Practical issues for binary code pattern unwrapping in fringe projection method - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 478

FIGURE 3 Photometric calibration of the projector-camera system. Red area: should not be
considered in input gray level of pattern; dotted green line: middle area after gamma correc-
tion to make linear photometric projection function for the projector-camera system.
This nonlinear behavior will cause acute problems in producing the phase map. In order
to avoid this problem, the range of black-and-white areas in the fringe paterns was changed
from 0-255 to 50-200. Hence a 0 and b 0 were defined as a 0 = 50 and b 0 = 200. However, when
working with shiny or very bright objects, defining the b 0 value to 150 will help signiicantly
reduce calculation errors and leads to beter results in practice.
Phase P = ωt + p 0 as a function of t is illustrated in Figure 4 . The next step toward making the
middle part of the function a linear photometric function is to do gamma correction. It is done
by applying a calibrated exponential function on input gray levels or directly using a look-up-
table between input-output gray levels. So we have:
FIGURE 4 Calculated fringe patterns assuming values a 0 = 50 and b 0 = 150.
I = a 0 + (b 0 -a 0 )*[(1 + cos( P ))/2] ∧ γ which γ is the gamma parameter.
Considering the fact that by growing the t value the phase P will be increased, in immense
values of P, Matlab will calculate the cos(P) with some volumes of errors, due to approxima-
tion of the Taylor expansion (truncation error).
Therefore, in calculating the phase P, it is beter to calculate the value of function cos(P) after
omitting the 2*k*π(2kπ) coefficients where k is an integer number used to count the number
of coefficients of 2π. For calculating the reduced phase, the following code was used:
P = P-loor(P/(2*pi))*2*pi.
The fringe paterns should result in an 8-bit integer picture. Accordingly, the following com-
mand was used to convert the real I values to integer values:
I = uint8(round(I)).
Figures 4 , 5 , and 6 show the calculated fringe paterns function, shifted fridge paterns pro-
iles (120°), and shifted fringe paterns for 0, 120, and − 120°.