Active Appearance Models with Rotation Invariant Kernels

2D Active Appearance Models (AAM) and 3D Morphable Models (3DMM) are widely used techniques. AAM provide a fast fitting process, but may represent unwanted 3D transformations unless strictly constrained not to do so. The reverse is true for 3DMM. The two approaches also require of a pre-alignment of their 2D or 3D shapes before the modeling can be carried out which may lead to errors. Furthermore, current models are insufficient to represent nonlinear shape and texture variations. In this paper, we derive a new approach that can model nonlinear changes in examples without the need of a pre-alignment step. In addition, we show how the proposed approach carries the above mentioned advantages of AAM and 3DMM. To achieve this goal, we take advantage of the inherent properties of complex spherical distributions, which provide invariance to translation, scale and rotation. To reduce the complexity of parameter estimation we take advantage of a recent result that shows how to estimate spherical distributions using their Euclidean counterpart, e.g., the Gaussians. This leads to the definition of Rotation Invariant Kernels (RIK) for modeling nonlinear shape changes. We show the superiority of our algorithm to AAM in several face datasets. We also show how the derived algorithm can be used to model complex 3D facial expression changes observed in American Sign Language (ASL).