Metric Learning on the Manifold of Oriented Ellipses: Application to Facial Expression Recognition

Abstract

In this paper we propose a new family of metrics on the manifold of oriented ellipses centered at the origin in Euclidean n-space, the double cover of the manifold of positive semi-definite matrices of rank two, in order to measure similarities between landmark representations. The metrics, whose distance functions are remarkably simple, are parametrized by the choice of a n-by-n positive semi-definite matrix P. This allows us to learn the parameter P from the training data and increase the efficiency of the metric. We evaluate the proposed metric on facial expression recognition from 2D facial landmarks. The conducted experiments demonstrate the effectiveness of the learned metric to classify facial shapes under different expressions.