Abstract
In this paper, we show how a variance matrix associated with a point cloud can be decomposed into components that account for uncertainty in position, size and shape. The decomposition is related to how the frame of reference of the point cloud is specified and it is shown that the decomposition corresponds to a frame of reference specification that minimises an aggregate measure of uncertainty based on the trace of a variance matrix. The decomposition provides a way of presenting uncertainty information associated with calibrated reference artefacts in which the contribution from uncertainty in position is minimised.
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