Noise & pattern: identity-anchored Tikhonov regularization for robust structural anomaly detection

TL;DR

This paper introduces a novel self-supervised autoencoder with structured corruption and Gaussian noise regularization, achieving state-of-the-art anomaly detection in industrial images by stabilizing reconstructions.

Contribution

It proposes a new identity-anchored Tikhonov regularization method that enhances anomaly detection by stabilizing autoencoder reconstructions with structured perturbations and Gaussian noise.

Findings

Achieves 99.9% I-AUROC on MVTec AD benchmark.

Outperforms existing methods in structural anomaly detection.

Validates the theoretical framework with practical results.

Abstract

Anomaly detection plays a pivotal role in automated industrial inspection, aiming to identify subtle or rare defects in otherwise uniform visual patterns. As collecting representative examples of all possible anomalies is infeasible, we tackle structural anomaly detection using a self-supervised autoencoder that learns to repair corrupted inputs. To this end, we introduce a corruption model that injects artificial disruptions into training images to mimic structural defects. While reminiscent of denoising autoencoders, our approach differs in two key aspects. First, instead of unstructured i.i.d.\ noise, we apply structured, spatially coherent perturbations that make the task a hybrid of segmentation and inpainting. Second, and counterintuitively, we add and preserve Gaussian noise on top of the occlusions, which acts as a Tikhonov regularizer anchoring the Jacobian of the reconstruction function toward identity. This identity-anchored regularization stabilizes reconstruction and further improves both detection and segmentation accuracy. On the MVTec AD benchmark, our method achieves state-of-the-art results (I/P-AUROC: 99.9/99.4), supporting our theoretical framework and demonstrating its practical relevance for automatic inspection.