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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Spatially Coupled Phase-to-Depth Calibration for Fringe Projection Profilometry

Sehoon Tak, Jae-Sang Hyun

Department of Mechanical Engineering, Yonsei University, Seoul 03722, South Korea.

Fringe Projection Profilometry Metric Depth Estimation 3D Reconstruction

Open paper AskPDF arXiv

In fringe projection profilometry (FPP), depth is commonly recovered by fitting a phase-to-depth relation independently at each camera pixel. Although such pixel-wise calibration achieves high local accuracy, neighboring pixels can acquire markedly different calibration functions even when they observe the same smooth surface, producing spatially inconsistent geometry and structured surface artifacts. We propose a spatially coupled phase-depth transformation in which all pixels share a single low-dimensional mapping-global phase scalars combined with affine spatial terms on the undistorted reference-camera grid-rather than independent per-pixel fits, optionally augmented by a bounded, spatially smooth correction field. We further introduce a native-grid pairing scheme that constructs phase-depth calibration pairs directly on the reference-camera grid: when depth supervision comes from a rectified active-stereo pipeline, planes are fitted in stereo 3D and sampled back onto the camera grid along native rays, so the phase maps are never rectified. On a dental target with high-resolution scanner ground truth, the proposed model attains point-to-surface RMSE comparable to an active-stereo reference (about 12μm aggregate) while substantially improving spatial coherence over pixel-wise polynomial and rational calibration, and reduces the runtime mapping to a few element-wise operations per pixel with negligible parameter storage.

Abstract

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