Bernoulli-guided multi-scale EKF method for motion error compensation in phase-shifting profilometry

This Letter presents a novel, to our knowledge, multi-scale EKF-based phase shift estimation for motion-induced compensation. A phase state space model is constructed using fringe information, and an EKF phase shift estimator is established based on the Bernoulli distribution. A multi-scale sliding window is designed to traverse the full-field fringe pattern, and the Bernoulli distribution-based guidance yields enhanced estimation accuracy at the edge of the measured object. The actual phase shifts are evaluated to effectively reduce the motion-induced phase error. The experimental results of the proposed method demonstrate the reliability in the rotation and translation motion and achieve accurate 3D shape reconstruction in dynamic scenes.