Weiyang Liu, Yandong Wen, Zhiding Yu, Ming Li, Bhiksha Raj, Le Song
This paper addresses deep face recognition (FR) problem under open-set protocol, where ideal face features are expected to have smaller maximal intra-class distance than minimal inter-class distance under a suitably chosen metric space. However, few existing algorithms can effectively achieve this criterion. To this end, we propose the angular softmax (A-Softmax) loss that enables convolutional neural networks (CNNs) to learn angularly discriminative features. Geometrically, A-Softmax loss can be viewed as imposing discriminative constraints on a hypersphere manifold, which intrinsically matches the prior that faces also lie on a manifold. Moreover, the size of angular margin can be quantitatively adjusted by a parameter $m$. We further derive specific $m$ to approximate the ideal feature criterion. Extensive analysis and experiments on Labeled Face in the Wild (LFW), Youtube Faces (YTF) and MegaFace Challenge show the superiority of A-Softmax loss in FR tasks. The code has also been made publicly available.
| Task | Dataset | Metric | Value | Model |
|---|---|---|---|---|
| Facial Recognition and Modelling | CK+ | Accuracy | 93.8 | SphereFace |
| Facial Recognition and Modelling | Trillion Pairs Dataset | Accuracy | 43.76 | A-Softmax |
| Facial Recognition and Modelling | Trillion Pairs Dataset | Accuracy | 43.89 | A-Softmax |
| Face Verification | CK+ | Accuracy | 93.8 | SphereFace |
| Face Verification | Trillion Pairs Dataset | Accuracy | 43.76 | A-Softmax |
| Face Reconstruction | CK+ | Accuracy | 93.8 | SphereFace |
| Face Reconstruction | Trillion Pairs Dataset | Accuracy | 43.76 | A-Softmax |
| Face Reconstruction | Trillion Pairs Dataset | Accuracy | 43.89 | A-Softmax |
| 3D | CK+ | Accuracy | 93.8 | SphereFace |
| 3D | Trillion Pairs Dataset | Accuracy | 43.76 | A-Softmax |
| 3D | Trillion Pairs Dataset | Accuracy | 43.89 | A-Softmax |
| 3D Face Modelling | CK+ | Accuracy | 93.8 | SphereFace |
| 3D Face Modelling | Trillion Pairs Dataset | Accuracy | 43.76 | A-Softmax |
| 3D Face Modelling | Trillion Pairs Dataset | Accuracy | 43.89 | A-Softmax |
| 3D Face Reconstruction | CK+ | Accuracy | 93.8 | SphereFace |
| 3D Face Reconstruction | Trillion Pairs Dataset | Accuracy | 43.76 | A-Softmax |
| 3D Face Reconstruction | Trillion Pairs Dataset | Accuracy | 43.89 | A-Softmax |