Characteristic number regression for facial feature extraction

Facial feature extraction plays an important role in many multimedia and vision applications. Recent regression methods for extraction lack the explicit shape constraints for faces, and require a large number of facial images covering great appearance variations. This paper introduces a novel projective invariant, named characteristic number (CN), to explicitly characterize the intrinsic geometries of facial points shared by human faces, which is inherently invariant to pose changes. By further developing a shape-to-gradient regression framework, we provide a robust and efficient feature extractor for facial images in the wild. The computation of our model can be successfully addressed by learning the descent directions using point-CN pairs without the need of large collections for appearance training. Extensive experiments on challenging benchmark data sets demonstrate the effectiveness of our proposed detector against other state-of-the-art approaches.