General Self-Correction Algorithm for Nonlinear Errors Based on the Real-Time Generative Look-Up-Table

Nonlinear errors, caused by the gamma effect, are very common in a certain fringe projection system. Therefore, we propose a general self-correction algorithm to address this problem even in severe cases. First, the Nelder-Mead algorithm is employed to detect the system gamma value by optimizing a probability-density-function (pdf) related objective function. Second, a look-up table (LUT) will be generated in situ based on the detected result to perform compensation. This real-time generative LUT (RG-LUT) allows for a self-correction process because there are no precalibration or inverse function procedures. The Nelder-Mead algorithm not only reduces computational time initially but also expedites the search process again when the gamma value varies over time. Moreover, the processing can be further accelerated by a pregenerative strategy for the LUT sequence. Experimental results demonstrate that the proposed self-correction algorithm can improve the accuracy by a factor of 9 under severe nonlinear errors.