# Iterative energy-based projection on a normal data manifold for anomaly localization

arXiv: https://arxiv.org/abs/2002.03734 · HTML: https://mlsanity.com/paper/2002.03734/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2020.

## Built on by (most cited first, 30 of 47)

- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [A Unified Model for Multi-class Anomaly Detection](https://mlsanity.com/paper/2206.03687/) (2022)
- [Deep Industrial Image Anomaly Detection: A Survey](https://mlsanity.com/paper/2301.11514/) (2023)
- [OpenGAN: Open-Set Recognition via Open Data Generation](https://mlsanity.com/paper/2104.02939/) (2021)
- [Deep Learning for Unsupervised Anomaly Localization in Industrial Images: A Survey](https://mlsanity.com/paper/2207.10298/) (2022)
- [Deep One-Class Classification via Interpolated Gaussian Descriptor](https://mlsanity.com/paper/2101.10043/) (2021)
- [IM-IAD: Industrial Image Anomaly Detection Benchmark in Manufacturing](https://mlsanity.com/paper/2301.13359/) (2023)
- [Prototypical Residual Networks for Anomaly Detection and Localization](https://mlsanity.com/paper/2212.02031/) (2022)
- [DiffusionAD: Norm-guided One-step Denoising Diffusion for Anomaly Detection](https://mlsanity.com/paper/2303.08730/) (2023)
- [Self-Supervised Masking for Unsupervised Anomaly Detection and Localization](https://mlsanity.com/paper/2205.06568/) (2022)
- [ADTR: Anomaly Detection Transformer with Feature Reconstruction](https://mlsanity.com/paper/2209.01816/) (2022)
- [Industrial Anomaly Detection with Domain Shift: A Real-world Dataset and Masked Multi-scale Reconstruction](https://mlsanity.com/paper/2304.02216/) (2023)
- [Constrained unsupervised anomaly segmentation](https://mlsanity.com/paper/2203.01671/) (2022)
- [Contextual Affinity Distillation for Image Anomaly Detection](https://mlsanity.com/paper/2307.03101/) (2023)
- [Curved Geometric Networks for Visual Anomaly Recognition](https://mlsanity.com/paper/2208.01188/) (2022)
- [Energy-Based Test Sample Adaptation for Domain Generalization](https://mlsanity.com/paper/2302.11215/) (2023)
- [Unsupervised Two-Stage Anomaly Detection](https://mlsanity.com/paper/2103.11671/) (2021)
- [AnomalyHop: An SSL-based Image Anomaly Localization Method](https://mlsanity.com/paper/2105.03797/) (2021)
- [Visual Anomaly Detection for Images: A Survey](https://mlsanity.com/paper/2109.13157/) (2021)
- [A Survey of Visual Sensory Anomaly Detection](https://mlsanity.com/paper/2202.07006/) (2022)
- [Siamese Transition Masked Autoencoders as Uniform Unsupervised Visual Anomaly Detector](https://mlsanity.com/paper/2211.00349/) (2022)
- [Normal Reference Attention and Defective Feature Perception Network for Surface Defect Detection](https://mlsanity.com/paper/2211.10060/) (2022)
- [AI-based Anomaly Detection for Clinical-Grade Histopathological Diagnostics](https://mlsanity.com/paper/2406.14866/) (2024)
- [Energy-Inspired Self-Supervised Pretraining for Vision Models](https://mlsanity.com/paper/2302.01384/) (2023)
- [Statistical Test for Anomaly Detections by Variational Auto-Encoders](https://mlsanity.com/paper/2402.03724/) (2024)
- [UP-CrackNet: Unsupervised Pixel-Wise Road Crack Detection via Adversarial Image Restoration](https://mlsanity.com/paper/2401.15647/) (2024)
- [AnomalySD: Few-Shot Multi-Class Anomaly Detection with Stable Diffusion Model](https://mlsanity.com/paper/2408.01960/) (2024)
- [Data Invariants to Understand Unsupervised Out-of-Distribution Detection](https://mlsanity.com/paper/2111.13362/) (2021)
- [DMAD: Dual Memory Bank for Real-World Anomaly Detection](https://mlsanity.com/paper/2403.12362/) (2024)
- [Unsupervised Anomaly Detection via Masked Diffusion Posterior Sampling](https://mlsanity.com/paper/2404.17900/) (2024)

## Abstract (arXiv)

Autoencoder reconstructions are widely used for the task of unsupervised anomaly localization. Indeed, an autoencoder trained on normal data is expected to only be able to reconstruct normal features of the data, allowing the segmentation of anomalous pixels in an image via a simple comparison between the image and its autoencoder reconstruction. In practice however, local defects added to a normal image can deteriorate the whole reconstruction, making this segmentation challenging. To tackle the issue, we propose in this paper a new approach for projecting anomalous data on a autoencoder-learned normal data manifold, by using gradient descent on an energy derived from the autoencoder's loss function. This energy can be augmented with regularization terms that model priors on what constitutes the user-defined optimal projection. By iteratively updating the input of the autoencoder, we bypass the loss of high-frequency information caused by the autoencoder bottleneck. This allows to produce images of higher quality than classic reconstructions. Our method achieves state-of-the-art results on various anomaly localization datasets. It also shows promising results at an inpainting task on the CelebA dataset.