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~
I p,1
I p,1
~
f
M p,1
1 / e 1
~
~
I p,2
Q
I p,2
Σ
w( M p , q ) I p , q
~
M p ,2
f
1 / e 2
I p
q =1
~
Q
I p,Q
Σ
w( M p , q )
I p,Q
q =1
1 / e ~
M p,Q
f
Figure 6.11 Flowchart for radiometric self-calibration.
(From [Mitsunaga and Nayar 99] c
2009
IEEE.)
The authors tested the method on synthetic images with an appropriate amount
of noise deliberately added. They found that using N
10 (i.e., 11 polynomial
coefficients) gives sufficiently accurate results, and fewer than 10 iterations are
needed to determine the final values. Figure 6.11 illustrates the conceptual pro-
cess of each iteration ( I is used in place of f ( n ) (
=
in the figure). Mitsunaga
and Nayar's self-calibration algorithm does not need exposure time information
to accurately reproduce the response curve. Furthermore, noise can be reduced by
employing a time averaging of pixel values for images in a video sequence. Also,
because the solution method solves a system of linear equations rather than em-
ploying a nonlinear optimizer, the algorithm is very fast. A drawback, however, is
that the polynomial model requires increasingly many coefficients as the dynamic
range increases, and therefore cannot cover an unbounded range. Debevec and
Malik's method does not have this limitation. Nonetheless, the self-calibration
algorithm has been shown to work very well in practical cases, except for those
having an extremely large dynamic range.
M
)
6.3.2 HDR Video Capture and Display
In 2003, Sing Bing Kang, Matthew Uyttendaele, Simon Winder, and Richard
Szeliski presented the paper “High Dynamic Range Video” [Kang et al. 03]. This
paper describes a general method of generating an HDR video from a sequence
of frames captured with different exposures. The basic idea is to capture the
sequence of frames using a wide range of exposure times. Each frame in the se-
quence therefore has a significantly different exposure than the previous frame.
Widely varying the exposure times between frames results in a set of images hav-
ing a much greater dynamic range than could be captured with a conventional dig-
ital video camera ( Figure 6.12 ) . The problem, though, is that the images change
between frames. The methods described so far in this chapter all assume a static
environment, so they do not apply to HDR video capture. The steps in the al-
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