# Capturing Longitudinal Changes in Brain Morphology Using Temporally Parameterized Neural Displacement Fields

arXiv: https://arxiv.org/abs/2504.09514 · HTML: https://mlsanity.com/paper/2504.09514/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 51 references that are in the map.
- First posted on arXiv 13 Apr 2025.

## Builds on (most cited first, 21 of 21)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [A Probabilistic U-Net for Segmentation of Ambiguous Images](https://mlsanity.com/paper/1806.05034/) (2018)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [A Deep Learning Framework for Unsupervised Affine and Deformable Image Registration](https://mlsanity.com/paper/1809.06130/) (2018)
- [Learning Conditional Deformable Templates with Convolutional Networks](https://mlsanity.com/paper/1908.02738/) (2019)
- [Conditional Deformable Image Registration with Convolutional Neural Network](https://mlsanity.com/paper/2106.12673/) (2021)
- [Learning the Effect of Registration Hyperparameters with HyperMorph](https://mlsanity.com/paper/2203.16680/) (2022)
- [Local Deep Implicit Functions for 3D Shape](https://mlsanity.com/paper/1912.06126/) (2019)
- [Robust deformable image registration using cycle-consistent implicit representations](https://mlsanity.com/paper/2310.01934/) (2023)
- [Limitations of Out-of-Distribution Detection in 3D Medical Image Segmentation](https://mlsanity.com/paper/2306.13528/) (2023)
- [A Deep Network for Joint Registration and Reconstruction of Images with Pathologies](https://mlsanity.com/paper/2008.07628/) (2020)
- [TLRN: Temporal Latent Residual Networks For Large Deformation Image Registration](https://mlsanity.com/paper/2407.11219/) (2024)
- [NODER: Image Sequence Regression Based on Neural Ordinary Differential Equations](https://mlsanity.com/paper/2407.13241/) (2024)
- [Image registration of low signal-to-noise cryo-STEM data](https://mlsanity.com/paper/1710.09281/) (2017)
- [Longitudinal Image Registration with Temporal-order and Subject-specificity Discrimination](https://mlsanity.com/paper/2008.13002/) (2020)
- [HyperPredict: Estimating Hyperparameter Effects for Instance-Specific Regularization in Deformable Image Registration](https://mlsanity.com/paper/2403.02069/) (2024)

## Built on by (most cited first, 3 of 3)

- [Semi-disentangled spatiotemporal implicit neural representations of longitudinal neuroimaging data for trajectory classification](https://mlsanity.com/paper/2510.09936/) (2025)
- [HULFSynth : An INR based Super-Resolution and Ultra Low-Field MRI Synthesis via Contrast factor estimation](https://mlsanity.com/paper/2511.14897/) (2025)
- [Modelling Geographic Atrophy Progression using Implicit Neural Representations](https://mlsanity.com/paper/2608.10807/) (2026)

## Abstract (arXiv)

Longitudinal image registration enables studying temporal changes in brain morphology which is useful in applications where monitoring the growth or atrophy of specific structures is important. However this task is challenging due to; noise/artifacts in the data and quantifying small anatomical changes between sequential scans. We propose a novel longitudinal registration method that models structural changes using temporally parameterized neural displacement fields. Specifically, we implement an implicit neural representation (INR) using a multi-layer perceptron that serves as a continuous coordinate-based approximation of the deformation field at any time point. In effect, for any N scans of a particular subject, our model takes as input a 3D spatial coordinate location x, y, z and a corresponding temporal representation t and learns to describe the continuous morphology of structures for both observed and unobserved points in time. Furthermore, we leverage the analytic derivatives of the INR to derive a new regularization function that enforces monotonic rate of change in the trajectory of the voxels, which is shown to provide more biologically plausible patterns. We demonstrate the effectiveness of our method on 4D brain MR registration.