Image Processing Reference
In-Depth Information
Frequency space
Real space
p
/√2
fy
1/√2
p
fd
p
1/√2
p
1/2
p
1/2
p
p
(a)
fx
1/2
p
1/√2
p
p
Pixel square array
Pixel interleaved
array
(c)
p
/√2
p
/√2
(b)
FIGURE 7.5
Pixel arrays in real space and Nyquist frequency of each array: (a) pixel square array; (b) pixel interleaved array;
(c) Nyquist frequency.
it was shown that the structure ratio of vertical and horizontal lines are statistically higher
than other angles in huge number of images. Thus, a way to create efficiency in accordance
with the characteristics of the human eye and the statistical nature of objects is desirable.
The explanation so far is for the case of monochromatic use, in which each pixel has cor-
relations with its neighboring pixels and a reasonable response or output can be supposed
from each pixel. But the situation is quite different in the case of a one-chip color system,
that is, one color filter at one pixel.
Before the discussion proceeds, some points concerning the characteristics of the human
eye should be made. As mentioned in Section 6.4, the human eye and brain perceive color
as a set of stimulus values of cones S, M, and L. There, what contributes most, that is, the
highest sensitivity frequency is around 550 nm, which is from green to yellow-green. So,
the pixel that contributes most to sensitivity and resolution is the green filter pixel; there-
fore, the green pixel array is important.
First, the Bayer configuration filter applied to a pixel square array sensor is discussed.
Each Nyquist frequency of G, R, and B is considered as well as the previous case of mono-
chrome by focusing on the array of each color.
As shown in Figure 7.6a, the G pixel configuration is an interpolated array and the verti-
cal and horizontal pitch is
p
, which is the same as in the monochrome case. Therefore, the
Nyquist frequency of green in the vertical and horizontal directions is 1/2
p
, which is the
same with monochrome as shown in Figure 7.6b, which in the monochrome case is indi-
cated by B/W. Thus, the combination of a square array sensor and the Bayer configuration
is well made.* The pitches of R and B in the vertical and horizontal directions are 2
p
and
the Nyquist frequency is 1/4
p
, as shown in the figure.
* This is not surprising because the concept of Bayer's invention (Reference [6] in Chapter 1) is to arrange the
resolution contributory color in a checkerwise fashion.
