Inferring 3D shape from incomplete 2D pose using a Gaussian prior

In this paper we construct a simple full-covariance Gaussian prior for personspecific facial pose at a number of points on the face. When the relative orientation and translation of the camera and head are known, this simple model permits triangulation and correspondence to be expressed in a straightforward manner: For orthographic cameras, triangulating points amounts to linear regression, and for perspective cameras, we iteratively approach the solution by linearizing about the current pose. The correspondence problem under this prior is NP-hard, but we have achieved good correspondence by initializing using linear assignment, then searching locally using pairwise swaps in the correspondence matrix. Using facial motion capture data, we show that previous models of facial pose relying on subspace constraints can produce significant errors unless high numbers of dimensions are used, and evaluate the performance of our prior for both the triangulation and correspondence problems.