Digital fringe projection profilometry (DFPP) is a widely used technique for full-field, non-contact 3D surface measurement, offering precision from the sub-micrometer-to-millimeter scale depending on system geometry and fringe design. This review provides a consolidated synthesis of advances reported between 2022 and 2025, covering projection and imaging architectures, phase formation and unwrapping strategies, calibration approaches, high-speed implementations, and learning-based reconstruction methods. A central contribution of this review is the integration of these developments within a metrological perspective, explicitly relating phase–height transformation, fringe parameters, system geometry, and calibration to dominant uncertainty sources and error propagation. Recent progress highlights trade-offs between sensitivity, robustness, computational complexity, and applicability to non-ideal surfaces, while learning-based and hybrid optical–computational approaches demonstrate substantial improvements in reconstruction reliability under challenging conditions. Remaining challenges include measurements on reflective or transparent surfaces, dynamic scenes, environmental instability, and real-time operation. The review outlines emerging research directions such as physics-informed learning, digital twins, programmable optics, and autonomous calibration, providing guidance for the development of next-generation DFPP systems for precision metrology.

Circle detection has numerous applications towards industry, robotics, and science in general. Therefore, a significant effort has been made in order to develop an accurate and fast method for circle extraction. Commonly, different techniques such as the ones based on the Hough transform have been widely used because of their robustness. However, these techniques usually demand a considerable computational load and large storage, and therefore meta‐heuristic approaches such as evolutionary and swarm‐based algorithms have been studied as an alternative. This study introduces a circle‐detection method based on a recently proposed meta‐heuristic technique: the teaching learning based optimisation algorithm, which is a population‐based technique that is inspired by the teaching and learning processes. The algorithm uses the encoding of three points as candidate circles over the edge image. To evaluate if such candidate circles are actually present within the edge map, an objective function is used to guide the search. To validate the efficacy of the proposed approach, several tests using noisy and complex images as input were carried out, and the results were compared with different approaches for circle detection.

In computer vision, estimating geometric relations between two different views of the same scene has great importance due to its applications in 3D reconstruction, object recognition and digitization, image registration, pose retrieval, visual tracking and more. The Random Sample Consensus (RANSAC) is the most popular heuristic technique to tackle this problem. However, RANSAC-like algorithms present a drawback regarding either the tuning of the number of samples and the threshold error or the computational burden. To relief this problem, we propose an estimator based on a metaheuristic, the Teaching–Learning-Based Optimization algorithm (TLBO) that is motivated by the teaching–learning process. We use the TLBO algorithm in the problem of computing multiple view relations given by the homography and the fundamental matrix. To improve the method, candidate models are better evaluated with a more precise objective function. To validate the efficacy of the proposed approach, several tests, and comparisons with two RANSAC-based algorithms and other metaheuristic-based estimators were executed.

Fringe projection profilometry (FPP) is established as a dual-role metrological instrument: a calibration source for physics-based analytical models and a validation benchmark for machine learning surrogates of thermoelastic out-of-plane deformation. A three-stage framework is presented with three principal contributions: (i) physics-consistent synthetic data generation via the Kirchhoff–Love plate solution, with boundary condition factor κ calibrated from FPP phase-unwrapping measurements; (ii) comparative training of five baseline surrogates, including four classical regressors and a physics-free multilayer perceptron (MLP), and a physics-informed neural network (PINN) with residual architecture, physics branch, gating mechanism, and curriculum learning, embedding flexural rigidity, thermal bending moment, and the scaling relation α ⋅ Δ T ⋅ L 2 / t as physics-informed inputs; all neural network models were evaluated across five random seeds to report mean ± standard deviation; and (iii) external metrological validation against FPP displacement maps at three thermal states ( Δ T = 65 , 123 , and 172 K ) on an aluminum 1060 plate, with measurement uncertainty explicitly characterized. The first state serves as the κ calibration anchor; the remaining two constitute independent validation points. The PINN achieves RMSE = 2.90 ± 0.26 μ m and MAPE = 1.82 ± 0.16 % (mean ± std over five seeds), outperforming the best classical baseline (Gradient Boosting, RMSE = 5.28 μ m) by 45 % in root mean square error (RMSE) and the physics-free MLP (RMSE = 10.27 ± 3.08 μ m) by 72 % , with the performance gap attributable to physics embedding rather than network capacity. Against FPP measurements, PINN prediction errors are 0.9%, 0.9%, and 18.2% at the three states—closely matching the calibrated analytical model alone (0.87%, 0.85%, 18.16%), and consistently below the errors of an industrial-grade SolidWorks finite element method model (6.0%, 12.9%, 23.4%), used here as a reference without a documented mesh convergence study (section 4.6.2), rather than a fully verified benchmark, at the two lower states. An out-of-distribution generalization experiment confirms that the PINN degrades 50.6 % less than the best tuned classical model in physically demanding extrapolation zones. These results demonstrate that FPP can anchor both calibration and independent validation of physics-informed surrogates on a single specimen and thermal loading configuration, establishing a reproducible methodology for dimensional stability assessment in precision engineering.