Outlier rejection in high-dimensional deformable models

Deformable model tracking is a powerful methodology that allows us to track the evolution of high-dimensional parameter vectors from uncalibrated monocular video sequences. The core of the approach consists of using low-level vision algorithms, such as edge trackers or optical flow, to collect a large number of 2D displacements, or motion measurements, at selected model points and mapping them into 3D space with the model Jacobians. However, the low-level algorithms are prone to errors and outliers, which can skew the entire tracking procedure if left unchecked. There are several known techniques in the literature, such as RANSAC, that can find and reject outliers. Unfortunately, these approaches are not easily mapped into the deformable model tracking framework, where there is no closed-form algebraic mapping from samples to the underlying parameter space. In this paper, we present three simple, yet effective ways to find the outliers. We validate and compare these approaches in an 11-parameter deformable face tracking application against ground truth data.