Multi-Frequency Nonlinear Methods for 3D Shape Measurement of Semi-Transparent Surfaces Using Projector-Camera Systems

Measuring the 3D shape of semi-transparent surfaces with projector-camera 3D scanners is a difficult task because these surfaces weakly reflect light in a diffuse manner, and transmit a large part of the incident light. The task is even harder in the presence of participating background surfaces. The two methods proposed in this paper use sinusoidal patterns, each with a frequency chosen in the frequency range allowed by the projection optics of the projector-camera system. They differ in the way in which the camera-projector correspondence map is established, as well as in the number of patterns and the processing time required. The first method utilizes the discrete Fourier transform, performed on the intensity signal measured at a camera pixel, to inventory projector columns illuminating directly and indirectly the scene point imaged by that pixel. The second method goes beyond discrete Fourier transform and achieves the same goal by fitting a proposed analytical model to the measured intensity signal. Once the one (camera pixel) to many (projector columns) correspondence is established, a surface continuity constraint is applied to extract the one to one correspondence map linked to the semi-transparent surface. This map is used to determine the 3D point cloud of the surface by triangulation. Experimental results demonstrate the performance (accuracy, reliability) achieved by the proposed methods.