Convexity and Bayesian constrained local models

The accurate localization of facial features plays a fun- damental role in any face recognition pipeline. Constraine d local models (CLM) provide an effective approach to lo- calization 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 enforc- ing convexity of the patch response surfaces. In this pa- per, CQF is generalized to a Bayesian inference problem, in which it appears as a particular maximum likelihood so- lution. The Bayesian viewpoint holds many advantages: for example, the task of feature localization can explicitly bu ild on previous face detection stages, and multiple sets of patc h responses can be seamlessly incorporated. A second contri- bution 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 La - beled Faces in the Wild and BioID data sets.