Subspace Constrained Mean-shift

Deformable model fitting has been actively pursued in the computer vision community for over a decade. As a result, numerous approaches have been proposed with varying degrees of success. A class of approaches that has shown substantial promise is one that makes independent predictions regarding locations of the model’s landmarks, which are combined by enforcing a prior over their joint motion. A common theme in innovations to this approach is the replacement of the distribution of probable landmark locations, obtained from each local detector, with simpler parametric forms. This simplification substitutes the true objective with a smoothed version of itself, reducing sensitivity to local minima and outlying detections. In this work, a principled optimization strategy is proposed where a nonparametric representation of the landmark distributions is maximized within a hierarchy of smoothed estimates. The resulting update equations are reminiscent of mean-shift but with a subspace constraint placed on the shape’s variability. This approach is shown to outperform other existing methods on the task of generic face fitting.