Curved Geometric Networks for Visual Anomaly Recognition.

Area of Science:

• Computer Vision
• Machine Learning
• Data Science

Background:

• Latent embeddings are crucial for understanding data distribution, typically in Euclidean spaces.
• Curved spaces (spherical, hyperbolic) may offer richer structural information for improved data representation.
• Analyzing anomalous, open-set, or out-of-distribution (OOD) data remains a challenge.

Purpose of the Study:

• To investigate the benefits of curved embedding spaces for anomaly detection.
• To develop novel methods for analyzing anomalous and OOD data using geometric constraints.
• To enhance the discriminative power of representations for complex data analysis.

Main Methods:

• Utilizing embeddings in spherical, hyperbolic, or mixed-curvature spaces.
• Formulating anomaly score functions tailored for curved embeddings.
• Proposing geometric-in-one (GiO) and geometric-in-two (GiT) modules for Euclidean classifiers.
• Integrating geometric modules to compute anomaly scores from curved embeddings.

Main Results:

• Consistent improvements observed across diverse visual recognition tasks.
• Demonstrated effectiveness in multiclass and one-class OOD detection.
• Showcased efficacy in multiclass and one-class anomaly segmentation.
• Empirical validation of the proposed geometric approaches.

Conclusions:

• Curved embedding spaces provide significant advantages for anomaly detection and OOD analysis.
• The proposed GiO and GiT models offer a flexible and effective approach to incorporate geometric constraints.
• This work advances the state-of-the-art in visual recognition by leveraging non-Euclidean geometry.