Spherical Confidence Learning for Face Recognition

An emerging line of research has found that spherical spaces better match the underlying geometry of facial im-ages, as evidenced by the state-of-the-art facial recognition methods which benefit empirically from spherical representations. Yet, these approaches rely on deterministic embeddings and hence suffer from the feature ambiguity dilemma, whereby ambiguous or noisy images are mapped into poorly learned regions of representation space, leading to inaccuracies. Probabilistic Face Embeddings (PFE) [17] is the first attempt to address this dilemma. However, we theoretically and empirically identify two main failures of PFE when it is applied to spherical deterministic embeddings aforementioned. To address these issues, in this paper, we propose a novel framework for face confidence learning in spherical space. Mathematically, we extend the von Mises Fisher density to its r-radius counterpart and derive a new optimization objective in closed form. Theoretically, the proposed probabilistic framework provably allows for better interpretability, leading to principled feature comparison and pooling. Extensive experimental results on multiple challenging benchmarks confirm our hypothesis and theory, and showcase the advantages of our framework over prior probabilistic methods and spherical deterministic embed-dings in various face recognition tasks.