Graphics Reference
In-Depth Information
ing Equation (6.5), but it is better to recompute each
E
i
using the reconstructed
response function
g
. From Equation (6.4),
ln
E
i
=
g
[
Z
ij
]
−
ln
Δ
t
j
.
A more robust method is to recompute
E
i
as the weighted average of the pixel
values
Z
ij
in all the images:
p
j
ω
(
Z
ij
)(
g
[
Z
ij
]
−
ln
t
j
)
=
∑
=
1
ln
E
i
.
p
j
1
ω
(
Z
ij
)
∑
=
Doing it this way has several advantages. Summing over all the images re-
duces noise in the images, and using the weighted average ensures that the pixel
values near the middle of the range are weighted most heavily. Also, the sum-
mation can be taken over more images than were used to reconstruct
g
,whichis
likely to produce a better average.
Formally, the
radiance map
is the set of radiance values
L
i
that represent the
actual radiance received at pixel
i
, which is related to the irradiance
E
i
by Equa-
tion (5.6). Assuming the radiance is constant over the pixel, and omitting the term
cos
4
(which is eliminated by the optics of some cameras anyway),
L
i
becomes
proportional to
E
i
. Actually,
E
i
represents the physical sensor irradiance only up
to an unknown constant factor. For many rendering purposes this constant is not
important, because the pixel values are eventually mapped to the middle range
of a device anyway. However, some applications may need the true radiometric
values. The constant associated with the absolute irradiance (and radiance) comes
from the “speed” of the film. Formulas relating the film speed to the film response
are sometimes available, either from the film manufacturer or from other litera-
ture. Most high-end digital cameras provide the effective film speed in standard
(ASA or ISO) format so the same formulas can be applied.
1
A radiance map constructed by Debevec and Malik's method is one form of
a
high dynamic range (HDR) image
. Sometimes “HDR image” is shortened to
just “HDRI,” but this is more often applied to the process of high dynamic range
imaging
. Debevec used the term “HDRI” specifically for images of unlimited
brightness range, but just about any image having a higher dynamic range than
what is produced by a conventional camera can properly be called a “high dy-
namic range” image.
θ
1
Commercial digital cameras normally apply a correction curve as a postprocess to the captured
pixel values. This complicates the recovery of the HDR response curve. At the present time, only
high-end single-lens reflex digital cameras provide the unaltered sensor output.
