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Anomalies are by definition rare, thus labeled examples are very limited ornonexistent, and likely do not cover unforeseen scenarios. Unsupervisedlearning methods that don't necessarily encounter anomalies in training wouldbe immensely useful. Generative vision models can be useful in this regard butdo not sufficiently represent normal and abnormal data distributions. To thisend, we propose constant curvature manifolds for embedding data distributionsin unsupervised visual anomaly detection. Through theoretical and empiricalexplorations of manifold shapes, we develop a novel hyperspherical VariationalAuto-Encoder (VAE) via stereographic projections with a gyroplane layer - acomplete equivalent to the Poincar\'e VAE. This approach with manifoldprojections is beneficial in terms of model generalization and can yield moreinterpretable representations. We present state-of-the-art results on visualanomaly benchmarks in precision manufacturing and inspection, demonstratingreal-world utility in industrial AI scenarios. We further demonstrate theapproach on the challenging problem of histopathology: our unsupervisedapproach effectively detects cancerous brain tissue from noisy whole-slideimages, learning a smooth, latent organization of tissue types that provides aninterpretable decisions tool for medical professionals.

Manifolds for Unsupervised Visual Anomaly Detection