# Wavelet-Assisted Adaptive EKF Phase Shift Estimation Approach for Motion-Induced Error Compensation

## TL;DR

This paper introduces a new method to reduce errors in 3D imaging caused by motion during phase-shifting profilometry.

## Contribution

A wavelet-assisted adaptive EKF approach is proposed for accurate phase shift estimation in dynamic scenes.

## Key findings

- The method effectively reduces 3D reconstruction errors caused by motion.
- It accurately estimates initial carrier frequency and phase shift maps.
- The approach is extendable to N-step PSP systems.

## Abstract

Phase-shifting profilometry (PSP) suffers from motion-induced phase-step variations in dynamic scenes. The breakdown of the fixed phase shift assumption results in issues such as ripples, distortions and accuracy decline in PSP systems. To reduce motion-induced phase errors, we propose a wavelet-assisted adaptive extended Kalman filter (WAEKF) to estimate varied pixel-wise phase shift. A wavelet-based strategy is presented to extract an initial spatial carrier frequency at each row from fringe patterns for EKF estimation. A state-space model employing the quadrature phase component and carrier frequency is established in this paper. The unknown phase shifts can be evaluated by using a forward–backward filter. Experiments show that the proposed method can acquire an accurate initial carrier frequency and phase shift map, which effectively reduces 3D reconstruction error and can be extended to N-step PSP systems.