Robust phase unwrapping by probabilistic consensus

Structured light scanning works by projecting over the scene a supplement of controlled information: the captured signal is processed to provide a unique label (namely a code) for each observed point, and then proceed to geometrical triangulation. In phase shift profilometry sinusoidal patterns are projected and each point is labelled according to the observed phase. Then, due to the periodic nature of the signal, a disambiguation method (known as phase unwrapping) is needed. Several unwrapping techniques have been proposed in the literature, since noisy signals lead to inaccuracies in phase estimation. This paper presents a novel phase unwrapping approach based on a probabilistic framework. The method involves the projection of multiple sinusoidal patterns with distinct period lengths, encoding different phase values at each point location. Phase values are then modelled as samples from a Wrapped Gaussian distribution with an unknown mean, determined by the projector code that generated the values. This formulation allows us to robustly perform phase unwrapping via Maximum Likelihood Estimation, recovering code values from the observed phases. Furthermore, the same likelihood function can be exploited to identify and correct faulty unwrappings by gauging mutual support in a spatial neighbourhood. An extensive experimental assessment validates the Gaussian distribution hypothesis and verifies the improvements in coding accuracy when compared to other classical unwrapping techniques.