# 3D Face Profilometry Based on Galvanometer Scanner with Infrared Fringe Projection in High Speed
## 1 Introduction  
Three-dimensional (3D) face measurement has been widely employed in 3D-aided face recognition to overcome the effects of pose, expression, and illumination variations in facial images with great potential in many applications [1]. Dense and accurate 3D point cloud data of a human face can be obtained by fringe projection profilometry (FPP) approaches [2], which have proven to be one of the most promising techniques [3; 4; 5; 6; 7] in 3D measurement, and the scanning result is more realistic and accurate than the multi-view images method [8]. Various methods based on projecting different kinds of structured light patterns have been developed and used for face 3D measurement. PS. [PERSON] et al. [9] measured a human face by removing the colour filter of a digital light processing (DLP) projector. In this case, the three sinusoidal fringe patterns with a 120-deg phase shift between neighbouring channels can be compressed tothe red, green and blue channels of a one-colour image, and this allows very fast phase-shifted fringe pattern acquisition. [PERSON] et al. [10; 11; 12] used different numbers of encoded 1-bit binary dithered patterns or just defocus binary fringes to realize fast 3D surface measurements and a good result was obtained under laboratory conditions. In these works, the performance of TI's digital micro-mirror device (DMD) projector with high-speed binary images projection was fully developed. [PERSON] et al. [13] presented a four-step triangular pattern phase-shifting 3D measurement using the motion blur method to measure the moving hand and were able to record 3D data in real time. [PERSON] et al. [14] used bi-frequency tripolar pulse-width-modulation fringe projection to realize a high-speed three-dimensional shape measurement technique for dynamic scenes; the tripolar pulse-width-modulation technique is employed to generate ideal fringe patterns with a slight defocus. In Reference [15], a novel method of properly optimizing sinusoidal pulse width modulation patterns according to some criteria to further improve the defocusing technique was proposed. [PERSON] [16] proposed a binarized dual phase-shifting approach to improve the phase quality, which can realize error reduction for the binary defocusing technique while maintaining its advantage of 1-bit projection with high-speed. [PERSON] et al. [17] proposed a method to solve the problem of gamma nonlinearity in triangular-pattern phase-shifting profilometry by using synthesizing triangular intensity fringes. All of the above methods modify the DLP projector based on the characteristics of 1-bit fast projection. However, Projector modification is very difficult and the equipment cost is high. [PERSON] and [PERSON] [18] reviewed some dynamic 3D measurement methods based on Fast Fourier Transform (FFT) fringe analysis with 2-D grating pattern projection and measured a 3D face, however, this method is sensitive to light and the environment for face 3D measurements. [PERSON] et al. [19] measured a vibrating Chinese drum and dynamic vortex shape in real-time using the Fast Fourier Transform. Except to use the phase information of fringe projection to encode the object surface, some other methods of labelling the object surface by random statistical patterns were proposed. [PERSON] et al. [20] also proposed a method to improve the measurement accuracy by using one colour speckle projection as a set of speckle, but the colour crosstalk increases the instability of the measurement results. In order to achieve high precision and robust 3D measurement required by 3D face recognition, [PERSON] et al. [21] presented a phase unwrapping method with pixel-by-pixel based geometric constraints of the structured light system without requiring additional cameras. This has the advantage of taking high-speed measurements without increasing the system complexity or cost. [PERSON] et al.