Shape change along geodesics with application to cleft lip surgery

Abstract

Continuous shape change is represented as curves in the shape space. A method for checking the closeness of these curves to a geodesic is presented. Three large databases of short human motions are considered and shown to be well approximated by geodesics. The motions are thus approximated by two shapes on the geodesic and the rate of progress along the path. An analysis of facial motion data taken from a study of subjects with cleft lip or cleft palate is presented that allows the motion to be considered independently from the static shape. Inferential methods for assessing the change in motion are presented. The construction of predicted animated motions is discussed.

Figures

Fig. 1

Location of the 38 face markers: the average static face is shown; lines suggest the location of the eyebrows, nose, lips and chin

Fig. 2

PC scores for a control subject: (a) scores for the first PC plotted against time (frames); (b) scores for the second PC

Fig. 3

Relative percentage change in the distances between the lip corners over time: (a) observed data; (b) projection onto the geodesic

Fig. 4

Mean effect of surgery on the maximal smile of patients (the face is viewed from the front): ◊, mean extremal position before surgery; ♦, mean extremal position after surgery; lines connect these extremal positions with the initial position

Fig. 5

Change in mean PC scores by subject due to surgery: subjects showing some evidence of change are labelled

Fig. 6

Change in pose before and after surgery for (a) subject RR31 and (b) subject RR15: O, mean before pose; →, end at the after-surgery mean pose