# Learning Volumetric Neural Deformable Models to Recover 3D Regional Heart Wall Motion from Multi-Planar Tagged MRI

arXiv: https://arxiv.org/abs/2411.15233 · HTML: https://mlsanity.com/paper/2411.15233/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 64 references that are in the map.
- First posted on arXiv 21 Nov 2024.

## Builds on (most cited first, 10 of 10)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [UTNet: A Hybrid Transformer Architecture for Medical Image Segmentation](https://mlsanity.com/paper/2107.00781/) (2021)
- [Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flows](https://mlsanity.com/paper/2007.10973/) (2020)
- [Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow](https://mlsanity.com/paper/2203.08652/) (2022)
- [DeepTag: An Unsupervised Deep Learning Method for Motion Tracking on Cardiac Tagging Magnetic Resonance Images](https://mlsanity.com/paper/2103.02772/) (2021)
- [Deep Implicit Statistical Shape Models for 3D Medical Image Delineation](https://mlsanity.com/paper/2104.02847/) (2021)
- [Neural Deformable Models for 3D Bi-Ventricular Heart Shape Reconstruction and Modeling from 2D Sparse Cardiac Magnetic Resonance Imaging](https://mlsanity.com/paper/2307.07693/) (2023)

## Built on by (most cited first, 1 of 1)

- [Learning Where to Look: Anatomical Grounding and Guided Attention for Cardiac MRI Vision-Language Models](https://mlsanity.com/paper/2609.39899/) (2026)

## Abstract (arXiv)

Multi-planar tagged MRI is the gold standard for regional heart wall motion evaluation. However, accurate recovery of the 3D true heart wall motion from a set of 2D apparent motion cues is challenging, due to incomplete sampling of the true motion and difficulty in information fusion from apparent motion cues observed on multiple imaging planes. To solve these challenges, we introduce a novel class of volumetric neural deformable models (upsilonNDMs). Our upsilonNDMs represent heart wall geometry and motion through a set of low-dimensional global deformation parameter functions and a diffeomorphic point flow regularized local deformation field. To learn such global and local deformation for 2D apparent motion mapping to 3D true motion, we design a hybrid point transformer, which incorporates both point cross-attention and self-attention mechanisms. While use of point cross-attention can learn to fuse 2D apparent motion cues into material point true motion hints, point self-attention hierarchically organised as an encoder-decoder structure can further learn to refine these hints and map them into 3D true motion. We have performed experiments on a large cohort of synthetic 3D regional heart wall motion dataset. The results demonstrated the high accuracy of our method for the recovery of dense 3D true motion from sparse 2D apparent motion cues. Project page is at https://github.com/DeepTag/VolumetricNeuralDeformableModels.