The intensity distribution in three-beam CBED patterns from centrosymmetric crystals can be inverted analytically to enable the direct measurement of crystal structure amplitudes and three-phase invariants. The accuracy of the measurements depends upon the accuracy and precision with which specific loci within the discs can be identified. The present work exploits the equivalence in form of the intensity distribution along these loci to provide an algorithm for their automated location, enabling the rapid and unequivocal identification of their position. Moreover, it demonstrates how the loci can be used to determine directly the relative magnitudes of structure amplitudes with superior accuracy and without recourse to complex pattern-matching calculations.