Image Processing Reference
Fig. 13.5 Converting the RGB image to a gray-scale image
Fred had calibrated the robot to the table, so that the robot could pick up coins
if their position on the table were provided. The position of the coins found by
the image processing software therefore needed to be mapped into the coordinate
system of the table, i.e. the robot. From the system they developed for the bartender
they knew the solution was to find four corresponding points in the two coordinate
systems and then find the mapping using the theory of homography. To increase the
precision of the mapping they decided to use 16 points instead of four. They placed
16 coins on the table in a regular grid spanning the entire table. They first measured
the position of each coin with respect to the origin of the table (defined to be the
lower left corner) and then measured their positions in the image. They now had 16
corresponding points, which they loaded into a program they found on the web and
hocus-pocus, out came the coefficients of Eq. 10.12. They put the coefficients into
Eqs. 10.13 and 10.14 and they could now map from the image coordinates to the
coordinates of the robot. Now they just needed to find the coins and their type.
The first idea that came to mind when they discussed how to distinguish the different
types of coins from each other was to use the color of the coins. Fred, however,
quickly undermined that idea by showing them how the color of a coin can change
after being exposed to different circumstances such as extensive sunlight or acid.
Having accepted that they decided to convert the input RGB image to a gray-scale
image in order to reduce the amount of data. They played around with different
weighting schemes, see Eq. 3.3, but in the end it turned out that simply using the
red part of the image, that is W R =
0, gave the best result.
They argued among themselves that the reason was that the coins contains more red
material. 1 In Fig. 13.5 the conversion is illustrated.
1 and W G =
W B =
1 The explanation could of course also be that the lighting in the scene is more reddish, but they
never investigated that.