77.361 7，5 778.479 5）
旋转	r₂	（-2.126 8，1.639 6，0.561 6）	t₂	（322.073 9，-77.338 5，5 777.949 4）
复合	r₁	（-2.019 6，1.612 8，0.667 7）	t₁	（295.585 2，-83.717 2，4 554.343 4）
复合	r₂	（-2.019 7，1.612 7，0.667 5）	t₂	（295.583 4，-83.718 4，4 554.566 1）

变化方式	对比方法	重投影误差/像素
变化方式	对比方法	最大值	最大值偏差	最小值	最小值偏差	平均值	平均值偏差
平移	张氏方法	0.012 97	0.000 31	0.011 94	0.000 18	0.012 51	0.000 27
平移	本文方法	0.013 28	—	0.012 12	—	0.012 78	—
旋转	张氏方法	0.018 64	0.000 87	0.012 21	0.000 18	0.015 53	0.000 38
旋转	本文方法	0.019 51	—	0.012 39	—	0.015 92	—
复合	张氏方法	0.012 54	0.001 38	0.011 91	0.000 25	0.012 17	0.000 55
复合	本文方法	0.013 92	—	0.012 16	—	0.012 72	—

特征点数	估计方法	旋转向量	平移向量	重投影误差/像素
N_P=10	文献[16]方法	（-2.083 0，-2.835 7，-0.286 7）	（-106.700 4，-57.805 7，5 280.475 8）	1.171
	文献[18]方法	（-2.060 5，-2.749 3，-0.179 1）	（-106.947 0，-57.871 4，5 280.642 5）	0.906
	文献[25]方法	（-2.180 5，-2.075 6，-0.109 1）	（-106.583 7，-57.071 2，5 280.343 6）	0.584
	本文方法	（-2.212 2，-2.114 5，-0.109 5）	（-106.593 4，-57.031 9，5 280.377 8）	0.232
N_P=5	文献[16]方法	（-2.482 8，-2.060 3，0.207 2）	（-90.305 6，-58.704 9，13 821.011 2）	1.778
	文献[18]方法	（-2.387 0，-2.018 9，0.200 3）	（-90.899 9，-58.990 2，13 802.440 5）	1.115
	文献[25]方法	（-2.230 9，-2.201 6，0.123 4）	（-91.223 8，-58.172 3，13 556.375 8）	0.554
	本文方法	（-2.258 9，-2.263 1，0.199 6）	（-91.283 5，-58.156 6，13 586.842 2）	0.219
N_P=0	文献[16]方法	—	—	—
	文献[18]方法	—	—	—
	文献[25]方法	—	—	—
	本文方法	（-2.234 6，-2.105 2，0.183 1）	（-51.933 6，-57.716 9，1 350.579 4）	0.253

特征点	像点坐标		世界坐标
特征点	x/像素	y/像素	X_W/mm	Y_W/mm	Z_W/mm
1	-84.14	-68.99	36 589.41	25 273.32	2 195.17
1'	-84.13	-68.98	36 589.40	25 273.31	2 195.16
2	-53.40	82.61	37 631.08	31 324.51	728.69
2'	-53.39	82.60	37 631.07	31 324.50	728.68
3	-14.78	-76.63	39 100.97	24 934.98	2 386.50
3'	-14.77	-76.62	39 100.96	24 934.97	2 386.49
4	10.46	64.63	40 426.54	30 319.81	757.31
4'	10.45	64.62	40 426.53	30 319.80	757.30

组别	方法	X_S	Y_S	Z_S	φ	ω	κ	单位权中误差
第1组	空间后方交会	39 785.57	27 496.44	7 570.18	-0.002 593	-0.001 165	-0.066 702	0.000 106
第1组	马氏方法	39 786.67	27 497.14	7 570.29	-0.002 757	-0.001 383	-0.066 654	0.000 103
第2组	空间后方交会	39 784.78	27 494.62	7 651.00	-0.002 480	-0.001 054	-0.066 725	0.000 111
第2组	马氏方法	39 785.88	27 496.44	7 651.97	-0.002 600	-0.001 286	-0.066 650	0.000 103
第3组	空间后方交会	39 783.99	27 493.80	7 571.83	-0.002 367	-0.000 944	-0.066 747	0.000 117
第3组	马氏方法	39 786.20	27 497.32	7 571.91	-0.002 711	-0.001 393	-0.066 623	0.000 105