As Danielsson says in his comment on the paper by Arsenault, the phase information is not used and the same signature vectors can have different shapes. However, in practice the method works well.
© 1989 Optical Society of America
Henri H. Arsenault, "Rotation-invariant digital pattern recognition using circular harmonic expansion: author’s reply to comments," Appl. Opt. 28, 1614-1615 (1989)