Convexity and Bayesian constrained local models

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 feature localization performance are illustrated on the Labeled Faces in the Wild and BioID data sets.