3D face alignment and registration in the presence of facial expression differences

Abstract

This paper deals with the problem of 3D alignment of faces in the presence of some facial expression changes. The data are three dimensional and obtained using a laser scanner. Our approach is based on the differential geometry of the surface and computes the intrinsic local fiducial points on the surface and on curves that reside on the surface. Because these fiducial points are local, they allow partial alignment, where part of the face is viewed. Moreover, since the fiducial points are relatively affine‐invariant to local affine transformations, they allow matching and alignment when facial expression changes affect part of the face. A fast, noniterative alignment procedure is presented in this paper that establishes reliable correspondences between fiducial points without any prior knowledge of the overall nonlinear global transformation that takes place after the changes in facial expressions. This is achieved through the construction of a set of ordered novel absolute local affine invariants. With enough fiducial points set as correspondents, the overall nonlinear transformation is computed and the face before and after the transformation are aligned. For comparison, we also compare the alignment performance of our method with that of the iterative closest point (ICP) method and the coherent point drift (CPD) method which is based on the Gaussian mixture model by looking at the between‐to‐within variation (signal‐to‐noise ratio, SNR) between these two classes (match vs nonmatch) based on the average alignment errors for the genuine matches and nonmatches, normalized by their respective within variation, and by running it on the 3D face database GavabDB. The separation between the true match and nonmatch is best for our zero‐torsion method (SNR of 1.2), followed by the ICP method (SNR of 0.37)and the CPD method (SNR of 0.15). It is interesting to observe here that, although the alignment error for the true match cases is lowest for the CPD method, it is also extremely low for the nonmatch cases, which would mean that the method would force a query into a wrong face, yielding poor specificity (lots of false alarms). © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

3D ear alignment based on geometry invariant

“…Local and invariant intrinsic properties are presented by the Frenet frames [8], which points that for a curve r(s) parameterized by arc length s, the tangent t(s) = r(l) (s), the curvature k(s) = l2) (s), the vector b(s) = t(s)x k(s), and the torsion 't(s) = -<l2)(S), b(I)(S» determines as a set of local coordinates on the curve at each point that completely characterizes the curve at that point, where r(k) (s)stands the IC h order derivative of r with respect to s, and x is the cross product operation.…”

“…Finally, the alignment between two surfaces is processed. Surface registration methods can be categorized into polynomial transformation [3], similarity-based [4] surface-based [5], energy-based [6] and fiducial point -based registration [7][8].…”