Sparse multi-path corrections in fringe projection profilometry

Three-dimensional scanning by means of structured light illumination is an active imaging technique involving projecting and capturing a series of striped patterns and then using the observed warping of stripes to reconstruct the target object's surface through triangulating each pixel in the camera to a unique projector coordinate corresponding to a particular feature in the projected patterns. The undesirable phenomenon of multi-path occurs when a camera pixel simultaneously sees features from multiple projector coordinates. Bimodal multi-path is a particularly common situation found along step edges, where the camera pixel sees both a foreground and background surface. Generalized from bimodal multi-path, this paper examines the phenomenon of sparse or N-modal multi-path as a more general case, where the camera pixel sees no fewer than two reflective surfaces, resulting in decoding errors. Using fringe projection profilometry, our proposed solution is to treat each camera pixel as an underdetermined linear system of equations and to find the sparsest (least number of paths) solution by taking an application-specific Bayesian learning approach. We validate this algorithm with both simulations and a number of challenging real-world scenarios, demonstrating that it outperforms state-of-the-art techniques.