# 90

Hub Design

ID

X

Y

1

10

20

2

20

30

3

0

-10

(a)

Measured ID

Model ID

1

2

2

3

3

1

ID

X

Y

3

20

30

1

0

-10

2

10

20

(b)

(c)

Table 7.1 a) Measured centroids in an ideal world. b) Model centroids in an ideal world. c) Correspondence between centroids in an ideal world.

1.

For each centroid in the list of measured centroids, do.

2.

For each centroid in the list of model centroids, do.

3.

Find the Cartesian distance between the model and measured centroids.

4.

Repeat from Step 2.

5.

If the closest centroid in the list of model centroids is less than a maximum allowable distance then assign a correspondence between the current measured centroid and this model centroid and remove both from the lists.

6.

Repeat from Step 1.

fter the above steps have been executed for every centroid in the list of measured cen- troids, and provided the algorithm is successful, then a correspondence between the cen- troids in both lists is known. The final step is to relate the model centroids back to the 3D coordinates that they were created from. This mapping is known and the final output is a collection of correspondences between 2D centroid coordinates and the corresponding 3D coordinates. The maximum allowable distance in Step 5 is chosen to limit erroneous matches. It is set to a value of a few pixels.

There are a number of things that could cause the algorithm to fail and these are discussed below. Firstly, the algorithm assumes that there is a correspondence between the measured centroids and the 3D marker points. However, this may not always be the case. For exam- ple if the camera modules’ poses are not known accurately, the model list of centroids may be sufficiently different from the measured centroids such that the algorithm cannot make any matches.

nother possibility is that the algorithm produces a correspondence between the two sets of centroids but that this correspondence is not correct. This could happen for three rea- sons. Firstly, there may be enough noise and uncertainties in the system to lead the algo- rithm into wrongly assigning a correspondence between two centroids. This could happen if the noise makes a centroid appear closer than the correct centroid. This may seem un- likely but the problem can be exaggerated if the distance between centroids within either