# Implicit field learning for unsupervised anomaly detection in medical images

arXiv: https://arxiv.org/abs/2106.05214 · HTML: https://mlsanity.com/paper/2106.05214/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 16 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 11 of 11)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [Autoencoders for Unsupervised Anomaly Segmentation in Brain MR Images: A Comparative Study](https://mlsanity.com/paper/2004.03271/) (2020)
- [Unsupervised Anomaly Localization using Variational Auto-Encoders](https://mlsanity.com/paper/1907.02796/) (2019)
- [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)
- [Anomaly detection through latent space restoration using vector-quantized variational autoencoders](https://mlsanity.com/paper/2012.06765/) (2020)
- [Detecting Outliers with Foreign Patch Interpolation](https://mlsanity.com/paper/2011.04197/) (2020)

## Built on by (most cited first, 17 of 17)

- [Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields](https://mlsanity.com/paper/2309.03185/) (2023)
- [SQUID: Deep Feature In-Painting for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2111.13495/) (2021)
- [MedIAnomaly: A comparative study of anomaly detection in medical images](https://mlsanity.com/paper/2404.04518/) (2024)
- [AutoRG-Brain: Grounded Report Generation for Brain MRI](https://mlsanity.com/paper/2407.16684/) (2024)
- [I-MedSAM: Implicit Medical Image Segmentation with Segment Anything](https://mlsanity.com/paper/2311.17081/) (2023)
- [Exploiting Structural Consistency of Chest Anatomy for Unsupervised Anomaly Detection in Radiography Images](https://mlsanity.com/paper/2403.08689/) (2024)
- [Self-supervised Tumor Segmentation through Layer Decomposition](https://mlsanity.com/paper/2109.03230/) (2021)
- [Implicit U-Net for volumetric medical image segmentation](https://mlsanity.com/paper/2206.15217/) (2022)
- [AutoPaint: A Self-Inpainting Method for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2305.12358/) (2023)
- [Position-Guided Prompt Learning for Anomaly Detection in Chest X-Rays](https://mlsanity.com/paper/2405.11976/) (2024)
- [ASC-Net: Unsupervised Medical Anomaly Segmentation Using an Adversarial-based Selective Cutting Network](https://mlsanity.com/paper/2112.09135/) (2021)
- [Unsupervised Brain Tumor Segmentation with Image-based Prompts](https://mlsanity.com/paper/2304.01472/) (2023)
- [Weakly Supervised Anomaly Detection for Chest X-Ray Image](https://mlsanity.com/paper/2311.09642/) (2023)
- [Spatial-aware Attention Generative Adversarial Network for Semi-supervised Anomaly Detection in Medical Image](https://mlsanity.com/paper/2405.12872/) (2024)
- [Unsupervised Anomaly Detection on Implicit Shape representations for Sarcopenia Detection](https://mlsanity.com/paper/2502.09088/) (2025)
- [Iterative Deployment Exposure for Unsupervised Out-of-Distribution Detection](https://mlsanity.com/paper/2406.02327/) (2024)
- [SP-Mamba: Spatial-Perception State Space Model for Unsupervised Medical Anomaly Detection](https://mlsanity.com/paper/2507.19076/) (2025)

## Abstract (arXiv)

We propose a novel unsupervised out-of-distribution detection method for medical images based on implicit fields image representations. In our approach, an auto-decoder feed-forward neural network learns the distribution of healthy images in the form of a mapping between spatial coordinates and probabilities over a proxy for tissue types. At inference time, the learnt distribution is used to retrieve, from a given test image, a restoration, i.e. an image maximally consistent with the input one but belonging to the healthy distribution. Anomalies are localized using the voxel-wise probability predicted by our model for the restored image. We tested our approach in the task of unsupervised localization of gliomas on brain MR images and compared it to several other VAE-based anomaly detection methods. Results show that the proposed technique substantially outperforms them (average DICE 0.640 vs 0.518 for the best performing VAE-based alternative) while also requiring considerably less computing time.