Graphics Reference
In-Depth Information
Film A
Ideal (linear)
response
Film B
M
(pixel value)
Figure 6.10
Radiometric response functions of two kinds of films. Neither matches the ideal linear
response function very closely. (From [Mitsunaga and Nayar 99] c
2009 IEEE.)
The physical process of camera imaging was described in Chapter 5. The
camera lens focuses scene radiance
L
onto each pixel, which produces an irra-
diance
E
on the pixel. The time-integrated irradiance during the time
t
that
the shutter is open is the ideal exposure
I
;
4
assuming the irradiance is constant
over the exposure time,
I
Δ
t
. An ideal camera records the exposure exactly;
however, the relationship between exposure and a pixel value is governed by
the response function of the camera. The biggest challenge in HDR imaging
is the reconstruction of the camera response curve. Figure 6.10 contains plots of
the response functions of two different kinds of film, compared to the ideal linear
response of an ideal camera.
The scene radiance
L
at a particular point on the image plane of an ideal
camera is related to the ideal pixel exposure
I
=
E
Δ
t
according to the formula
given in Equation (5.4.5). The formula can be rearranged as
=
E
Δ
cos
4
π
t
e
d
2
4
Δ
θ
I
=
L
,
F
2
k
where
F
is the distance from the sensor plane to the lens and
d
is the aperture
diameter. The value of
k
is constant for each pixel, as long as the camera is not
refocused;
e
is a function of the aperture size and the exposure time. This refac-
toring
I
keL
thus combines the essential two variables that affect exposure, the
aperture size and the exposure time, into a single variable
e
.If
M
is the recorded
value of a pixel, Mitsunaga and Nayar model the inverse response function as a
=
4
In Section 6.1,
X
was used to denote the ideal exposure;
I
is used here to match the notation of
Mitsunaga and Nayar's paper. The paper also uses
M
for the pixel values rather than
Z
.
