On the estimation of rigid body rotation from noisy data

We derive an exact solution to the problem of estimating the rotation of a rigid body from noisy 3D image data. Our approach is based on total least squares (TLS), but unlike previous work involving TLS, we include the constraint that the transformation matrix should be orthonormal. It turns out that the solution to the estimation problem has the same form as if the data are not noisy, and thus the solution to the standard Procrustes problem can be applied.