Curved Geometric Networks for Visual Anomaly Recognition

TL;DR

This paper explores the use of curved geometric spaces, such as spherical and hyperbolic geometries, for improved anomaly detection in visual data, demonstrating consistent performance gains across multiple recognition tasks.

Contribution

It introduces a unified framework for embedding data in curved spaces with adaptable geometric constraints, enhancing anomaly detection capabilities beyond traditional Euclidean methods.

Findings

Curved space embeddings improve anomaly detection accuracy.

Unified geometric constraints are effective across diverse tasks.

Proposed models outperform Euclidean baselines in experiments.

Abstract

Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that curved spaces might encode more structural information, leading to better discriminative power and hence richer representations. In this work, we investigate benefits of the curved space for analyzing anomalies or out-of-distribution objects in data. This is achieved by considering embeddings via three geometry constraints, namely, spherical geometry (with positive curvature), hyperbolic geometry (with negative curvature) or mixed geometry (with both positive and negative curvatures). Three geometric constraints can be chosen interchangeably in a unified design given the task at hand. Tailored for the embeddings in the curved space, we also formulate functions to compute the anomaly score. Two types of geometric modules (i.e., Geometric-in-One and Geometric-in-Two models) are proposed to plug in the original Euclidean classifier, and anomaly scores are computed from the curved embeddings. We evaluate the resulting designs under a diverse set of visual recognition scenarios, including image detection (multi-class OOD detection and one-class anomaly detection) and segmentation (multi-class anomaly segmentation and one-class anomaly segmentation). The empirical results show the effectiveness of our proposal through the consistent improvement over various scenarios.