Fig. 1. Directed graph G33 on S=0,1,2, the path demonstrated by a red directed dotted line is an Eulerian tour

Fig. 2. Relationship between four-step phase-shifting waveform, encoding sequence orders k', and phase orders k

Fig. 3. Encoded period order sequences in this paper

Fig. 4. Generation of color fringe patterns. (a) Four phase-shifting patterns; (b) phase order encoded fringes; (c) four color phase-shifting encoded fringes

Fig. 5. Fringe borders extraction. (a) Four captured color images; (b) average grayscale image I˜¯; (c) combined gradient curve of a specific scanline in I˜¯; (d) fringe borders

Fig. 6. Decoding process. (a) Grayscale distribution in a specific scanline of I˜¯G and I˜¯B; (b) grayscale curves calculated by Eq. (8) from the curve in Fig. 6(a); (c) decoded results

Fig. 7. Results of color crosstalk compensation. (a) Image before compensation; (b) image after compensation; grayscale values of (c) R channel, (d) G channel, and (e) B channel before and after compensation in a specific scanline

Fig. 8.

Decoded results of four methods. (a) Adjacency-hopping de Bruijn sequence encoded pattern; (b) de Bruijn sequence encoded pattern; (c) de Bruijn sequence encoded pattern with black slits; (d) encoded pattern of Zhangsmethod^[14]; (e)-(h) images captured by camera and (i)-(l) decoded results of a scanline

Fig. 9. Measurement of occluded workpieces. (a) Occluded workpiece; (b) rough matching result; (c) corrected result; (d) 3D measurement result

Fig. 10. Measurement results of a fox mask. (a) Color fringe images captured by camera; (b) wrapped phase ϕ; (c) period orders k; (d) wrapped phase ϕ and period orders k in a specific scanline; (e) unwrapped phase Φ; (f) 3D measurement result

Fig. 11. Measurement results of a plaster model. (a) Plaster model to be measured; (b) unwrapped phase Φ; (c) 3D measurement result