Master Thesis - Fachbereich Informatik

3.2. CAMERA SETUP 35
eachcolorchannelisreduced. Toovercomethisproblem,onehastointerpolatethetwo
missing color channels at each pixel position. There are several interpolation approaches
also denoted as BAYER demosaicing. With respect to speed it is important to use a not
too expensive computation. The F-033C computes R-G-B values at virtual points Pi at
the center of each local 2 × 2 neighborhood as follows [3]:
= R1
P 1red
P 1green = 1
P 1blue
P 2red
P 2green = 1
P 2blue
P 3red
P 3green = 1
P 3blue
2 (G1+G3)
= B1
= R2
2 (G1+G4)
= B1
= R2
2 (G2+G4)
= B2
(3.1)
where the location of the different points can be found in Figure 3.2. Obviously, this
interpolation technique reduces the resolution of the sensor in all channels, since values
can be computed only at positions where four pixels meet and not at the boundaries of
the image. 1
If the inspection task can be performed at gray scale images, gray scale cameras should
be used instead of color cameras. Intuitively, the accuracy of a color camera can not be
the same as that of a gray scale camera, because this requires two interpolation steps.
First, one interpolates the R-G-B color channels as introduced before, and then has to
estimate the image brightness from these interpolated values. A gray scale camera offers
a more direct transformation between light intensity and image values, thus, leading not
only to more accurate images, but also to higher frame rates. This can be supported by
the following experiment.
A test image of graph paper has been captured once with the F-033C and once with the
F-046B. A 16mm fix-focal length lens has been used respectively, and the distance between
camera and graph paper as well as the viewing direction has been the same. The focus of
the optical system was adjusted to obtain a sharp image in both cases. The results can
be found in Figure 3.3. The color image in (a) has been converted into gray level values
using the following equation:
I(x, y) =0.299R(x, y)+0.587G(x, y)+0.114B(x, y) (3.2)
where R, G, B represent the three color channels for red, green, and blue respectively
and I is the resulting gray level image.
The grid appears to be more sharp in the image of the gray scale camera, although the
color image was also at focus during acquisition. The profiles of two scan lines of equal
length through an edge of the grid (visualized in (b) and (d)) can be found in Figure 3.3(e).
1 There are also color cameras that are provided with three chip sensors. The incoming light is split into
different wavelength ranges via a prism. Thus, each sensor yields a full resolution image of one color
channel and interpolation is not necessary. These cameras, however, are quite expensive and could not
be tested.