Fig. 3.

The left hand image shows lips with anatomical landmarks (red), a linear reference curve (black), some illustrative points on the manifold (yellow), and the corresponding perpendicular distances (blue) to the closest points on the reference curve (green). The middle image shows the points from the manifold in the 2D space defined by signed distance to the closest point on the reference curve and arc length along the reference curve to the location of the closest point. The colour coding of the points shows the relative strengths of the maximum curvature at each location, on a topographic scale. The right hand image shows a smooth surface representation, with the flexible estimate of the ridge curve in this 2D space indicated by the red line.