Image Processing Reference
In-Depth Information
color perception system. The comparisons are carried out on spatially filtered
L
-,
M
-, and
S
-signals combined linearly (additions or subtractions preceded by spatial
summation) rather than the original cone signals. One can therefore expect that a
color perception model can be built by a spatial summation filtering of
L
,
M
, and
S
signals combined with pointwise operations that probably include addition, subrac-
tion, and normalization to achieve color constancy. Next, we outline such a plausible
theory.
In Land's retinex theory [146], which is in part found in that of Ewald Hering
(1834-1918) [105], the color sensation algorithm is suggested as
f
i
(
x, y
)
g
(
x, y
)
R
i
(
x, y
)=log
(2.1)
∗
f
i
(
x, y
)
where
g
is a spatial lowpass filter that is used to average large areas of the retina,
is
the operation that performs local averaging (we will discuss such operations further
in Section 7.3), and
f
i
is one of the cone signal response combinations,
∗
L
+
M, L
+
{
M
S, L
M
, above. There exist simulation studies of this model, including on
how the order of convolution and log functions affects the result, and how a Gaussian
and other functions perform [127], confirming a fairly accurate prediction of the
color constancy.
−
−
}
2.4 The 1931 CIE Chromaticity Diagram and Colorimetry
The
chromaticity diagram
, constructed in 1931 by the Committe International de
l'Eclairage,
1
CIE
, links the wavelength of light to perceived colors as an interna-
tional standard, (Fig. 2.2). It is used for a variety of purposes, including to compare
colors produced by color-producing devices, e.g., PC monitors, printers, and cam-
eras. The science of quantifying color is called
colorimetry
.
The CIE diagram is a projection of a 3D color space, called
XYZ color space
,
to 2D. The
X, Y, Z
coordinates are found as follows. The light emitted by a device,
or light reflected from a surface consists of photons with different wavelengths. The
amount of photons with a certain wavelength,
λ
, in a given light composition is rep-
resented by the function
C
(
λ
). The CIE diagram comprises three functions
μ
X
(
λ
),
μ
Y
(
λ
),
μ
Z
(
λ
) (Fig. 2.3). With these functions one can calculate three scalars, called
X
,
Y
,
Z
,
X
=
C
(
λ
)
μ
X
(
λ
)
dλ
Y
=
C
(
λ
)
μ
Y
(
λ
)
dλ
(2.2)
Z
=
C
(
λ
)
μ
Z
(
λ
)
dλ
There are devices that can measure
X
,
Y
, and
Z
by use of filters and photosensors.
Because the functions
C
and
μ
.
are positive, the scalars
X
,
Y
,
Z
are real and non-
negative. These measurements represent the color coordinates of the observed light
in the CIE-XYZ color system. The projection to the CIE diagram is obtained via
1
French for illumination
