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Figure 8.21. Zhang et al.'s color stripe pattern created using a de Bruijn sequence of order 3
over five symbols.
(
(
Figure 8.22. (a) An image of an object illuminated using the stripe pattern in Figure 8.21 .
(b) Recovering the correspondence between the projected and observed color patterns using
dynamic programming.
Zhang et al. [ 568 ] proposed a good example of a color-stripe technique based on de
Bruijn sequences. Their goal was to select a color stripe pattern such that every stripe
differed from its neighbor in at least one color channel, and that each subsequence
of three stripe transitions was unique. They thus used a de Bruijn sequence of order
3 over five symbols to create the 125-stripe pattern illustrated in Figure 8.21 . 12
Zhang et al. also used Caspi et al.'s color model in Equation ( 8.5 ) to preprocess
the camera colors to be better correlated with the color instructions to the projector.
Finally, they used dynamic programming (Appendix A.1 ) to correlate the observed
stripe pattern along a scanline with the known projected pattern. As illustrated in
Figure 8.22 , dynamic programming works well to obtain this correspondence when
the stripes don't change positions (i.e., the surface is sufficiently smooth). In cases
where the order of stripes is non-monotonic, Zhang et al. applied multiple passes
of dynamic programming to recover each “piece” of the correspondence, removing
the rows and columns of the dynamic programming graph corresponding to already
found pieces. The cost function for the dynamic program is based on a model of con-
sistency between two candidate color transitions. Finally, Zhang et al. incorporated
12 In this application, N
5, not 8, since Zhang et al. did not allow adjacent stripes to be the same
color, and ruled out neighbors in which the red and green channels changed at the same time.
=
 
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