High-Precision 6DOF Pose Estimation via Global Phase Retrieval in Fringe Projection Profilometry for 3D Mapping

Sehoon Tak; Keunhee Cho; Sangpil Kim; Jae-Sang Hyun

cs.CVMar 12, 2026

High-Precision 6DOF Pose Estimation via Global Phase Retrieval in Fringe Projection Profilometry for 3D Mapping

Authors: Sehoon Tak, Keunhee Cho, Sangpil Kim, Jae-Sang Hyun

Organizations: Department of Mechanical Engineering, Yonsei University, Seoul 03722, South Korea. · Department of Artificial Intelligence, Korea University, Seoul

Abstract

Digital fringe projection (DFP) enables micrometer-level 3D reconstruction, yet extending it to large-scale mapping remains challenging because six-degree-of-freedom pose estimation often cannot match the reconstruction's precision. Conventional iterative closest point (ICP) registration becomes inefficient on multi-million-point clouds and typically relies on downsampling or feature-based selection, which can reduce local detail and degrade pose precision. Drift-correction methods improve long-term consistency but do not resolve sampling sensitivity in dense DFP point clouds.We propose a high-precision pose estimation method that augments a moving DFP system with a fixed, intrinsically calibrated global projector. Using the global projector's phase-derived pixel constraints and a PnP-style reprojection objective, the method estimates the DFP system pose in a fixed reference frame without relying on deterministic feature extraction, and we experimentally demonstrate sampling invariance under coordinate-preserving subsampling. Experiments demonstrate sub-millimeter pose accuracy against a reference with quantified uncertainty bounds, high repeatability under aggressive subsampling, robust operation on homogeneous surfaces and low-overlap views, and reduced error accumulation when used to correct ICP-based trajectories. The method extends DFP toward accurate 3D mapping in quasi-static scenarios such as inspection and metrology, with the trade-off of time-multiplexed acquisition for the additional projector measurements.

Figures & tables

Component	Poses	Points/pose	$\mathrm{RMS}_{\text{px}}$
Camera (local)	16	147	0.039 $\pm$ 0.007
Projector (local)	16	147	0.043 $\pm$ 0.008
Projector (global)	16	147	0.044 $\pm$ 0.008

TABLE I : Calibration dataset and residual statistics.

Condition	Plane thickness ( $\mu$ m)	# acquisitions
Within-session	7.91 $\pm$ 5.72	$20$
Restart-to-restart	9.88 $\pm$ 7.08	$20$

TABLE II : 3D reconstruction accuracy and repeatability on a planar target. Plane thickness is computed as the RMS distance to a best-fit plane.

Fig. 2 : Pose drift under injected spatially correlated noise. Median (IQR) drift vs perturbation magnitude

\sigma

for (a) translation

\delta_{t}

(mm) and (b) rotation

\delta_{R}

(mrad) over

K=20

trials per

\sigma

. (Sec. IV-D ).

Metric	$d_{t}=\\|\mathbf{t}-\tilde{\mathbf{t}}\\|_{2}$ (mm)	$d_{R}=\angle(\tilde{\mathbf{R}}^{\top}\mathbf{R})$ (mrad)
Mean $\pm$ SD	0.37 $\pm$ 0.19	0.56 $\pm$ 0.31
Median (IQR)	0.37 (0.25)	0.55 (0.40)
Worst-case (max)	0.92	1.75

TABLE III : Sampling repeatability over

K=400

trials on fixed 3D data. Repeatability is measured relative to the trial-median pose

\tilde{\mathbf{T}}

Fig. 3 : Sampling repeatability on fixed 3D data over

K=400

trials. ECDF of (a) translation repeatability

d_{t}

(mm) and (b) rotation repeatability

d_{R}

(mrad), defined relative to the trial-median pose. Dashed and dotted vertical lines indicate the median and IQR. (Sec. IV-E1 ).

