Automatic identification and removal of outliers for high-speed fringe projection profilometry

Automatic identification and removal of outliers for high-speed fringe projection profilometry

Shijie Feng, Qian Chen, Chao Zuo, Rubin Li, Guochen Shen and Fangxiaoyu Feng

Jiangsu Key Laboratory of Spectral Imaging & Intelligent Sense,

Nanjing University of Science and Technology, Nanjing, Jiangsu Province 210094, China

Abstract

Phase-shifting profilometry combining with the two-frequency temporal phase unwrapping is widely used for high-speed, real-time acquisition of three-dimensional shapes. However, when the object is not motionless during the acquisition process, some unreliable results may emerge, especially around the contours of the measured object. The main reason for this is that the same point in the projected pattern sequence can map to different points within the camera images resulting from depth changes over time. We present a novel approach for identifying those invalid pixels affected by such an error. By carefully examining the captured fringe pattern, comparing two modulation maps, utilizing the phase relationship between two neighboring pixels, and employing a Gaussian filter to detect the protruding points, the bad measurement pixels can be detected and filtered out effectively. The whole procedure is of low computational complexity because of the introduced lookup table-based fast data processing method. Some experimental results are presented to verify the validity of our method.

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Citations

Feng, S., Chen, Q., Zuo, C.,Li, R., Shen, G., & Feng, F. (2013). Automatic identification and removalof outliers for high-speed fringe projection profilometry. Optical Engineering,52(1), 013605-013605.

Results

Fig. 1. Captured phase shift images of two frequencies fringe patterns for 3-D measurement of a moving hand: (a) high frequency fringe image (90 deg.); (b) high frequency fringe image (180 deg.); (c) high frequency fringe image (270 deg.); (d) high frequency fringe image (360 deg.); (e) low frequency fringe image (90 deg.); (f) low frequency fringe image (180 deg.); (g) low frequency fringe image (270 deg.); (h) low frequency fringe image (360 deg.).

Fig. 2. 3-D reconstruction result of a moving hand: (a) 3-D result without invalid pixels identification; (b) 3-D result after the first step; (c) 3-D result after the second step; (d) 3-D result after the third step; (e) accurate 3-D result after all the steps.

Fig. 3. Real-time measurement of a rotating dixie cup: (a) high frequency fringe image (90 deg); (b) low frequency fringe image (90 deg); (c) 3-D reconstruction result of a rotating dixie cup before invalid pixels elimination; (d) 3-D result of a rotating dixie cup after four-step invalid pixels elimination.

Methods

Fig. 1. Comparison between and from each frequency pattern: (a) from high frequency pattern at phase shift 90 deg; (b) corresponding from high frequency pattern at phase shift 90 deg; (c) detected invalid pixels in high frequency pattern; (d) from low frequency pattern at phase shift 90 deg; (e) corresponding from low frequency pattern at phase shift 90 deg; (f) detected invalid pixels in low frequency pattern.

By employing four-step phase-shifting and two- frequency phase-unwrapping techniques, phase values from two frequencies images were acquired. For high frequency, we put its phase value into the form of , namely the (n=1, 2, 3, 4). One value is shown in Fig. 1(a). By solving Eq. (13), we had (n=1, 2, 3, 4), at the same shifted phase, the corresponding map is shown in Fig. 1(b). After computing the root mean square error and comparing it with the Error, invalid pixels were detected, and are shown in Fig. 1(c). Similarly, for low frequency, the same procedures could be adopted. One pair of and values is shown in Fig. 1(d) and 1(e), respectively. Although, this result was not as notable as the one obtained from high frequency, it actually detected a few invalid pixels surviving from the prior process, as shown in Fig. 1(f).

Fig. 2. (a) Modulation map derived from high frequency pattern; (b) modulation map derived from low frequency pattern; (c) invalid pixels detected by comparing the two modulation maps; (d) invalid pixels eliminated by phase monotonicity method; (e) invalid pixels removed by using a Gaussian filter.

Compare two modulations of each pixel; the pixels with large modulation variation are invalid pixels; according to modified phase monotonicity criterion eliminate incorrect pixels with unreliable unwrapped phase; compare smoothed final phase map with origin final phase map to identify undesirable pixels.

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Contact

Shijie Feng

Ph.D. Candidate of NJUST

Email:geniusshijie@163.com ( or 311040574@njust.edu.cn)

Nanjing University of Science and Technology, Jiangsu Province (210094), P.R.China

Qian Chen

Dean of the school of Electronic and Optical Engineering

Email: chenqian@njust.edu.cn

Nanjing University of Science and Technology, Jiangsu Province (210094), P.R.China

Chao Zuo

Associate professor at the school of Electronic and Optical Engineering

Email: surpasszuo@163.com

Nanjing University of Science and Technology, Jiangsu Province (210094), P.R.China