Degree Name

Doctor of Philosophy


School of Electrical, Computer and Telecommunications Engineering


Fringe projection profilometry (FPP) is an effective optical scanning technique for high-speed and high-accuracy three-dimensional (3D) shape measurement. With FPP, the shape information is carried in the phase map, which can be retrieved using fringe analysis and phase unwrapping. In many applications, noise and disturbances are inevitable during the generation, projection, and acquisition of the fringe patterns, leading to errors in the ultimate 3D reconstruction. This thesis presents the research work on the development of new methods for reducing and eliminating the influence of these errors, mainly by means of robust principal component analysis (RPCA).

RPCA is a powerful technique for data analysis, image processing and signal processing. Fast, reliable phase unwrapping is a very important part of FPP. Therefore, the first work presented in the thesis is a brief review on RPCA, followed by a new phase unwrapping scheme based on speckle-embedded patterns and RPCA. The proposed scheme utilizes composite patterns consisting of standard sinusoidal fringe patterns and randomly generated speckles. The low-rankness of the sinusoidal fringe patterns and the sparse nature of the speckle patterns are examined and utilized. RPCA is applied to effectively separate these patterns from the captured images, which are then used for phase retrieval and phase unwrapping, respectively. The proposed scheme enables reliable phase unwrapping to be realized using only a single projection. Since the quality of fringe patterns plays a critical role in FPP, the second work applies RPCA to fringe pattern denoising. By accounting for the impulsive nature of strong noises, a denoising scheme based on RPCA is developed to improve the quality of the captured fringe images, which is applicable to general FPP systems.

Temporal phase unwrapping is important for high-resolution, high-accuracy FPP, especially when discontinuous objects are measured. However, fringe order errors may still arise due to such factors as noise and variation in the reflectivity on the object surface. There are several ways to reduce or correct the fringe order errors, but existing solutions are often based on one-dimensional (1D) processing of fringe order sequences. The third work in this thesis develops a scheme featuring two-dimensional (2D) of the fringe order maps such that the 2D correlation of the fringe orders can be better exploited. For typical applications with temporal phase unwrapping, the fringe order errors are demonstrated to be impulsive and can thus be modeled using a sparse matrix, while the true fringe order maps are shown to be low-rank. Exploiting a low-rank-plus-sparse model of the erroneous fringe orders, a RPCA-based approach is designed to effectively correct the fringe order errors. The tuning of the hyperparameters in RPCA is also studied for optimizing the performance.

The above fringe order correction method can improve the quality of the unwrapped phase by removing unwrapping errors, but other errors can still severely degrade the ultimate reconstruction results. In order to further enhance performance, a new absolute phase error correction method based on RPCA is proposed. The method models the recovered absolute phase as the summation of the low-rank phase map, sparsely distributed phase unwrapping errors, and random, unstructured errors. By exploiting this new model, a novel phase error correction method is designed to retrieve the true absolute phase map, which can effectively improve the quality of the absolute phase at a low complexity.

Simulation and experimental studies are carried out to verify the proposed approaches. It is found that they can effectively correct the errors associated with FPP processing and improve the performance of 3D shape measurement. The limitation of the current study is also analyzed and potential future work is identified.

FoR codes (2008)




Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.