General framework of a two-dimensional complex wavelet for fringe projection profilometry

Abstract

Single-shot high-accuracy reconstruction of three-dimensional (3D) objects plays an essential role in many fields. Wavelet-based fringe projection profilometry (WFPP) is a popular single-shot imaging method due to its multiple-resolution analysis and non-contact property. However, the construction of mother wavelets for high-accuracy WFPP is still challenging. In this paper, a general framework of two-dimensional (2D) compact support complex wavelet employing the dual-tree concept combined with the one-dimensional (1D) asymmetric wavelet function is proposed. The constructed wavelet has an asymmetric frequency envelope in the radial direction and concentrated energy in a single quadrant of the frequency domain. A method that the constructed wavelet applied in dual-angle rotation-based 2D WFPP is presented for higher accuracy. The theoretical analysis of the proposed method is presented, and a comparison of frequency characteristics between the constructed wavelet and other popular wavelets is conducted. Computer simulations and experiments have demonstrated that the proposed method provides a better reconstruction of 3D shapes in single-shot WFPP.