## 1 Introduction  
Optical three dimensional (3D) shape measurement based on fringe projection is widely used in many fields such as industry inspection [1], 3D thermal deformation measurement of electronic devices [2], 3D point cloud reconstruction [3], 3D printing [4], face recognition [5] and so on with its advantages of noncontacting measurement, full-field acquisition, high precision, and ease of information processing. The traditional static or online 3D shape measurement methods based on fringe projection may be hard to satisfy the demand of real-time or dynamic 3D shape measurement. With the rapid development of digital light projector (DLP) devices, digital imaging acquisition devices, and personal computers [6, 7], many dynamic 3D shape measurement techniques have been proposed. The existed methods for dynamic 3D shape measurement mainly contain Fourier transform profilometry (FTP) [8, 9], single-one color fringe projection profilometry [10], and multiple fringes phase measuring profilometry (PMP) based on high-speed projection system [11, 12]. The FTP proposed by [PERSON] et al. [13] can achieve dynamic 3D measurement [14] because it can reconstruct 3D shape from one deformed pattern, but its measuring accuracy is probably limited due to the filtering procedure. In order to improve the measuring accuracy, the single-one color fringe projection profilometry [15] becomes an effective method. When a color sinusoidal fringe whose red (R), green (G), and blue (B) components comprise three sinusoidal fringes with an equivalent shifting-phase of \(2\pi/3\) is projected onto the measured object [16], the corresponding color deformed pattern modulated by the profile of the measured object can be captured by a color charge coupled device (CCD) camera. The corresponding phase-shifting deformed patterns can be retrieved simply from the R, G, and B components of the captured color deformed pattern. So the 3D shape of the measured object can be reconstructed successfully with three-step PMP. However, the color cross-talk and the grayscale imbalance problems caused by the color overlapping among the R, G, and B channels one another may lead to extracting the phase-shifting deformed patterns incompletely [17]. Thus, some corresponding color decoupling compensation and grayscale imbalance correction methods are proposed [18; 19; 20; 21]. [PERSON] et al. proposed an improved RGB tricolor based fast phase measuring profilometry in which the chroma transfer function (CTF) was introduced to correct the color cross-talk and grayscale imbalance problems among R, G, and B channels [22]. This method can reduce the effect of these problems and improve the measuring accuracy, but it may be hard to avoid these problems completely and needs additional calibration experiments. [PERSON] et al. proposed software-based and hardware-based methods to compensate for the color coupling and grayscale imbalance errors by designing a three-CCD camera system and three color filters detect system [20]. It worked well, the measuring system may be complicated due to the additional multiple CCD cameras and color filters. [PERSON] et al. proposed a color fringe-projected technique based on bidimensional empirical mode decomposition to decouple to color cross-talk among color channels [19]. It did reduce the errors caused by the color cross-talk, but its computational process may be complicated and time consuming. Although the above methods can reduce the effect of color cross-talk and grayscale imbalance problems existed in color CCD camera, these methods may be hard to solve the above problems completely and more time consuming. In order to avoid the color cross-talk problem completely, the multiple fringes PMP based on high-speed projection system [23] is proposed to realize dynamic 3D shape measurement. This method mainly utilized the high-speed digital light projector (HDLP) to project the \(N\) frames of phase-shifting sinusoidal fringes onto the measured object at \(N\) times of dynamic frame rate.