# Bayesian Atlas Building with Hierarchical Priors for Subject-specific Regularization

arXiv: https://arxiv.org/abs/2107.05698 · HTML: https://mlsanity.com/paper/2107.05698/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 32 references that are in the map.
- First posted on arXiv 12 Jul 2021.

## Builds on (most cited first, 1 of 1)

- [Temporal Registration in Application to In-utero MRI Time Series](https://mlsanity.com/paper/1903.02959/) (2019)

## Built on by (most cited first, 8 of 8)

- [SADIR: Shape-Aware Diffusion Models for 3D Image Reconstruction](https://mlsanity.com/paper/2309.03335/) (2023)
- [Geo-SIC: Learning Deformable Geometric Shapes in Deep Image Classifiers](https://mlsanity.com/paper/2210.13704/) (2022)
- [RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representations](https://mlsanity.com/paper/2305.12854/) (2023)
- [Conditional Deformable Image Registration with Spatially-Variant and Adaptive Regularization](https://mlsanity.com/paper/2303.10700/) (2023)
- [MetaMorph: Learning Metamorphic Image Transformation With Appearance Changes](https://mlsanity.com/paper/2303.04849/) (2023)
- [MGAug: Multimodal Geometric Augmentation in Latent Spaces of Image Deformations](https://mlsanity.com/paper/2312.13440/) (2023)
- [HyperPredict: Estimating Hyperparameter Effects for Instance-Specific Regularization in Deformable Image Registration](https://mlsanity.com/paper/2403.02069/) (2024)
- [Pro-t-VAE: Closed-Form Student's t Mixtures for Robust Prototype Discovery](https://mlsanity.com/paper/2610.14894/) (2026)

## Abstract (arXiv)

This paper presents a novel hierarchical Bayesian model for unbiased atlas building with subject-specific regularizations of image registration. We develop an atlas construction process that automatically selects parameters to control the smoothness of diffeomorphic transformation according to individual image data. To achieve this, we introduce a hierarchical prior distribution on regularization parameters that allows multiple penalties on images with various degrees of geometric transformations. We then treat the regularization parameters as latent variables and integrate them out from the model by using the Monte Carlo Expectation Maximization (MCEM) algorithm. Another advantage of our algorithm is that it eliminates the need for manual parameter tuning, which can be tedious and infeasible. We demonstrate the effectiveness of our model on 3D brain MR images. Experimental results show that our model provides a sharper atlas compared to the current atlas building algorithms with single-penalty regularizations. Our code is publicly available at https://github.com/jw4hv/HierarchicalBayesianAtlasBuild.