# Rethinking Structural Anomaly Detection: From Decision Boundaries to Projection Operators

arXiv: https://arxiv.org/abs/2606.15280 · HTML: https://mlsanity.com/paper/2606.15280/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 13 Jun 2026.

## Builds on (most cited first, 23 of 23)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [CutPaste: Self-Supervised Learning for Anomaly Detection and Localization](https://mlsanity.com/paper/2104.04015/) (2021)
- [DRAEM -- A discriminatively trained reconstruction embedding for surface anomaly detection](https://mlsanity.com/paper/2108.07610/) (2021)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [SPot-the-Difference Self-Supervised Pre-training for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2207.14315/) (2022)
- [Improving Unsupervised Defect Segmentation by Applying Structural Similarity to Autoencoders](https://mlsanity.com/paper/1807.02011/) (2018)
- [SimpleNet: A Simple Network for Image Anomaly Detection and Localization](https://mlsanity.com/paper/2303.15140/) (2023)
- [Gradient Magnitude Similarity Deviation: A Highly Efficient Perceptual Image Quality Index](https://mlsanity.com/paper/1308.3052/) (2013)
- [PANDA: Adapting Pretrained Features for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2010.05903/) (2020)
- [RealNet: A Feature Selection Network with Realistic Synthetic Anomaly for Anomaly Detection](https://mlsanity.com/paper/2403.05897/) (2024)
- [Inpainting Transformer for Anomaly Detection](https://mlsanity.com/paper/2104.13897/) (2021)
- [A Unified Anomaly Synthesis Strategy with Gradient Ascent for Industrial Anomaly Detection and Localization](https://mlsanity.com/paper/2407.09359/) (2024)
- [Variational Autoencoder with Learned Latent Structure](https://mlsanity.com/paper/2006.10597/) (2020)
- [Progressive Boundary Guided Anomaly Synthesis for Industrial Anomaly Detection](https://mlsanity.com/paper/2412.17458/) (2024)
- [Deep Unsupervised Clustering Using Mixture of Autoencoders](https://mlsanity.com/paper/1712.07788/) (2017)
- [Conditional diffusion models for guided anomaly detection in brain images using fluid-driven anomaly randomization](https://mlsanity.com/paper/2506.10233/) (2025)
- [Detecting Anomalous Faces with 'No Peeking' Autoencoders](https://mlsanity.com/paper/1802.05798/) (2018)
- [Partial Optimality of Dual Decomposition for MAP Inference in Pairwise MRFs](https://mlsanity.com/paper/1708.03314/) (2017)
- [Active anomaly detection based on deep one-class classification](https://mlsanity.com/paper/2309.09465/) (2023)
- [Optimizing for Measure of Performance in Max-Margin Parsing](https://mlsanity.com/paper/1709.01562/) (2017)

## Abstract (arXiv)

Most existing anomaly detection methods rely on estimating a probability density or learning an enclosing decision boundary, implicitly assuming that normal data occupies a region of non-zero volume in the ambient space. In contrast, structural anomaly detection considers data that lies near a low-dimensional manifold, creating a mismatch between the inductive bias of existing methods and the structure of the data, often resulting in degraded performance. To address this mismatch, we introduce a geometric perspective. Specifically, we learn a projection operator onto the manifold of normal samples and define a sample as anomalous if it is altered by this projection. This formulation naturally integrates the inductive bias of manifold-supported data and reframes anomaly detection in terms of a projection residual, thereby resolving issues arising from modeling degenerate distributions. Notably, it provides a unifying interpretation of reconstruction-based methods by explaining their success and failure in terms of projection quality. In particular, it explains the strong generalization ability of projection-aligned models as a consequence of contraction behavior toward the manifold. Moreover, by decoupling anomaly detection from probabilistic modeling, it reduces the tendency to misclassify rare but normal samples, a widely recognized limitation of existing approaches. Empirically, we demonstrate that projection-aligned methods achieve strong performance, outperforming boundary-based methods while improving upon existing reconstruction-based approaches.