# Constrained unsupervised anomaly segmentation

arXiv: https://arxiv.org/abs/2203.01671 · HTML: https://mlsanity.com/paper/2203.01671/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 54 references that are in the map.
- First posted on arXiv 3 Mar 2022.

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Attention-based Deep Multiple Instance Learning](https://mlsanity.com/paper/1802.04712/) (2018)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [Identifying the Best Machine Learning Algorithms for Brain Tumor Segmentation, Progression Assessment, and Overall Survival Prediction in the BRATS Challenge](https://mlsanity.com/paper/1811.02629/) (2018)
- [Uninformed Students: Student-Teacher Anomaly Detection with Discriminative Latent Embeddings](https://mlsanity.com/paper/1911.02357/) (2019)
- [Improving Unsupervised Defect Segmentation by Applying Structural Similarity to Autoencoders](https://mlsanity.com/paper/1807.02011/) (2018)
- [Latent Space Autoregression for Novelty Detection](https://mlsanity.com/paper/1807.01653/) (2018)
- [Autoencoders for Unsupervised Anomaly Segmentation in Brain MR Images: A Comparative Study](https://mlsanity.com/paper/2004.03271/) (2020)
- [Deep Autoencoding Models for Unsupervised Anomaly Segmentation in Brain MR Images](https://mlsanity.com/paper/1804.04488/) (2018)
- [Towards Visually Explaining Variational Autoencoders](https://mlsanity.com/paper/1911.07389/) (2019)
- [Constrained Convolutional Neural Networks for Weakly Supervised Segmentation](https://mlsanity.com/paper/1506.03648/) (2015)
- [Prior-aware Neural Network for Partially-Supervised Multi-Organ Segmentation](https://mlsanity.com/paper/1904.06346/) (2019)
- [Unsupervised Detection of Lesions in Brain MRI using constrained adversarial auto-encoders](https://mlsanity.com/paper/1806.04972/) (2018)
- [Unsupervised Lesion Detection via Image Restoration with a Normative Prior](https://mlsanity.com/paper/2005.00031/) (2020)
- [Context-encoding Variational Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1812.05941/) (2018)
- [Constrained-CNN losses for weakly supervised segmentation](https://mlsanity.com/paper/1805.04628/) (2018)
- [Constrained Deep Weak Supervision for Histopathology Image Segmentation](https://mlsanity.com/paper/1701.00794/) (2017)
- [Iterative energy-based projection on a normal data manifold for anomaly localization](https://mlsanity.com/paper/2002.03734/) (2020)
- [An Adversarial Learning Approach to Medical Image Synthesis for Lesion Detection](https://mlsanity.com/paper/1810.10850/) (2018)
- [Constrained Deep Networks: Lagrangian Optimization via Log-Barrier Extensions](https://mlsanity.com/paper/1904.04205/) (2019)
- [Intracranial Hemorrhage Segmentation Using Deep Convolutional Model](https://mlsanity.com/paper/1910.08643/) (2019)
- [Training Adversarial Discriminators for Cross-channel Abnormal Event Detection in Crowds](https://mlsanity.com/paper/1706.07680/) (2017)
- [Curriculum semi-supervised segmentation](https://mlsanity.com/paper/1904.05236/) (2019)
- [Challenging Current Semi-Supervised Anomaly Segmentation Methods for Brain MRI](https://mlsanity.com/paper/2109.06023/) (2021)
- [Learning to Play in a Day: Faster Deep Reinforcement Learning by Optimality Tightening](https://mlsanity.com/paper/1611.01606/) (2016)
- [AVID: Adversarial Visual Irregularity Detection](https://mlsanity.com/paper/1805.09521/) (2018)

