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Submitted version of the thesis - Airlab, the Artificial Intelligence ...

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54 Chapter 5. Vision<br />

Figure 5.2: Perspective projection in a pinhole camera<br />

means <strong>the</strong> object can be represented by a X,Y,Z position in <strong>the</strong> world coordinate<br />

system, with Z=0. This reduces <strong>the</strong> transformation into a 2D-2D<br />

transformation, and needs a new H matrix.<br />

We need to calculate <strong>the</strong> transformation matrix between <strong>the</strong> robot and<br />

) coordinates. The transformation matrix between world frame<br />

camera (TR C<br />

andcamera(T C W )coordinatesisknownfrom<strong>the</strong>externalcameraparameters.<br />

The world frame to robot frame transformation matrix TR W is calculated by<br />

<strong>the</strong> target object position and robot center (shown in Figure 5.3). TR C is<br />

derived as follows:<br />

T R C = TR W ∗TW C<br />

For <strong>the</strong> ball localization case, <strong>the</strong> calculation is made for <strong>the</strong> pixel diameter<br />

Dpx <strong>of</strong> <strong>the</strong> ball at known distance l and <strong>the</strong> real diameter Dball. For <strong>the</strong><br />

camera, we introduced a parameter f ∗ , to indicate <strong>the</strong> dimension <strong>of</strong> a unit<br />

pixel, which is a statical parameter <strong>of</strong> <strong>the</strong> camera. Using this information,<br />

<strong>the</strong> distance <strong>of</strong> <strong>the</strong> ball lnew can be calculated by counting <strong>the</strong> pixels <strong>of</strong> <strong>the</strong><br />

diameter <strong>of</strong> <strong>the</strong> ball Dpx and by multiplying this by f ∗ .<br />

f ∗ = l<br />

∗Dpx<br />

Dball<br />

lnew = f∗<br />

∗Dball<br />

Dpx<br />

The next step is converting <strong>the</strong> direction from camera to <strong>the</strong> ball −−−→<br />

d c ball

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