Optical 3D shape measurements, such as fringe projection profilometry (FPP), are popular methods for recovering the surfaces of an object. However, traditional FPP cannot be applied to measure regions that contain strong interreflections, resulting in failure in 3D shape measurement. In this study, a method based on single-pixel imaging (SI) is proposed to measure 3D shapes in the presence of interreflections. SI is utilized to separate direct illumination from indirect illumination. Then, the corresponding points between the pixels of a camera and a projector can be obtained through the direct illumination. The 3D shapes of regions with strong interreflections can be reconstructed with the obtained corresponding points based on triangulation. Experimental results demonstrate that the proposed method can be used to separate direct and indirect illumination and measure 3D objects with interreflections.
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