Parameter Characterization of Complex Wavelets and its use in 3D Reconstruction

Fringe projection is an optical method used to perform three-dimensional reconstruction of objects by applying structured light and phase detection algorithms. Some of these algorithms make use of the wavelet transform, which is a function that splits a signal into sub-signals with different scales at different levels of resolution. However, despite the above characteristics, the use and implementation of the wavelet transform requires good parameterization of the many variables involved for each wavelet function (scale and translation coefficient variation), in addition to analyze different wavelet functions such as Morlet, Paul Mother, and Gaussian, among others. Based on these requirements, the present paper aims to develop an in-depth analysis of the most suitable parameters for the Shannon, B-Spline and Morlet Wavelets that ensure the most efficient 3D reconstruction. The experimental results are presented using a set of virtual objects and can be applied to a real object for the purpose of validation.