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 tot al least squares (TLS), but unlike previous work involving TLS, we inc lude the constraint that the transformation matrix should be orthonorm al. It turns out that the solution to the estimation problem has the s ame form as if the data are not noisy, and thus the solution to the st andard Procrustes problem can be applied.