# NISF++: Geometrically-grounded implicit representations of 3D+time cardiac function from 2D short- and long-axis MR views

arXiv: https://arxiv.org/abs/2608.00752 · HTML: https://mlsanity.com/paper/2608.00752/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 1 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Spatial Functa: Scaling Functa to ImageNet Classification and Generation](https://mlsanity.com/paper/2302.03130/) (2023)
- [Image-GS: Content-Adaptive Image Representation via 2D Gaussians](https://mlsanity.com/paper/2407.01866/) (2024)
- [NISF: Neural Implicit Segmentation Functions](https://mlsanity.com/paper/2309.08643/) (2023)
- [Learning Shape Priors for Robust Cardiac MR Segmentation from Multi-view Images](https://mlsanity.com/paper/1907.09983/) (2019)
- [DeepMesh: Mesh-based Cardiac Motion Tracking using Deep Learning](https://mlsanity.com/paper/2309.14306/) (2023)
- [Learning Large-scale Neural Fields via Context Pruned Meta-Learning](https://mlsanity.com/paper/2302.00617/) (2023)
- [Whole Heart 3D+T Representation Learning Through Sparse 2D Cardiac MR Images](https://mlsanity.com/paper/2406.00329/) (2024)
- [Intensity-based 3D motion correction for cardiac MR images](https://mlsanity.com/paper/2404.00767/) (2024)

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

- [MRI-Guided Reslice-Refined Cross-Slice SDF Reconstruction of the Left Ventricle from Cardiac MRI with Sparse Axial Supervision](https://mlsanity.com/paper/2609.08148/) (2026)

## Abstract (arXiv)

Clinical acquisition in cardiac magnetic resonance (CMR) imaging involves obtaining cross-sectional planes of the heart along the radial and longitudinal directions. Despite these planes being 2D cross-sectional images of the heart, radiologists understand the 3D spatial and continuous temporal nature of the organ being imaged. The same can not be said about the conventional deep learning architectures used to process CMR images, which rely on in-plane and grid-based operations, and are hence unable to organically integrate information from all imaging planes. This paper builds upon previous work on neural implicit segmentation functions (NISF) to overcome unaddressed challenges in cardiac function modeling in the CMR domain. For a given subject, our architecture builds a shared 3D+time representations from all available acquisition planes regardless of orientation. By design, predictions along any imaging plane orientation are cross-sections of the same 3D representation, leading to spatio-temporal consistency across all slices. Moreover, our architecture makes the rotation and translation parameters of imaging planes learnable, allowing us to correct for the commonplace respiratory and patient motion between slice acquisitions under a rigid assumption. Furthermore, interpolation of intensities and segmentation can be performed in 4D at any desired resolution. We perform our study on a 120 subject sub-cohort of CMR imaging data from the UK-Biobank. Our in-plane segmentation performance is on-par with existing CMR segmentation methods and explore how the majority of failure cases arise from limitations in the ground-truth segmentation, for which our representations make predictions with better anatomical accuracy than its original training data. We also evaluate our motion-correction capabilities, displaying quantitative and qualitative improvements in slice alignment.