Phase retrieval with high accuracy remains one of the most challenging problems in Fourier fringe projection profilometry (FPP). The variational image decomposition TV-Hilbert-${{\rm{L}}^2}$ model has been proved to be a powerful tool for phase retrieval. In this paper, we first propose a modified fuzzy c-means (FCM) clustering algorithm to remove background from fringe projection patterns. In order to further improve the accuracy, we combine the modified FCM and the variational image decomposition TV-Hilbert-${{\rm{L}}^2}$ model and propose a new method to get the fringe part from the single frame fringe projection pattern. We evaluate the performance of this method via application to two simulated and one experimental fringe projection patterns and comparison with the Fourier transform, morphological operation-based bi-dimensional empirical mode decomposition, and variational image decomposition TV-Hilbert-${{\rm{L}}^2}$ model. The experiment results show that our method improves the accuracy of phase retrieval for TV-Hilbert-${{\rm{L}}^2}$ model and can achieve similar accuracy to the phase-shifting method.

中文翻译：

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基于改进FCM和变分图像分解的Fourier FPP高精度相位检索方法

高精度相位检索仍然是傅里叶条纹投影轮廓测量法 (FPP) 中最具挑战性的问题之一。变分图像分解 TV-Hilbert- ${{\rm{L}}^2}$模型已被证明是相位检索的强大工具。在本文中，我们首先提出了一种改进的模糊 c 均值 (FCM) 聚类算法，以从条纹投影图案中去除背景。为了进一步提高准确率，我们结合了改进的 FCM 和变分图像分解 TV-Hilbert- ${{\rm{L}}^2}$模型并提出了一种从单帧条纹投影图案中获取条纹部分的新方法。我们通过应用于两个模拟和一个实验条纹投影模式并与傅立叶变换、基于形态学运算的二维经验模式分解和变分图像分解 TV-Hilbert- ${\rm{ L}}^2}$模型。实验结果表明，我们的方法提高了TV-Hilbert- ${{\rm{L}}^2}$模型的相位检索精度，并且可以达到与相移方法相似的精度。