Here we find a global, analytical, and semantic representation for facial expressions to replace state of the art FACS approach. A promising direction is to use the manifold of facial expressions as a unified framework for facial expression analysis. Under the manifold framework, an expressive facial image with N pixels can be considered as a point in an N-dimensional image space, and the variability of facial image classes can be represented as low dimensional manifolds embedded in image space. Since people change facial expressions continuously over time, it is a reasonable assumption that all images of someone’s facial expressions make a smooth manifold in the N-dimensional image space with the “neutral” face as the central reference point. The intrinsic dimension of the manifold is much lower than N. On the manifold of expression, similar expressions are points in the local neighborhood on the manifold. The basic emotional expressions with increasing intensity become curves on the manifold extended from the center. The blends of expressions will lie between those curves, so they can be defined analytically by the positions of the main curves.
From our own experience it seems that locally linear embedded learning (LLE) is most suitable for intuitive visualization of facial expressions. An example of LLE representation of facial expressions is shown in the figure here where a tree-shape distribution well represents facial expressions.