## Built on by (most cited first, 19 of 19)

- [Patched Diffusion Models for Unsupervised Anomaly Detection in Brain MRI](https://mlsanity.com/paper/2303.03758/) (2023)
- [MedIAnomaly: A comparative study of anomaly detection in medical images](https://mlsanity.com/paper/2404.04518/) (2024)
- [Unsupervised Anomaly Detection in Medical Images Using Masked Diffusion Model](https://mlsanity.com/paper/2305.19867/) (2023)
- [Unsupervised Pathology Detection: A Deep Dive Into the State of the Art](https://mlsanity.com/paper/2303.00609/) (2023)
- [AutoRG-Brain: Grounded Report Generation for Brain MRI](https://mlsanity.com/paper/2407.16684/) (2024)
- [Guided Reconstruction with Conditioned Diffusion Models for Unsupervised Anomaly Detection in Brain MRIs](https://mlsanity.com/paper/2312.04215/) (2023)
- [ICH-SCNet: Intracerebral Hemorrhage Segmentation and Prognosis Classification Network Using CLIP-guided SAM mechanism](https://mlsanity.com/paper/2411.04656/) (2024)
- [CardiacNet: Learning to Reconstruct Abnormalities for Cardiac Disease Assessment from Echocardiogram Videos](https://mlsanity.com/paper/2410.20769/) (2024)
- [Correcting Deviations from Normality: A Reformulated Diffusion Model for Multi-Class Unsupervised Anomaly Detection](https://mlsanity.com/paper/2503.19357/) (2025)
- [MAD-AD: Masked Diffusion for Unsupervised Brain Anomaly Detection](https://mlsanity.com/paper/2502.16943/) (2025)
- [DISYRE: Diffusion-Inspired SYnthetic REstoration for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2311.15453/) (2023)
- [REFLECT: Rectified Flows for Efficient Brain Anomaly Correction Transport](https://mlsanity.com/paper/2508.02889/) (2025)
- [CLISC: Bridging clip and sam by enhanced cam for unsupervised brain tumor segmentation](https://mlsanity.com/paper/2501.16246/) (2025)
- [MCDDPM: Multichannel Conditional Denoising Diffusion Model for Unsupervised Anomaly Detection in Brain MRI](https://mlsanity.com/paper/2409.19623/) (2024)
- [Unsupervised Brain Tumor Segmentation with Image-based Prompts](https://mlsanity.com/paper/2304.01472/) (2023)
- [Quantitative Benchmarking of Anomaly Detection Methods in Digital Pathology](https://mlsanity.com/paper/2506.19234/) (2025)
- [Attention to detail: inter-resolution knowledge distillation](https://mlsanity.com/paper/2401.06010/) (2024)
- [PathoSCOPE: Few-Shot Pathology Detection via Self-Supervised Contrastive Learning and Pathology-Informed Synthetic Embeddings](https://mlsanity.com/paper/2505.17614/) (2025)
- [Unsupervised Anomaly Detection in Brain MRI via Disentangled Anatomy Learning](https://mlsanity.com/paper/2512.21924/) (2025)

## Abstract (arXiv)

Current unsupervised anomaly localization approaches rely on generative models to learn the distribution of normal images, which is later used to identify potential anomalous regions derived from errors on the reconstructed images. However, a main limitation of nearly all prior literature is the need of employing anomalous images to set a class-specific threshold to locate the anomalies. This limits their usability in realistic scenarios, where only normal data is typically accessible. Despite this major drawback, only a handful of works have addressed this limitation, by integrating supervision on attention maps during training. In this work, we propose a novel formulation that does not require accessing images with abnormalities to define the threshold. Furthermore, and in contrast to very recent work, the proposed constraint is formulated in a more principled manner, leveraging well-known knowledge in constrained optimization. In particular, the equality constraint on the attention maps in prior work is replaced by an inequality constraint, which allows more flexibility. In addition, to address the limitations of penalty-based functions we employ an extension of the popular log-barrier methods to handle the constraint. Last, we propose an alternative regularization term that maximizes the Shannon entropy of the attention maps, reducing the amount of hyperparameters of the proposed model. Comprehensive experiments on two publicly available datasets on brain lesion segmentation demonstrate that the proposed approach substantially outperforms relevant literature, establishing new state-of-the-art results for unsupervised lesion segmentation, and without the need to access anomalous images.