The accurate localization of facial features plays a fundamental
role in any face recognition pipeline. Constrained
local models (CLM) provide an effective approach to localization
by coupling ensembles of local patch detectors
for non-rigid object alignment. A recent improvement has
been made by using generic convex quadratic fitting (CQF),
which elegantly addresses the CLM warp update by enforcing
convexity of the patch response surfaces. In this paper,
CQF is generalized to a Bayesian inference problem,
in which it appears as a particular maximum likelihood solution.
The Bayesian viewpoint holds many advantages: for
example, the task of feature localization can explicitly build
on previous face detection stages, and multiple sets of patch
responses can be seamlessly incorporated. A second contribution
of the paper is an analytic solution to finding convex
approximations to patch response surfaces, which removes
CQF’s reliance on a numeric optimizer. Improvements in...