Fringe projection profilometry (FPP) has become increasingly important in dynamic 3-D shape measurement. In FPP, it is necessary to retrieve the phase of the measured object before shape profiling. However, traditional phase retrieval techniques often require a large number of fringes, which may generate motion-induced error for dynamic objects. In this paper, a novel phase retrieval technique based on deep learning is proposed, which uses an end-to-end deep convolution neural network to transform a single or two fringes into the phase retrieval required fringes. When the object’s surface is located in a restricted depth, the presented network only requires a single fringe as the input, which otherwise requires two fringes in an unrestricted depth. The proposed phase retrieval technique is first theoretically analyzed, and then numerically and experimentally verified on its applicability for dynamic 3-D measurement.

Fringe projection profilometry (i.e., FPP) has been one of the most popular 3-D measurement techniques. The phase error due to system random noise becomes non-ignorable when fringes captured by a camera have a low fringe modulation, which are inevitable for objects’ surface with un-uniform reflectivity. The phase calculated from these low-modulation fringes may have a non-ignorable phase error and generate 3-D measurement error. Traditional methods reduce the phase error with losing details of 3-D shapes or sacrificing the measurement speed. In this paper, a deep learning-based fringe modulation-enhancing method (i.e., FMEM) is proposed, that transforms two low-modulation fringes with different phase shifts into a set of three phase-shifted high-modulation fringes. FMEM enables to calculate the desired phase from the transformed set of high-modulation fringes, and result in accurate 3-D FPP without sacrificing the speed. Experimental analysis verifies its effectiveness and accurateness.

Deep learning-based fringe projection profilometry (FPP) shows potential for challenging three-dimensional (3D) reconstruction of objects with dynamic motion, complex surface, and extreme environment. However, the previous deep learning-based methods are all supervised ones, which are difficult to be applied for scenes that are different from the training, thus requiring a large number of training datasets. In this paper, we propose a new geometric constraint-based phase unwrapping (GCPU) method that enables an untrained deep learning-based FPP for the first time. An untrained convolutional neural network is designed to achieve correct phase unwrapping through a network parameter space optimization. The loss function of the optimization is constructed by following the 3D, structural, and phase consistency. The designed untrained network directly outputs the desired fringe order with the inputted phase and fringe background. The experiments verify that the proposed GCPU method provides higher robustness compared with the traditional GCPU methods, thus resulting in accurate 3D reconstruction for objects with a complex surface. Unlike the commonly used temporal phase unwrapping, the proposed GCPU method does not require additional fringe patterns, which can also be used for the dynamic 3D measurement.

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