Beyond Control Points: Arcsecond Relative-Motion Estimation of Vision Measurement Platforms With Incomplete or Absent Control Fields

Meng Lian; Jian Wang; Shuixin Pan; Haibo Liu; Yueqiang Zhang; Yulan Guo

cs.CVAug 14, 2026

Beyond Control Points: Arcsecond Relative-Motion Estimation of Vision Measurement Platforms With Incomplete or Absent Control Fields

Authors: Meng Lian, Jian Wang, Shuixin Pan, Haibo Liu, Yueqiang Zhang, Yulan Guo

Organizations: Ministry of Natural Resources (MNR) Key Laboratory for Geo-Environmental Monitoring of Great Bay Area & Guangdong Key Laboratory of Urban Informatics, Shenzhen University, Shenzhen, China · Shenzhen Expressway Co., Ltd., Shenzhen, China · Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, the Shenzhen Key Laboratory of Intelligent Optical Measurement and Detection, and the College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China · School of Artificial Intelligence and Robotics, Hunan University, Changsha 410082, China ·

Abstract

Long-range vision-based deformation monitoring is highly sensitive to motion of the camera platform. Absolute-pose differencing typically relies on dedicated control data and propagates two independent pose errors into the relative-motion estimate. We develop a control-adaptive differential framework that estimates inter-frame platform motion directly from image displacements and known 3D points. With no dedicated control point, the framework recovers platform rotation from measurement-point observations. One surveyed control point enables prior-constrained translation recovery, while two nonparallel control rays recover full 3D translation. The framework requires neither nonlinear optimization nor an initial pose estimate. Excluding control data from the rotation stage makes the rotation estimate exactly immune to contamination confined to the control field. The inherited differential formulation also cancels translational extrinsic errors exactly. We derive the rotation observability condition, a leakage bound for unmodeled translation and nonrigid point motion, and the single-point axial-prior bias law. Under 0.5-pixel image noise, attitude changes of up to 30~~arcmin, and 3D point perturbations of up to 2~~mm, the multi-camera estimator achieves a rotation RMSE of 2.97~~arcsec and an average runtime of 0.46~~ms. With one surveyed control point, its prior-constrained translation RMSE is 1.19~~mm. In a bridge experiment without a stable control field, the median coordinate-wise displacement RMSE relative to total-station measurements is 0.85~~mm. The estimator also maintains zero divergence under the tested 3D coordinate perturbations on public RGB-D and stereo sequences. These results establish state-of-the-art accuracy, calibration robustness, and computational efficiency among the evaluated methods.

Figures & tables

Fig. 1: RMSE of the three attitude angles versus the number of measurement points: (a)–(c) monocular group; (d)–(f) multi-camera group.

Fig. 2: RMSE of the three attitude angles versus the image localization noise: (a)–(c) monocular group; (d)–(f) multi-camera group.

Fig. 3: Mean and median of the total rotation-angle error versus the image localization noise: (a)(b) monocular group; (c)(d) multi-camera group.

Fig. 4: RMSE of the three attitude angles versus the measurement-point perturbation: (a)–(c) monocular group; (d)–(f) multi-camera group.

Fig. 5: Influence of the extrinsic calibration errors on the rotation estimate: (a)(b) extrinsic rotation error; (c)(d) extrinsic translation error.

Fig. 6: Influence of the angle between the two optical axes on the rotation estimate of the multi-camera group.

Fig. 7: Cumulative distribution of the total rotation-angle error under the typical condition (0.5-pixel noise): (a) monocular group; (b) multi-camera group.

Fig. 8: Box plot of the rotation error under the typical condition: (a) monocular group; (b) multi-camera group.

Method	Mean $(^{\prime\prime})$	Median $(^{\prime\prime})$	RMSE $(^{\prime\prime})$	Max $(^{\prime\prime})$	Div. $(\%)$	Time (ms)
Monocular methods (pitch–yaw error)
LHM	47.97	8.14	248.12	2524.57	11.5	5.01
EPnP+GN	40.02	8.47	138.93	1423.42	4.5	4.06
RPnP	9.06	7.05	11.94	55.65	0	2.42
DLS	10.38	7.49	17.16	141.29	30	5.62
ASPnP	9.07	7.00	12.03	55.15	1.0	5.39

TABLE I: Rotation-Error Statistics (Arcsec) and Average Runtime Under the Typical Condition (Pitch–Yaw Error for the Monocular Group; Total Rotation Angle for the Multi-Camera Group)

Method	Rot. RMSE/ ′′	Rot. med./ ′′	Trans. RMSE/mm	Trans. med./mm	$\Delta Z$ RMSE/mm	Div. %
Monocular methods (pitch–yaw error)
LHM	89.67	6.40	34.64	27.07	34.48	5.0
EPnP+GN	52.30	6.93	44.99	42.02	44.82	3.0
RPnP	9.27	6.01	36.46	23.49	36.31	0
DLS	91.46	5.90	33.82	22.13	33.66	13.0
ASPnP	9.71	5.83	33.97	23.21	33.81	0

TABLE II: Error Statistics Under the All-Point Protocol With One Surveyed Control Point (Typical Condition, 200 Trials)

Method	Rot. RMSE/ ′′	Rot. med./ ′′	Trans. RMSE/mm	Trans. med./mm	$\Delta Z$ RMSE/mm	Div. %
Monocular methods (pitch–yaw error)
LHM	41.86	5.58	30.47	20.73	30.36	3.0
EPnP+GN	60.92	5.83	42.12	33.97	42.00	0
RPnP	7.78	5.57	33.09	21.26	32.96	0
DLS	27.08	5.33	28.75	18.47	28.61	6.5
ASPnP	7.54	5.31	29.95	18.43	29.82	1.0

TABLE III: Error Statistics Under the All-Point Protocol With Two Surveyed Control Points (One per Camera in the Multi-Camera Configuration; Both Viewed by the Single Camera in the Monocular Configuration)

Fig. 9: Distributions of the rotation and translation errors under the all-point protocol with one control point: (a) monocular rotation (pitch–yaw); (b) monocular translation; (c) multi-camera rotation (total angle); (d) multi-camera translation.

