Environmental Engineering Reference
In-Depth Information
First, using the same set up of the coordinate system, the position of P 1 =[P 1x , P 1y ] T can be
found as [2L-P x , P y ] T where L is the horizontal distance from the origin O to the mirror.
Then we can obtain the equations similar to Equations 3 and 4:
P
sin
P
cos
x
y
(9)
P
cos
P
sin
N
x
y
1
(2
LP
)sin
P
cos
x
y
(10)
(2
LP
)cos
P
sin
N
x
y
2
where λ is the focal length of the physical camera, θ is the angle of the camera, and N 1 and
N 2 are the projected positions of P and P 1 on the image plane.
Solve for P x and P y , we have
2
2
2
(
NN
)sin 2
2
N
sin
2
N
cos
12
2
1
P
L
x
2
(
NN
)sin 2
(
N
N
)
cos 2
12
1
2
.
(11)
N


sin
cos
1
P
P
y
x
sin
N
cos
1
Note that the result is simpler compare to the true stereovision method due to the equality
of focal length λ and rotation angle θ between the physical and virtual cameras.
Meanwhile, we need to cover the combined surface of both the physical screen and the
reflected one, so we can calibrate the angle θ to be π/4. In this case, the result can be
further simplified as
(
NN
)(
)
1
2
P
L
x
2
NN
N
12
1
1
(12)
P
P
y
x
N
4. Application considerations
4.1 Virtual boundary
Sometime, the pointer is away from the vicinity of the screen but is still close enough to be
picked up by the cameras. This can easily happen when a user is pondering for the next
action or is talking in front of the screen. As shown in Figure 5A, in true stereovision, a
virtual boundary can be set up in the algorithm to filter out the unwanted movements. Any
point P within the virtual boundary is considered legitimate and is processed accordingly.
Its motion will be reflected as the movement of the cursor on the screen. If the pointer is
outside the virtual boundary, like the position P' in Figure 5A, it can be considered idle and
an update is not necessary. However, in the background, the video stream is constantly
processed to extract the positions of P at both cameras. The distance of the pointer from the
screen surface needed to be constantly calculated and compared with the virtual boundary.
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