The demand for 360-degree 3D reconstruction has significantly increased in recent years across various domains such as the metaverse and 3D telecommunication. Accordingly, the importance of precise and wide-area 3D sensing technology has become emphasized. While the digital fringe projection method has been widely used due to its high accuracy and implementation flexibility, it suffers from fundamental limitations such as unidirectional projection and a restricted available light spectrum. To address these issues, this paper proposes a novel 3D reconstruction method based on a cylindrical mechanical projector. The proposed method consists of a rotational stage and a cylindrical pattern generator with ON/OFF slots at two distinct intervals, enabling omnidirectional projection of multi-frequency phase-shifted fringe patterns. By applying a multi-wavelength unwrapping algorithm and a quasi-calibration technique, the system achieves high-accuracy 3D reconstruction using only a single camera. Experimental results, supported by repeatability and reproducibility analyses together with a measurement uncertainty evaluation, confirm reliable measurement performance and practical feasibility for omnidirectional 3D reconstruction. The expanded uncertainty of the reconstructed depth was evaluated as 0.215 mm.
Figures & tables
Fig. 1: Schematic of the proposed cylindrical mechanical projector. The red dashed box highlights the ON/OFF slot structure on the cylindrical surface.
Feature
Prior projectors
Proposed projector
Pattern generator geometry
Planar wheel
Cylindrical
Projection coverage
Unidirectional
Omnidirectional
Slit configuration
Single-period
Dual-period
Absolute phase retrieval
Limited
Enabled
Measurement capability
Relative phase
Absolute phase
TABLE I: Comparison between prior mechanical projectors and the proposed projector
Fig. 2: Schematic diagram of the pattern generator. (a) Projection geometry illustrating the relationship between the angular interval θ , the perpendicular distance d , and the resulting fringe wavelength λ on the projection surface. (b) Dual-interval ON/OFF slots design on the cylindrical pattern generator, where θl and θh denote the angular intervals corresponding to the low-frequency slot region and the high-frequency slot region, respectively.
Fig. 3: Illustration of multiwavelength phase unwrapping process. A simulation case for λh=200 pixels and λl=250 pixels is shown. (a) Equivalent phase ϕeq obtained by combining ϕh and ϕl , resulting in a continuous phase. (b) Absolute phase Φ recovered by adding an integer multiple of 2π determined by the fringe order.
Fig. 4: Framework of the proposed 3D reconstruction method. Here, the subscripts L and R denote the left and right cameras, respectively, while h and l indicate the high frequency and low frequency.
Fig. 5: Experimental hardware system set up with mechanical projector.
Fig. 6: Side view of the setup illustrating the fringe pattern projection.
Fig. 7: Projection result of the proposed method (a) Fringe image from the proposed method, (b) Texture image obtained by integrating 25 phase-shifted fringe images, (c) Wrapped phase map calculated by the least square algorithm, (d) Absolute phase map retrieved using the multi-wavelength unwrapping algorithm.
Fig. 8: Calibration poses distribution and residual evaluation. (a) Spatial distribution of the calibration poses across the measurement volume (540 mm-620 mm), (b) Pose-wise plane residual RMSE for the 14 calibration poses.
Fig. 9: Experimental results of the plane (a) 3D results from the proposed method, (b) Error maps from the proposed method , (c) Error maps from the SV-based method, (d) Comparison of error histograms between the proposed method and the SV-based method. Each column presents the same type of result for consistent visual comparison across specimens.
Pose
RMSE (mm)
Proposed
SV-based
1
0.049
0.047
2
0.061
0.051
3
0.048
0.052
4
0.061
0.054
5
0.039
0.055
TABLE II: Reproducibility results for planar surface reconstruction.
Repetition
RMSE (mm)
Pose 1
Pose 2
Proposed
SV-based
Proposed
SV-based
1
0.073
0.044
0.050
0.044
2
0.082
0.043
0.058
0.043
3
0.085
0.044
0.056
0.044
4
0.078
0.043
0.063
0.042
TABLE III: Repeatability results for planar surface reconstruction.
Fig. 10: Experimental results of the sphere with 50 mm radius (a) 3D results from the proposed method, (b) Error maps from the proposed method , (c) Error maps from the SV-based method, (d) Comparison of error histograms between the proposed method and the SV-based method. Each column presents the same type of result for consistent visual comparison across specimens.
Pose
Radius (mm)
RMSE (mm)
Mean (mm)
STD (mm)
Proposed
SV-based
Proposed
SV-based
Proposed
SV-based
Proposed
SV-based
1
49.994
49.880
0.303
0.181
-0.003
-0.146
0.303
0.107
2
49.914
49.802
0.321
0.256
-0.102
-0.236
0.304
0.098
3
50.025
49.862
0.307
0.205
0.036
-0.175
0.305
0.108
4
49.950
49.812
0.407
0.252
-0.056
-0.227
0.403
0.110
5
50.119
49.860
0.398
0.212
0.152
-0.175
0.368
0.121
TABLE IV: Reproducibility results for spherical surface reconstruction.
