8.1 Noise sources
variation in centroid position due to sensor dark noise,
variation in centroid position due to number precision and variation in pose estima-
tion due to number precision,
pose algorithm optimisation noise,
correspondence algorithm errors, and the
non-uniformity in marker image due to viewing angle and distance.
The points at which these unknowns are introduced into the system are shown in Figure 8.1.
Pose estimation seeks to find only a camera’s extrinsic parameters. It assumes that the in- trinsic parameters are known and also that precise marker coordinates are available. For the developed pose algorithm (see Section 7.4) this means that, due to uncertainties, there is unlikely to be a value of q that will give F (q) = 0. The best performance that can be ex- pected cannot be better than what is dictated by the uncertainties in the constants. The 3D marker coordinates are probably only accurate to ±3 mm. Only the focal length and pixel size are modeled in the pinhole camera model used so the remaining intrinsic parameters will affect the accuracy further. Finally, the poses of the camera modules within the hub enclosure are also not precisely known. In the experiments in this chapter all LEDs are assumed to be identical, i.e., the variation in the markers due to the manufacturing process is assumed not to have an effect.
Of the varying unknowns, there are at least three that affect the variation in centroid posi- tion while the module is stationary. These are the background image noise, sensor dark pixel noise, and variation in marker intensity due to noise on the outputs of the LED
fourth source of noise is the numerical precision used to store the centroid,
however, this is small compared with the other unknowns so is ignored.
Background image noise is caused by the shutter being open sufficiently long so that the captured image contains the background and not just the markers themselves. The ma- jority of this testing has been performed with a shutter period of 300 µs that has, under normal operation, made the background invisible to the sensor. However, at this shutter period image noise may be present in the test environment. To ensure this source of noise does not affect the system, either the system must be used in a similar test environment or a new scheme must be researched to actively suppress the background image.
The second source of noise is referred to as sensor dark noise. This is the noise that would be recorded if the image sensor captured data in a dark environment. This noise is a combi- nation of a number of types of noise including thermal noise and noise introduced during