Enhancing phase unwrapping by noisy pixels identifying criteria and iterative adaptive filtering

Phase unwrapping is a challenging task due to the presence of noise in the wrapped phase map. This paper describes, to the best of our knowledge, a novel technique, termed as noisy pixels identifying criteria, for phase unwrapping to minimize fake phase jump errors caused by noise and phase residues to a minimum. Its characteristic lies in fully leveraging the information contained in fringe patterns that can accurately identify noise-contaminated pixels of the wrapped phase map by constructing a phase-shifting version of the wrapped phase map. Based on it, a locally selective adaptive filtering strategy is introduced where noise filtering is applied exclusively to the identified noisy pixels, thereby avoiding the blurring and detail loss commonly caused by global noise filtering. We must note that the window size of our filter can be dynamically adjusted based on the number of non-noisy pixels in the local neighborhood, and is automatically expanded when insufficient valid pixels are present. Moreover, we developed an explicit filtering termination criterion that can ensure both stability and efficiency of the filtering process when iteratively applying the proposed method to the noisy wrapped phase map. Finally, with the aid of the proposed noisy pixels identifying criteria and iterative adaptive filtering, the denoised wrapped phase is unwrapped correctly by the transport of intensity equation (TIE) based phase unwrapping algorithm. Both simulation and experimental results confirm that the proposed method achieves superior phase reconstruction accuracy and robustness, even under complex and noisy measurement conditions.