By introducing depth constraint into the traditional number-theoretical TPU, we only need to eliminate the phase ambiguity of each pixel within a small period range defined by the depth range, which means that our method just requires the two fringe frequencies to be coprime within the local period range instead of the conventional global range. In contrast, using low-frequency fringe patterns tends to make phase unwrapping more reliable, but more » at the expense of the measurement precision. However, the conventional number-theoretical TPU approach cannot provide sufficient stability to unwrap a high-frequency phase since it requires the two fringe frequencies to be coprime within the global range of the projector coordinate. As a classical algorithm for temporal phase unwrapping (TPU), the number-theoretical approach is suitable for the binary defocusing fringe projection system since it can retrieve an absolute phase without using low-frequency fringe patterns. In this study, we propose a high-speed three-dimensional (3-D) shape measurement technique for dynamic scenes using geometry-constraint-based number-theoretical phase unwrapping. Experimental results verify that our method can achieve high-speed, high-accuracy, robust 3D shape measurement with dense (64-period) fringe patterns at 5000 frames per second. These proposed techniques constitute a complete computational framework that allows to effectively recover an accurate, unambiguous, and distortion-free 3D point cloud with only 4 projected patterns. Finally, some mismatched regions are further corrected based on the proposed regional diffusion compensation technique (RDC). When the embedded speckle pattern is demodulated, the periodic ambiguities in the wrapped phase can be eliminated by combining the adaptive window image correlation with geometry constraint. We also present a simple and effective evaluation criterion for the correlation quality of the designed speckle pattern in order to improve the matching accuracy significantly. To solve this problem, we develop an optimized method for designing the composite pattern, in which the speckle pattern more » is embedded into the conventional 4-step phase-shifting fringe patterns without compromising the fringe modulation, and thus the phase measurement accuracy. However, in order to ensure the stability of phase unwrapping, the period of fringe is generally around 20, which limits the accuracy of 3D measurement. Stereo phase unwrapping, as a new-fashioned method for absolute phase retrieval based on the multi-view geometric constraints, can eliminate the phase ambiguities and obtain a continuous phase map without projecting any additional patterns. In this study, we propose a high-speed 3D shape measurement technique based on the optimized composite fringe patterns and stereo-assisted structured light system. Furthermore, experimental results demonstrate the success of more » our proposed SPU approach in recovering absolute 3D geometries of both simple and complicated objects with only three phase-shifted fringe images. Besides, two complementary techniques, including simplified left-right consistency check and feedback mechanism based on valid area, are introduced to further increase the robustness and flexibility of the ADC. By utilizing the spatio-temporal correlation of moving objects under measurement, a customized and tighter depth constraint can be defined, which helps enhance the robustness of SPU over a large measurement volume. In this paper, we proposed an adaptive depth constraint (ADC) approach for high-speed real-time 3D shape measurement, where the measurement depth volume for geometric constraints is adaptively updated according to the current reconstructed geometry.
Several auxiliary techniques have been proposed to enhance the robustness of SPU, but their flexibility still needs to be improved. However, when high-frequency fringes are used, the phase ambiguities will increase which makes SPU unreliable. Based on a pre-defined measurement volume, artificial maximum/minimum phase maps can be created solely using geometric constraints of the FPP system, permitting phase unwrapping on a pixel-by-pixel basis. Stereo phase unwrapping (SPU) has been increasingly applied to high-speed real-time fringe projection profilometry (FPP) because it can retrieve the absolute phase or matching points in a stereo FPP system without projecting or acquiring additional fringe patterns.
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