Fringe Order Correction for Fringe Projection Profilometry Based on Robust Principal Component Analysis

Yiwei Zhang,Qinghua Guo,Jun Tong,Yanguang Yu,Jiangtao Xi,Lei Lu

doi:10.1109/access.2021.3056063

Abstract

Temporal phase unwrapping is among the most robust and efficient phase unwrapping methods in fringe projection profilometry. They can recover the fringe orders even in the presence of surface discontinuities. However, fringe order errors may occur due to phase noise and poor measurement conditions. Such errors often exhibit an impulsive nature and introduce errors to the absolute phase map. Most existing fringe order error correction methods detect and correct the errors in a pixel-by-pixel manner, which may under-utilize the correlation of the fringe orders on different pixels. In this paper, we propose a new method to cope with the fringe order errors associated with temporal phase unwrapping. By exploiting the low-rankness of the fringe order map and sparse nature of the impulsive fringe order errors, we develop a robust principal component analysis (RPCA)-based approach to remove the impulsive fringe order errors. Experiments demonstrate that the proposed method is valid in eliminating the fringe order errors.

Highlights

Phase unwrapping is an essential task for implementing 3D shape measurement systems using fringe projection profilometry (FPP) [1]–[7]
This paper introduces a new method for correcting fringe order errors, by making use of the distinguished properties between the fringe order and errors associated with the phase maps
The fringe orders are recovered using the temporal phase unwrapping method in [19]–[21] and demonstrated in Fig. 2, showing that fringe order errors may occur in the following forms: 1. Fringe order error occurs on a single pixel in an impulsive manner

Summary

INTRODUCTION

Phase unwrapping is an essential task for implementing 3D shape measurement systems using fringe projection profilometry (FPP) [1]–[7]. For multi-frequency fringe projection phase unwrapping, Zhang et al [18] propose a method that calculates and ranks the quality of the pixels in the captured fringe patterns. Ding et al [19] propose a method that firstly divides the fringe order sequence into intervals with the aid of the wrapped phase and apply voting to correct errors. The fringe orders are recovered using the temporal phase unwrapping method in [19]–[21] and demonstrated, showing that fringe order errors may occur in the following forms: 1. RPCA-BASED FRINGE ORDER ERROR CORRECTION The fringe order map {k (x, y)} recovered by using temporal phase unwrapping [15]–[17] can be modeled as k (x, y) = k (x, y) + e(x, y),. Where Un+1, V n+1 and {σin+1} are, respectively, the left singular vector matrix, right singular vector matrix and singular values of

Update the multiplier

CHOICE OF THE HYPERPARAMETERS

Correct the phase value as follows:

SIMULATION AND EXPERIMENT RESULTS

CONCLUSION