Unsupervised Performance Analysis of 3D Face Alignment

We address the problem of analyzing the performance of 3D face alignment (3DFA) algorithms. Traditionally, performance analysis relies on carefully annotated datasets. Here, these annotations correspond to the 3D coordinates of a set of pre-defined facial landmarks. However, this annotation process, be it manual or automatic, is rarely error-free, which strongly biases the analysis. In contrast, we propose a fully unsupervised methodology based on robust statistics and a parametric confidence test. We revisit the problem of robust estimation of the rigid transformation between two point sets and we describe two algorithms, one based on a mixture between a Gaussian and a uniform distribution, and another one based on the generalized Student's t-distribution. We show that these methods are robust to up to 50\% outliers, which makes them suitable for mapping a face, from an unknown pose to a frontal pose, in the presence of facial expressions and occlusions. Using these methods in conjunction with large datasets of face images, we build a statistical frontal facial model and an associated parametric confidence metric, eventually used for performance analysis. We empirically show that the proposed pipeline is neither method-biased nor data-biased, and that it can be used to assess both the performance of 3DFA algorithms and the accuracy of annotations of face datasets.