Stochastic Phase Estimation and Unwrapping

Phase-shift is one of the most effective techniques in 3D structured-light scanning for its accuracy and noise resilience. However, the periodic nature of the signal causes a spatial ambiguity when the fringe periods are shorter than the projector resolution. To solve this, many techniques exploit multiple combined signals to unwrap the phases and thus recovering a unique consistent code. In this paper, we study the phase estimation and unwrapping problem in a stochastic context. Assuming the acquired fringe signal to be affected by additive white Gaussian noise, we start by modelling each estimated phase as a zero-mean Wrapped Normal distribution with variance σ2. Then, our contributions are twofolds. First, we show how to recover the best projector code given multiple phase observations by means of a ML estimation over the combined fringe distributions. Second, we exploit the Cramer-Rao bounds to relate the phase variance σ2 to the variance of the observed signal, that can be easily estimated online during the fringe acquisition. An extensive set of experiments demonstrate that our approach outperforms other methods in terms of code recovery accuracy and ratio of faulty unwrappings.