Fringe projection profilometry has become one of the most popular 3D information acquisition techniques being developed over the past three decades. However, the general and practical issues on valid point detection, including object segmentation, error correction and noisy point removal, have not been studied thoroughly. Furthermore, existing valid point detection techniques require multiple case-dependent thresholds which increase processing inconvenience. In this paper, we proposed a new valid point detection framework, which includes the k-means clustering for automatic background segmentation, unwrapping error correction based on theoretical analysis, and noisy point detection in both temporal and spatial directions with automatic threshold setting. Experimental results are given to validate the proposed framework.

A sub-voxel digital volume correlation (DVC) method combining the 3D inverse compositional GaussNewton (ICGN) algorithm with the 3D fast Fourier transform-based cross correlation (FFT-CC) algorithm is proposed to eliminate path-dependence in current iterative DVC methods caused by the initial guess transfer scheme. The proposed path-independent DVC method is implemented on NVIDIA compute unified device architecture (CUDA) for GPU devices. Powered by parallel computing technology, the proposed DVC method achieves a significant improvement in computation speed on a common desktop computer equipped with a low-end graphics card containing 1536 CUDA cores, i.e., up to 23.3 times faster than the sequential implementation and 3.7 times faster than the multithreaded implementation of the same DVC method running on a 6-core CPU. This speedup, which has no compromise with resolution, accuracy and precision, benefits from the coarsegrained parallelism that the points of interest (POIs) are processed simultaneously and also from the fine-grained parallelism that the calculation at each POI is performed with multiple threads in GPU. The experimental study demonstrates the superiority of the GPU-based parallel computing for acceleration of DVC over the multi-core CPU-based one, in particular on a PC level computer.

Some effective filtering methods for wrapped phase maps, a regularized phase-tracking method (RPT) without the regularization term, a multiple-parameter least-square method (MPLS), a windowed Fourier ridges method (WFR), an autocorrelation function method (ACF), and a sine/cosine average filter (SCAF), are analyzed in order to establish their transversal relationship. The analysis shows that principles of the RPT, MPLS, WFR, and ACF are equivalent and the SCAF also leads to the WFR by some extension, which elegantly unifies all these methods for filtering unwrapped phase maps.

A simple but effective approach for the demodulation of a single fringe pattern is proposed. The phase with an undetermined sign is directly obtained by taking the arccosine value of a preprocessed fringe pattern. The local frequencies, also with an undetermined sign, are then estimated by local matching. The sign ambiguity is then removed simply by forcing the continuity of the local frequencies. The priority of sign determination is guided by the value of total local frequency (fringe density) so that the critical points are processed last. The proposed approach is verified by successful demodulation of a simulated fringe pattern and two experimental fringe patterns.

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