Least-squares solution of absolute orientation with non-scalar weights

The absolute orientation problem involves finding the Euclidean transformation which minimises the sum of the squared errors between two pointsets. In the standard form of the problem a confidence may be attached to each of the errors via a set of positive scalar weights. In this paper we consider a generalisation of the standard problem in which the components of the error vectors are coupled via a set of weight matrices. We show how problems of this type arise and derive two distinct forms of the problem. We present a closed-form solution to the first form of the 3-D problem and iterative solutions to the second form of the 2-D problem and both forms of the 3-D problem