Fig. 10: Distributions of the rotation and translation errors under the all-point protocol with two control points; panels as in Fig. 9 .

Fig. 11: Verification of the depth-prior working boundary (multi-camera configuration): (a) translation RMS versus platform motion magnitude

T

; the hybrid scheme follows ( 26 ) and approaches the

T/\sqrt{3}

paraxial asymptote, while joint recovery remains at its noise floor; (b) rotation RMS, which remains nearly constant for both tested schemes over the translation sweep.

Fig. 12: Average runtime of all the methods versus the number of measurement points: (a) monocular group; (b) multi-camera group.

Panel of Figure 16 — Fig. 13: Experimental layout: (a) layout diagram (top); (b) on-site installation (bottom left) and an image captured by one of the station cameras (bottom right).

Camera	$f_{x}$ (pixel)	$f_{y}$ (pixel)	$c_{x}$ (pixel)	$c_{y}$ (pixel)
Camera 122	71034.47	71034.47	1920.5	1080.5
Camera 123	34719.93	34719.93	1920.5	1080.5
Camera 125	69386.41	69386.41	1920.5	1080.5

TABLE IV: Intrinsic Parameters of the Three Cameras of Station 1 (by Manufacturer Serial Number)

Fig. 14: Key point deformation measurement results: (a) horizontal displacement along the $X$ -axis; (b) vertical displacement along the $Y$ -axis.

Point	Mean error $X$ (mm)	RMSE $X$ (mm)	Mean error $Y$ (mm)	RMSE $Y$ (mm)
15-1-1	0.58	0.70	0.06	0.71
15-1-2	$-$ 0.23	0.51	0.72	1.07
15-2-1	$-$ 0.31	0.88	$-$ 1.08	1.88
15-2-2	$-$ 0.41	0.72	$-$ 0.54	0.89
15-3-1	0.53	0.81	$-$ 0.51	0.74
15-3-2	0.88	1.28	1.87	2.09

TABLE V: Comparison of the Measured Displacements With the Total Station

	fr1_xyz		fr2_desk
Method	skip 1	skip 30	skip 1	skip 30
Differential (GN)	1240 (0)	5747 (2)	850 (0)	5730 (9)
Differential (linear)	1240 (0)	5665 (2)	850 (0)	5736 (9)
EPnP	1397 (0)	5494 (5)	875 (0)	6167 (8)
SQPnP	1194 (0)	5632 (2)	848 (0)	5810 (9)
Iterative	1240 (0)	4997 (9)	850 (0)	5754 (10)

TABLE VI: Rotation RMSE and divergence rates on the clean TUM sequences. The RMSE is reported in arcseconds, and the divergence rate is reported in parentheses as a percentage.

Method	clean	$+$ 20 mm	$+$ 50 mm	8 pts $+$ 20 mm
Differential (GN)	1240 (0)	1237 (0)	1219 (0)	1590 (0)
SQPnP	1194 (0)	1193 (0)	1192 (0)	1596 (0)
EPnP	1397 (0)	1400 (0)	1426 (0)	2216 (1)
Iterative	1240 (0)	1858 (13)	8195 (67)	2776 (28)
RANSAC (2 px)	1486 (0)	7457 (16)	5626 (86)	3435 (96)

TABLE VII: Robustness to Per-Point 3D Coordinate Perturbations at a Frame Skip of 1. Rotation RMSE Is Reported in Arcseconds, and the Divergence Rate Is Reported in Percent.

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Relative Pose Estimation

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Accurate six-degree-of-freedom (6-DOF) motion estimation is essential for robotic manipulation, autonomous systems, and structural displacement monitoring. Conventional 3D-2D methods estimate absolute camera poses independently at each time and recover platform motion through camera-to-platform extrinsics, making them sensitive to extrinsic calibration errors, especially for micromotion. We present a differential pose estimation method that directly recovers platform motion from inter-frame image displacements and known 3D control points. By differencing perspective projection equations, using a depth-invariance approximation, and modeling motion on SE(3), the method avoids independent absolute-pose estimation and supports both monocular and multi-camera systems. We prove that translational extrinsic errors cancel exactly, while rotational errors induce a bounded perturbation determined by calibration error, motion magnitude, and observation geometry. We also derive generic observability conditions, a Cramer-Rao lower bound, and a bias-eliminated consistent estimator, and characterize the validity limits of the approximations. Extensive synthetic and real-world experiments establish a new state of the art for 6-DOF platform micromotion estimation, outperforming representative PnP and generalized-PnP methods in accuracy, calibration robustness, and computational efficiency. With five control points and 0.5-pixel image noise, the monocular solver obtains a combined pitch-yaw rotation RMSE of 10.09 arcsec, a translation RMSE of 3.70 mm, and a runtime of 0.34 ms. The binocular solver achieves a rotation RMSE of 10.58 arcsec, a translation RMSE of 3.91 mm, and a runtime of 0.27 ms. Code will be released upon publication at https://github.com/zyoungszu/pami2026.

Abstract

Relative Pose Estimation

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