  Face recognition technology has become an integral part of modern security
systems and user authentication processes. However, these systems are
vulnerable to spoofing attacks and can easily be circumvented. Most prior
research in face anti-spoofing (FAS) approaches it as a two-class
classification task where models are trained on real samples and known spoof
attacks and tested for detection performance on unknown spoof attacks. However,
in practice, FAS should be treated as a one-class classification task where,
while training, one cannot assume any knowledge regarding the spoof samples a
priori. In this paper, we reformulate the face anti-spoofing task from a
one-class perspective and propose a novel hyperbolic one-class classification
framework. To train our network, we use a pseudo-negative class sampled from
the Gaussian distribution with a weighted running mean and propose two novel
loss functions: (1) Hyp-PC: Hyperbolic Pairwise Confusion loss, and (2) Hyp-CE:
Hyperbolic Cross Entropy loss, which operate in the hyperbolic space.
Additionally, we employ Euclidean feature clipping and gradient clipping to
stabilize the training in the hyperbolic space. To the best of our knowledge,
this is the first work extending hyperbolic embeddings for face anti-spoofing
in a one-class manner. With extensive experiments on five benchmark datasets:
Rose-Youtu, MSU-MFSD, CASIA-MFSD, Idiap Replay-Attack, and OULU-NPU, we
demonstrate that our method significantly outperforms the state-of-the-art,
achieving better spoof detection performance.
