Performance analysis of 3-D shape measurement algorithm with a short baseline projector-camera system

A number of works for 3-D shape measurement based on structured light have been well-studied in the last decades. A common way to model the system is to use the binocular stereovision-like model. In this model, the projector is treated as a camera, thus making a projector-camera-based system unified with a well-established traditional binocular stereovision system. After calibrating the projector and camera, a 3-D shape information is obtained by conventional triangulation. However, in such a stereovision-like system, the short baseline problem exists and limits the measurement accuracy. Hence, in this work, we present a new projecting-imaging model based on fringe projection profilometry (FPP). In this model, we first derive a rigorous mathematical relationship that exists between the height of an object's surface, the phase difference distribution map, and the parameters of the setup. Based on this model, we then study the problem of how the uncertainty of relevant parameters, particularly the baseline's length, affects the 3-D shape measurement accuracy using our proposed model. We provide an extensive uncertainty analysis on the proposed model through partial derivative analysis, relative error analysis, and sensitivity analysis. Moreover, the Monte Carlo simulation experiment is also conducted which shows that the measurement performance of the projector-camera system has a short baseline.