Volume-Based Multisurface 3-D Measurement of Transparent Objects Using Fringe Projection Profilometry

The 3-D measurement of transparent objects is a challenging task for fringe projection profilometry (FPP), since each camera pixel captures an accumulation of information from multiple projector pixels. While existing frequency shift methods can decouple projector pixels, they cannot identify correct surface points from the decoupled results, due to the complexity of refraction and reflection. To address this challenge, a novel volume-based method is proposed for transparent object measurement. Specifically, a 3-D volume is built from the captured images, where each voxel of the volume corresponds to one 3-D point. The volume enables the integration of local and global geometric information from different directions in 3-D space, eliminating the need for manually designed energy function optimization. Our method uses an adaptive peak detector to initially identify surface point candidates. These points are then refined by integrating geometric priors into the volume through a series of morphological processes. This volume-based framework also enables the measurement of multisurface objects, including those with thin walls and uniform thickness—features that are difficult to handle with traditional techniques. Experimental results demonstrate that our method achieves more accurate and complete measurements of transparent objects compared with existing FPP approaches.