# Modeling the Distribution of Normal Data in Pre-Trained Deep Features for Anomaly Detection

arXiv: https://arxiv.org/abs/2005.14140 · HTML: https://mlsanity.com/paper/2005.14140/

## Key facts

- Cited by 115 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2020.

## Built on by (most cited first, 30 of 115)

- [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)
- [Anomaly Detection via Reverse Distillation from One-Class Embedding](https://mlsanity.com/paper/2201.10703/) (2022)
- [CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12571/) (2021)
- [A Unified Model for Multi-class Anomaly Detection](https://mlsanity.com/paper/2206.03687/) (2022)
- [FastFlow: Unsupervised Anomaly Detection and Localization via 2D Normalizing Flows](https://mlsanity.com/paper/2111.07677/) (2021)
- [A Unified Survey on Anomaly, Novelty, Open-Set, and Out-of-Distribution Detection: Solutions and Future Challenges](https://mlsanity.com/paper/2110.14051/) (2021)
- [DeSTSeg: Segmentation Guided Denoising Student-Teacher for Anomaly Detection](https://mlsanity.com/paper/2211.11317/) (2022)
- [Deep Industrial Image Anomaly Detection: A Survey](https://mlsanity.com/paper/2301.11514/) (2023)
- [Fully Convolutional Cross-Scale-Flows for Image-based Defect Detection](https://mlsanity.com/paper/2110.02855/) (2021)
- [Asymmetric Student-Teacher Networks for Industrial Anomaly Detection](https://mlsanity.com/paper/2210.07829/) (2022)
- [Natural Synthetic Anomalies for Self-Supervised Anomaly Detection and Localization](https://mlsanity.com/paper/2109.15222/) (2021)
- [DSR -- A dual subspace re-projection network for surface anomaly detection](https://mlsanity.com/paper/2208.01521/) (2022)
- [Divide-and-Assemble: Learning Block-wise Memory for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2107.13118/) (2021)
- [Omni-frequency Channel-selection Representations for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2203.00259/) (2022)
- [Explicit Boundary Guided Semi-Push-Pull Contrastive Learning for Supervised Anomaly Detection](https://mlsanity.com/paper/2207.01463/) (2022)
- [UIA-ViT: Unsupervised Inconsistency-Aware Method based on Vision Transformer for Face Forgery Detection](https://mlsanity.com/paper/2210.12752/) (2022)
- [ReContrast: Domain-Specific Anomaly Detection via Contrastive Reconstruction](https://mlsanity.com/paper/2306.02602/) (2023)
- [Exploring Plain ViT Reconstruction for Multi-class Unsupervised Anomaly Detection](https://mlsanity.com/paper/2312.07495/) (2023)
- [Multimodal Industrial Anomaly Detection by Crossmodal Feature Mapping](https://mlsanity.com/paper/2312.04521/) (2023)
- [Focus Your Distribution: Coarse-to-Fine Non-Contrastive Learning for Anomaly Detection and Localization](https://mlsanity.com/paper/2110.04538/) (2021)
- [Focus the Discrepancy: Intra- and Inter-Correlation Learning for Image Anomaly Detection](https://mlsanity.com/paper/2308.02983/) (2023)
- [AdaptCLIP: Adapting CLIP for Universal Visual Anomaly Detection](https://mlsanity.com/paper/2505.09926/) (2025)
- [Semi-orthogonal Embedding for Efficient Unsupervised Anomaly Segmentation](https://mlsanity.com/paper/2105.14737/) (2021)
- [SplatPose & Detect: Pose-Agnostic 3D Anomaly Detection](https://mlsanity.com/paper/2404.06832/) (2024)
- [ResAD: A Simple Framework for Class Generalizable Anomaly Detection](https://mlsanity.com/paper/2410.20047/) (2024)
- [LogicAD: Explainable Anomaly Detection via VLM-based Text Feature Extraction](https://mlsanity.com/paper/2501.01767/) (2025)
- [Self-Supervised Anomaly Detection in Computer Vision and Beyond: A Survey and Outlook](https://mlsanity.com/paper/2205.05173/) (2022)
- [Unsupervised Pathology Detection: A Deep Dive Into the State of the Art](https://mlsanity.com/paper/2303.00609/) (2023)

## Abstract (arXiv)

Anomaly Detection (AD) in images is a fundamental computer vision problem and refers to identifying images and image substructures that deviate significantly from the norm. Popular AD algorithms commonly try to learn a model of normality from scratch using task specific datasets, but are limited to semi-supervised approaches employing mostly normal data due to the inaccessibility of anomalies on a large scale combined with the ambiguous nature of anomaly appearance. We follow an alternative approach and demonstrate that deep feature representations learned by discriminative models on large natural image datasets are well suited to describe normality and detect even subtle anomalies in a transfer learning setting. Our model of normality is established by fitting a multivariate Gaussian (MVG) to deep feature representations of classification networks trained on ImageNet using normal data only. By subsequently applying the Mahalanobis distance as the anomaly score we outperform the current state of the art on the public MVTec AD dataset, achieving an AUROC value of 95.8 ± 1.2 (mean ± SEM) over all 15 classes. We further investigate why the learned representations are discriminative to the AD task using Principal Component Analysis. We find that the principal components containing little variance in normal data are the ones crucial for discriminating between normal and anomalous instances. This gives a possible explanation to the often sub-par performance of AD approaches trained from scratch using normal data only. By selectively fitting a MVG to these most relevant components only, we are able to further reduce model complexity while retaining AD performance. We also investigate setting the working point by selecting acceptable False Positive Rate thresholds based on the MVG assumption. Code available at https://github.com/ORippler/gaussian-ad-mvtec