# 7.3 Marker registration

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# Camera model

# Camera pose

Collection of centroids

Correspondence Algorithm

Correspondence between centroids and markers

Collection of markers and their known 3D world co-ordinates

Figure 7.4 The correspondence algorithm matches a 2D centroid with the 3D coordinates of the corresponding marker.

collection of marker centroids with a list of the markers’ 3D points.

s Figure 7.4 shows,

the algorithm requires as input a camera pose, a camera model, a collection of centroids for matching, and a collection of known markers with their 3D coordinates. If the algorithm is successful, the output is the correspondence between each centroid and the 3D coordinates

of the marker.

The algorithm uses the pose of the hub enclosure to model the expected 2D coordinates of the markers that would be in view based on the known world data. Views are simulated for the camera modules by using the camera model that is input into the algorithm. Currently a pinhole camera model is used although a more sophisticated model could be used if it were proved necessary. The result of this modeling is a list of 2D coordinates. The problem becomes one of processing the list of 2D coordinates and the measured centroid coordinates to find which centroid from the first list corresponds to which centroid from the second list. In an ideal world, the camera would be perfectly modeled and the camera’s pose known exactly. The measured list of centroids would be free of noise and if this were true it would be a case of finding the coordinates of each centroid in the first list which match the coordinates of each centroid in the second list and noting that a match had occurred.

To illustrate this, consider the data in Table 7.1a and 7.1b. Table 7.1a lists three centroids returned by a camera module and their identifiers. Table 7.1b lists the centroids generated by modeling the camera and calculating the 2D positions based on the 3D positions of the three markers. By matching the coordinates of the model points and the measured points the correspondence can be derived as shown in Table 7.1c.

Unfortunately, this example portrays a simplified version of the real world.

In the real

world measurement noise, uncertainties in the camera pose, and simplifications in the model all cause the coordinates in both lists not to match exactly. method to find a match between the two lists of centroids given these uncertainties is required. The method de- vised is unlikely to be optimal but it is easy to implement. The approach has the following

steps.