Anomaly as Non-Conformity via Training-Free Graph Laplacian Energy Minimization

2026-05-27

AI Summary

This work proposes ANoCo, a training-free image anomaly detection method under the setting where only normal samples are available. ANoCo constructs a cosine-similarity-weighted bipartite graph between query image patches and normal patches, explicitly removing edges between same-type nodes to prevent evidence dilution. The anomaly score is defined as the magnitude of feature updates required to satisfy normality constraints. Innovatively treating the graph Laplacian as an inconsistency operator, the method formulates a convex optimization problem anchored to known normal nodes and minimizes its energy to directly obtain anomaly scores from closed-form feature drifts—eliminating the need for learnable parameters, message passing, or sampling. Experiments demonstrate that ANoCo significantly outperforms existing approaches on standard benchmarks, achieving state-of-the-art image-level AUROC, stable localization maps, and enhanced robustness.

Abstract

Detecting subtle visual anomalies in images remains challenging, particularly when only normal samples are available a priori. Such unsupervised anomaly detection is typically solved by measuring feature similarity of a query patch to a memory of normal patches. However, similarity alone does not reveal how strongly a query patch violates the structure of the normal feature manifold. We propose a training-free Laplacian graph energy optimization formulation, named ANoCo that scores Anomaly by the cost of Non-Conformity of a query patch to align with a fixed normal manifold. For each query patch, we construct a bipartite query to normal graph weighted by cosine affinity, explicitly removing query-query and normal-normal edges to prevent evidence dilution. We formulate anomaly scoring as a convex Laplacian energy with anchored normal nodes, and solve in closed form. In particular, we do not use the optimized features themselves-the anomaly score is the magnitude of the update required to satisfy normality constraints, reframing the graph Laplacian as a non-conformity operator rather than a smoothing prior. The proposed method introduces no learnable parameters, message passing, or sampling, and has complexity comparable to a single linear solve. Across standard benchmarks, it delivers strong image-level AUROC, stable localization maps, and improved robustness over prior methods, demonstrating the effectiveness of using optimization-induced feature drift as anomaly measure.

Problem

• anomaly detection
• unsupervised learning
• graph Laplacian
• non-conformity
• visual anomalies

Innovation

• training-free
• graph Laplacian energy
• anomaly detection
• non-conformity scoring
• unsupervised learning