CF3DNet: A learning-based approach for single-shot 3D reconstruction from circular fringes

3D reconstruction by fringe projection is an ill-posed problem that is of significance in many practical applications. Conventional algorithms employ multiple steps like fringe analysis, phase unwrapping, and calibration to reconstruct the 3D profile. Recent deep learning (DL) methods circumvent this multi-step approach by directly mapping the deformations in linear fringes caused by objects to the absolute phase shifts. However, this mapping is not one-to-one for the discontinuous objects due to 2 pi periodicity of linear fringes, and hence it is impossible to reconstruct using a single deformed fringe. In this work, we propose Circular Fringe-to-3D reconstruction Network (CF3DNet), a learning-based approach for 3D reconstruction from circular fringes, that can establish a one-to-one mapping between the phase deformations and the absolute phase shifts. This is viable because the radially symmetric circular fringes can distinctly record the lateral shifts caused by objects, and the learning-based approach can uniquely map them to absolute phase shifts. Thus, the proposed CF3DNet can reconstruct discontinuous object profiles, which is infeasible with linear fringe-based methods. Further, to evade the tedious process of real data collection and to bring generalization, the model is trained with synthetically generated smooth, discontinuous and Computer-Aided Design (CAD) object profiles. The results demonstrate that the proposed method led to tenfold improved performance over linear fringe-based methods in 3D reconstruction of various synthetic objects, and accurately estimate the real object profile compared to the other state-of-art methods. The extensive analysis presented in this work shows that the proposed method can work with carrier frequencies as low as 10 cycles/row to reconstruct dynamic ranges up to 100 radians under high noise, paving a way for the development of a cost-effective fringe projection system.