relative error u03b5 i rel d i u2212 d i ref d i ref here d i denotes the i th distance and d i ref is the corresponding reference distance the distributions of u03b5 abs and u03b5 rel are shown in fig1 d and 1e respectively the standard deviation of u03b5 abs is 5 89 mm for geodesic distances and 12 03 mm for euclidean ones a difference of 104 3 the standard deviation of u03b5 rel was 15 85 for geodesic distances and 39 6 for euclidean ones a difference of 150 2 the conclusion of this experiment is two fold first the changes of the geodesic distances due to facial expressions are insignificant for exaggerated expressions which justifies the present model secondly euclidean distances are much more sensitive to changes due to facial expressions compared to the geodesic ones this observation will be reinforced by the results presented hereinbelow where we compare our method to a method that treats facial surfaces as rigid objects the geometry of the face is acquired by a range camera and has to be processed before the canonical form is computed the raw range data is given as a cloud of points that can be triangulated or represented as a parametric manifold as shown in fig1 c preprocessing according to the present embodiments is illustrated in the flow chart of fig3 as illustrated the process includes three steps i geometric processing of the facial surface s 3 1 geometric processing s 3 1 is shown in greater detail in the flow chart of fig4 to include three stages of spike removal s 4 1 hole filling s 4.