Repetition
Radius (mm)
RMSE (mm)
Mean (mm)
Pose 1
Pose 2
Pose 1
Pose 2
Pose 1
Pose 2
Proposed
SV-based
Proposed
SV-based
Proposed
SV-based
Proposed
SV-based
Proposed
SV-based
Proposed
SV-based
1
50.161
49.784
49.955
49.736
0.438
0.281
0.375
0.334
0.202
-0.258
-0.049
-0.315
2
50.185
49.784
50.013
49.767
0.454
0.280
0.394
0.300
0.231
-0.258
0.021
-0.277
3
50.126
49.747
49.986
49.772
0.416
0.320
0.393
0.295
0.159
-0.302
-0.011
-0.273
4
50.199
49.771
49.969
49.767
0.463
0.295
0.378
0.299
0.248
-0.274
-0.033
-0.278
TABLE V: Repeatability results for spherical surface reconstruction under identical measurement conditions.
Fig. 11: Experimental results for multiple objects with arbitrary surface (a) Texture images of the statues, (b) Wrapped phase maps from the proposed method, (c) Unwrapped phase maps, (d) 3D reconstruction results of multiple objects with arbitrary surface. Each row corresponds to a different object, and each column presents the same type of result across all objects, enabling consistent visual comparison.
Component
Symbol
Type
Standard uncertainty (mm)
Measurement repeatability
urep
A
0.008
Measurement reproducibility
urepr
A
0.015
Reference sphere tolerance
uref
B
0.029
Calibration residual
ucal
A
0.085
Rotation stage resolution
ustage
B
0.057
Combined standard uncertainty
uc(Z)
0.108
TABLE VI: Summary of the uncertainty budget.
Region along u -axis
Image area (%)
Mean RMSE (mm)
Central region
30
0.060
Outer region
30
0.071
TABLE VII: Regional RMSE comparison along the u -axis in the planar reproducibility experiment.
This paper presents a contact-based 3-D surface measurement method based on a Digital Fringe Projection (DFP) system, belonging to the vision-based tactile sensing family pioneered by the commercially successful GelSight sensor. Such sensors have proven effective for robotic fingertip manipulation and contact sensing. However, because GelSight employs photometric stereo with RGB LEDs, it does not measure absolute depth directly but instead infers it by integrating estimated surface gradients, which can accumulate reconstruction errors; in addition, it becomes increasingly difficult to calibrate as the sensing area grows, and its depth accuracy is challenged on highly reflective or transparent objects. To overcome these drawbacks, we propose a fringe-projection-based contact measurement technique that performs triangulation-based 3-D reconstruction on a coated silicone contact surface, providing dense per-pixel surface geometry and full-field 3-D shape measurement over the contact region. By integrating high-accuracy digital fringe projection into the sensor, our approach simplifies calibration over larger areas and enhances depth precision for complex surfaces. Experimental results, including a direct comparison with a GelSight Mini sensor, a sphere-fitting accuracy evaluation, and an uncertainty analysis, confirm that the proposed method significantly improves the accuracy and stability of structured-light-based 3-D measurements, allowing reliable reconstruction of objects with diverse optical properties.
Ingu Yeo, Hyung-Gun Chi, Jae-Sang Hyun
Department of Mechanical Engineering and the Yonsei Institute for Embodied Intelligence, Yonsei University, Seoul 03722, South Korea
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.
Sehoon Tak, Keunhee Cho, Sangpil Kim +1
Department of Mechanical Engineering, Yonsei University, Seoul 03722, South Korea. · Department of Artificial Intelligence, Korea University, Seoul
Single-shot fringe projection profilometry (FPP) has been actively studied for real-time measurement, dynamic object reconstruction, and motion-sensitive environments. Composite fringe patterns are advantageous in single-shot FPP because multiple frequency components can be encoded in a single pattern, enabling phase ambiguity resolution. Existing approaches mainly rely on Fourier transform-based methods or supervised deep learning methods. However, Fourier transform-based methods often suffer from limited accuracy and degraded performance in complex regions, while supervised methods require dense phase or depth labels, which are costly to obtain. In this work, we propose a self-supervised phase refinement framework for single-shot composite fringe patterns without requiring phase or depth labels. The proposed method exploits the scale and direction relationships between low- and high-frequency phase gradients, improving the reliability of phase separation. We also introduce a soft edge consistency loss to preserve object boundaries and fine geometric structures. Experimental results show that the proposed method achieves MAE_z and RMSE_z of 0.367 mm and 1.804 mm, respectively, outperforming the best-performing transform-based baseline, which obtains 0.402 mm and 2.785 mm. The proposed method also improves the valid-pixel ratio from 84.75 % to 95.07 %. These results demonstrate the effectiveness of self-supervised dual-frequency phase refinement for reliable single-shot 3D reconstruction without ground-truth label supervision.