# Uncertainty Estimation for Heatmap-based Landmark Localization

arXiv: https://arxiv.org/abs/2203.02351 · HTML: https://mlsanity.com/paper/2203.02351/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 4 Mar 2022.

## Builds on (most cited first, 18 of 18)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Confidence Calibration and Predictive Uncertainty Estimation for Deep Medical Image Segmentation](https://mlsanity.com/paper/1911.13273/) (2019)
- [Exploring Uncertainty Measures in Deep Networks for Multiple Sclerosis Lesion Detection and Segmentation](https://mlsanity.com/paper/1808.01200/) (2018)
- [Integrating Spatial Configuration into Heatmap Regression Based CNNs for Landmark Localization](https://mlsanity.com/paper/1908.00748/) (2019)
- [Super-FAN: Integrated facial landmark localization and super-resolution of real-world low resolution faces in arbitrary poses with GANs](https://mlsanity.com/paper/1712.02765/) (2017)
- [QU-BraTS: MICCAI BraTS 2020 Challenge on Quantifying Uncertainty in Brain Tumor Segmentation - Analysis of Ranking Scores and Benchmarking Results](https://mlsanity.com/paper/2112.10074/) (2021)
- [An Attention-Guided Deep Regression Model for Landmark Detection in Cephalograms](https://mlsanity.com/paper/1906.07549/) (2019)
- [Deep Learning-Based Regression and Classification for Automatic Landmark Localization in Medical Images](https://mlsanity.com/paper/2007.05295/) (2020)
- [Quantized Densely Connected U-Nets for Efficient Landmark Localization](https://mlsanity.com/paper/1808.02194/) (2018)
- [Deep Geodesic Learning for Segmentation and Anatomical Landmarking](https://mlsanity.com/paper/1810.04021/) (2018)
- [Modeling Annotation Uncertainty with Gaussian Heatmaps in Landmark Localization](https://mlsanity.com/paper/2109.09533/) (2021)
- [Fast Multiple Landmark Localisation Using a Patch-based Iterative Network](https://mlsanity.com/paper/1806.06987/) (2018)
- [CNN-based Landmark Detection in Cardiac CTA Scans](https://mlsanity.com/paper/1804.04963/) (2018)

## Built on by (most cited first, 6 of 6)

- [Tensor-based Multimodal Learning for Prediction of Pulmonary Arterial Wedge Pressure from Cardiac MRI](https://mlsanity.com/paper/2303.07540/) (2023)
- [Reliable uncertainty quantification for 2D/3D anatomical landmark localization using multi-output conformal prediction](https://mlsanity.com/paper/2503.14106/) (2025)
- [Interpretable Multimodal Learning for Cardiovascular Hemodynamics Assessment](https://mlsanity.com/paper/2404.04718/) (2024)
- [Reliability of deep learning models for anatomical landmark detection: The role of inter-rater variability](https://mlsanity.com/paper/2411.17850/) (2024)
- [Uncertainty Propagation for Echocardiography Clinical Metric Estimation via Contour Sampling](https://mlsanity.com/paper/2502.12713/) (2025)
- [RBA-FE: A Robust Brain-Inspired Audio Feature Extractor for Depression Diagnosis](https://mlsanity.com/paper/2506.07118/) (2025)

## Abstract (arXiv)

Automatic anatomical landmark localization has made great strides by leveraging deep learning methods in recent years. The ability to quantify the uncertainty of these predictions is a vital component needed for these methods to be adopted in clinical settings, where it is imperative that erroneous predictions are caught and corrected. We propose Quantile Binning, a data-driven method to categorize predictions by uncertainty with estimated error bounds. Our framework can be applied to any continuous uncertainty measure, allowing straightforward identification of the best subset of predictions with accompanying estimated error bounds. We facilitate easy comparison between uncertainty measures by constructing two evaluation metrics derived from Quantile Binning. We compare and contrast three epistemic uncertainty measures (two baselines, and a proposed method combining aspects of the two), derived from two heatmap-based landmark localization model paradigms (U-Net and patch-based). We show results across three datasets, including a publicly available Cephalometric dataset. We illustrate how filtering out gross mispredictions caught in our Quantile Bins significantly improves the proportion of predictions under an acceptable error threshold. Finally, we demonstrate that Quantile Binning remains effective on landmarks with high aleatoric uncertainty caused by inherent landmark ambiguity, and offer recommendations on which uncertainty measure to use and how to use it. The code and data are available at https://github.com/schobs/qbin.