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Picard 95]. Starting from this work, he was able to develop a more robust method
for reconstructing the response curve. The method, which is described in the
next subsection, was implemented and released as open source software known
as HDR Shop. This helped bring high dynamic range imaging to mainstream
computer graphics.
6.1.3 Recovering the Response Curve
The ultimate goal of Debevec's work was to construct an image in which each
pixel contains absolute real-world irradiance values rather than just the pixel ex-
posures. The value of a pixel then represents the actual radiance carried along
a ray coming off a (focused) object in the original scene. He described such
an image as a
high dynamic range radiance map
. The process of constructing
an HDR radiance map begins with a collection of photographs of the same scene
shot at different exposures. The first step is to reconstruct the response curve of
the camera or film used to capture the images, which is the function
f
defined by
Z
=
f
(
X
)=
f
(
E
t
)
.
(6.2)
The inverse of
f
maps pixel values to actual exposures, and from these the ir-
radiance can be recovered if the exposure time
t
is known. Rather than try to
reconstruct the response curve for each individual image, Debevec and Malik's
method performs a simultaneous global fit to all the images. The result is called
the
high dynamic range response curve
.
The input to the algorithm is a collection of
P
digitized images of the same
scene photographed under the same conditions and same camera settings except
for the shutter speed, which is varied over almost all speeds available. Then
N
representative pixels are chosen, and the pixel values of these
N
pixels are selected
over all the images;
Z
ij
denotes the value of pixel
i
in the image exposed for time
Δ
Δ
t
j
. The goal is to approximate the general response function
f
, or rather, its
inverse. This is best done logarithmically. Taking the natural logarithm of both
sides of Equation (6.2) (the
Z
values are never zero, by choice), we get
f
−
1
g
(
Z
)=
(
Z
)=
ln
E
+
ln
Δ
t
,
(6.3)
where
g
is the unknown inverse response function. Note that the right-hand side
of Equation (6.3) is not a direct function of the variable
Z
, so this equation does
not provide a formula for
g
—it only gives the relationship between values of
g
and the irradiance
E
, the other unknown.
Because the pixel values are discrete, the inverse function
g
has a finite do-
main running over the possible integer pixel values
Z
min
,...,
Z
max
(the process is
