# Heteroscedastic Uncertainty Estimation Framework for Unsupervised Registration

arXiv: https://arxiv.org/abs/2312.00836 · HTML: https://mlsanity.com/paper/2312.00836/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 1 Dec 2023.

## Builds on (most cited first, 19 of 19)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Deep Learning for Segmentation using an Open Large-Scale Dataset in 2D Echocardiography](https://mlsanity.com/paper/1908.06948/) (2019)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [On the uncertainty of self-supervised monocular depth estimation](https://mlsanity.com/paper/2005.06209/) (2020)
- [SynthMorph: learning contrast-invariant registration without acquired images](https://mlsanity.com/paper/2004.10282/) (2020)
- [Estimating and Exploiting the Aleatoric Uncertainty in Surface Normal Estimation](https://mlsanity.com/paper/2109.09881/) (2021)
- [Learning Accurate Dense Correspondences and When to Trust Them](https://mlsanity.com/paper/2101.01710/) (2021)
- [Stochastic Segmentation Networks: Modelling Spatially Correlated Aleatoric Uncertainty](https://mlsanity.com/paper/2006.06015/) (2020)
- [HyperMorph: Amortized Hyperparameter Learning for Image Registration](https://mlsanity.com/paper/2101.01035/) (2021)
- [XMorpher: Full Transformer for Deformable Medical Image Registration via Cross Attention](https://mlsanity.com/paper/2206.07349/) (2022)
- [Bilateral Cyclic Constraint and Adaptive Regularization for Unsupervised Monocular Depth Prediction](https://mlsanity.com/paper/1903.07309/) (2019)
- [An Adaptive Framework for Learning Unsupervised Depth Completion](https://mlsanity.com/paper/2106.03010/) (2021)
- [Fully Automated Left Atrium Segmentation from Anatomical Cine Long-axis MRI Sequences using Deep Convolutional Neural Network with Unscented Kalman Filter](https://mlsanity.com/paper/2009.13627/) (2020)
- [Learning correspondences of cardiac motion from images using biomechanics-informed modeling](https://mlsanity.com/paper/2209.00726/) (2022)
- [Adaptive Regularization of Some Inverse Problems in Image Analysis](https://mlsanity.com/paper/1705.03350/) (2017)
- [A Comparative Study for Non-rigid Image Registration and Rigid Image Registration](https://mlsanity.com/paper/2001.03831/) (2020)
- [A Bayesian Heteroscedastic GLM with Application to fMRI Data with Motion Spikes](https://mlsanity.com/paper/1612.00690/) (2016)

## Built on by (most cited first, 14 of 14)

- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [Adapting Vision Foundation Models for Real-time Ultrasound Image Segmentation](https://mlsanity.com/paper/2503.24368/) (2025)
- [Extending Foundational Monocular Depth Estimators to Fisheye Cameras with Calibration Tokens](https://mlsanity.com/paper/2508.04928/) (2025)
- [Hierarchical Uncertainty Estimation for Learning-based Registration in Neuroimaging](https://mlsanity.com/paper/2410.09299/) (2024)
- [ETA: Energy-based Test-time Adaptation for Depth Completion](https://mlsanity.com/paper/2508.05989/) (2025)
- [Encoder-Only Image Registration](https://mlsanity.com/paper/2509.00451/) (2025)
- [Uncertainty Estimation for Pretrained Medical Image Registration Models via Transformation Equivariance](https://mlsanity.com/paper/2509.23355/) (2025)
- [WaveDiT: Distribution-Aware Wavelet Flow Matching for Efficient 3D Brain MRI Synthesis](https://mlsanity.com/paper/2606.08670/) (2026)
- [Triangular Consistency as a Universal Constraint for Learning Optical Flow](https://mlsanity.com/paper/2606.19938/) (2026)
- [VisTa3D: A Dataset and Benchmark for Thin Object Reconstruction from Vision, Tactile, and 3D Point Clouds](https://mlsanity.com/paper/2608.20740/) (2026)
- [Learning Correlation-aware Aleatoric Uncertainty for 3D Hand Pose Estimation](https://mlsanity.com/paper/2509.01242/) (2025)
- [Adaptive Conditional Contrast-Agnostic Deformable Image Registration with Uncertainty Estimation](https://mlsanity.com/paper/2601.05981/) (2026)
- [Pareto-Guided Optimization for Uncertainty-Aware Medical Image Segmentation](https://mlsanity.com/paper/2601.19365/) (2026)
- [Recursive Uncertainty-Gated Image Registration for Learning-based Algorithms](https://mlsanity.com/paper/2609.28081/) (2026)

## Abstract (arXiv)

Deep learning methods for unsupervised registration often rely on objectives that assume a uniform noise level across the spatial domain (e.g. mean-squared error loss), but noise distributions are often heteroscedastic and input-dependent in real-world medical images. Thus, this assumption often leads to degradation in registration performance, mainly due to the undesired influence of noise-induced outliers. To mitigate this, we propose a framework for heteroscedastic image uncertainty estimation that can adaptively reduce the influence of regions with high uncertainty during unsupervised registration. The framework consists of a collaborative training strategy for the displacement and variance estimators, and a novel image fidelity weighting scheme utilizing signal-to-noise ratios. Our approach prevents the model from being driven away by spurious gradients caused by the simplified homoscedastic assumption, leading to more accurate displacement estimation. To illustrate its versatility and effectiveness, we tested our framework on two representative registration architectures across three medical image datasets. Our method consistently outperforms baselines and produces sensible uncertainty estimates. The code is publicly available at urlhttps://voldemort108x.github.io/heterouncertainty/.