Fringe Pattern Analysis With Message Passing Based Expectation Maximization for Fringe Projection Profilometry

Fringe projection profilometry (FPP) is a popular optical 3-D imaging approach, in which the images of deformed fringe patterns are analyzed to extract object surfaces (i.e., height maps of object surfaces). As an object surface normally does not change independently, height correlations of an object surface can be used to denoise and improve the measurement performance of the FPP. This paper investigates the issue of exploiting height correlations in FPP fringe pattern analysis. The challenge lies in that height correlations are unknown and they are different from object to object. In addition, the problem of interest is normally in a large scale. In this paper, we use autoregressive (AR) models with unknown parameters to model the unknown height correlations and formulate the FPP analysis problem (with height correlations exploited) under the framework of expectation maximization (EM). With EM, the unknown AR model parameters are determined based on observations, and the estimates of the heights with their correlations exploited can also be extracted. To deal with the large-scale problem, a message passing-based implementation of the formulated EM problem is studied and the relevant message updating rules are developed. The proposed approach has a linear complexity and it allows parallel processing due to the nature of message passing. Simulation and experimental results demonstrate a significant performance improvement by the proposed approach.