Fig. 4 : Minimum-overlap robustness. Median (IQR) repeatability vs overlap ratio

r

for (a)

d_{t}

(mm) and (b)

d_{R}

(mrad), over

K=120

trials per

r

. (Sec. IV-E2 )

Scheme	Points	$d_{t}$ (mm)	$d_{R}$ (mrad)
Random	501350	0.37 (0.26)	0.52 (0.37)
Uniform	501350	0.30 (0.23)	0.49 (0.38)
Voxel	492988	0.39 (0.27)	0.56 (0.41)

TABLE IV : Sampling scheme comparison under matched point counts. Reported as median (IQR) over

K=120

trials per scheme.

Setting	Default	Tested range
Batch size $B$	12	5–400
Points per batch $n$	120	1–400
Max iters $T$	2000	20–200000
Adam $\alpha_{0}$	1e-2	5e-4–1e-1
Adam $(\beta_{1},\beta_{2},\epsilon)$	(0.9, 0.999, 1e-8)	fixed
Stage-2 weight $\lambda$	0.01	0.001–1

TABLE V : Optimization defaults used throughout the paper and tested tolerance ranges.

GT traceability (used for

e_{t},e_{R}

)

Timing summary

Plane registration: GT pose source = Derived from calibrated global-projector frame

\{P_{g}\}

using projector residual statistics (Sec. IV-B ), Expanded uncertainty (95%):

\sigma_{t}^{GT}

= 0.01 mm,

\sigma_{R}^{GT}=0.0833

mrad ICP correction: GT trajectory source = Discrete pose locations established by physical markers; marker centers estimated in the calibrated global projector frame

\{P_{g}\}

; pose evaluated at marked placements, alignment provided using calipers and visual edge. Translation uncertainty dominated by caliper resolution (0.05 mm) and alignment repeatability.

Acquisition schedule (per pose/frame): local = 18-step + Graycode (5 images), global = 6-step per direction + Graycode (5 images) Achieved acquisition rate: 2.5–3 recon/s (limited by camera and sequence) Reconstruction+preprocess throughput (offline):

\sim

60 recon/s Estimator-only throughput: median

\sim

62 Hz, p95

\sim

21 Hz across 400 samples Success rate under stopping criteria: 83% (individual pose), 97% (result)

TABLE VI : Ground truth (GT) traceability and timing summary for Sec. V-A . Estimator-only timing excludes acquisition and reconstruction. Success rate is defined as batch hypotheses convergence rate (individual pose) and frame success rate (result).

Metric	Unit	$n$	Median $\Delta$	95% CI	$p$
$E_{T}$	mm	20	9.22	7.27, 15.80	$4.8\times 10^{-5}$
$E_{R}$	mrad	20	29.28	20.95, 42.36	$4.8\times 10^{-5}$
$\sigma_{T}$	mm	7	6.94	0.80, 33.52	0.156
$\sigma_{R}$	mrad	7	9.40	1.25, 29.97	0.156

TABLE VII : Paired Wilcoxon signed-rank tests for ICP vs ICP+Model.

\Delta

denotes paired improvement (ICP

-

ICP+Model); positive values favor ICP+Model. 95% CIs are bootstrap percentile over paired units.

Fig. 5 : Featureless plane registration. (a) Estimated trajectory vs GT in the global reference frame. (b) Per-pose pose error relative to GT: translation

e_{t}

(mm, left axis) and rotation

e_{R}

(mrad, right axis). (Sec. V-B )

Fig. 6 : Error accumulation reduction under downsampling. Median trajectories for ICP and ICP+Model. GT markers are shown for reference. ICP+Model closely overlaps GT; separation is quantified in the right panel. (b) Per-pose translation error

e_{t}

(mm) relative to GT (median with IQR over voxel sizes). (c) Per-pose rotation error

e_{R}

(mrad) relative to GT (median with IQR over voxel sizes). The y-axis is logarithmic to accommodate the large dynamic range between ICP and ICP+Model. (Sec. V-C ).

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