# Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slices

arXiv: https://arxiv.org/abs/2303.05286 · HTML: https://mlsanity.com/paper/2303.05286/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 8 Mar 2023.

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

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Convolutional Mesh Regression for Single-Image Human Shape Reconstruction](https://mlsanity.com/paper/1905.03244/) (2019)
- [Pix3D: Dataset and Methods for Single-Image 3D Shape Modeling](https://mlsanity.com/paper/1804.04610/) (2018)
- [Image-based 3D Object Reconstruction: State-of-the-Art and Trends in the Deep Learning Era](https://mlsanity.com/paper/1906.06543/) (2019)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence](https://mlsanity.com/paper/2006.07882/) (2020)
- [A Diffusion Model Predicts 3D Shapes from 2D Microscopy Images](https://mlsanity.com/paper/2208.14125/) (2022)
- [Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstruction](https://mlsanity.com/paper/2203.01703/) (2022)
- [The Weighted Euler Curve Transform for Shape and Image Analysis](https://mlsanity.com/paper/2004.11128/) (2020)
- [Persistent Homology with Improved Locality Information for more Effective Delineation](https://mlsanity.com/paper/2110.06295/) (2021)

## Built on by (most cited first, 6 of 6)

- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Differentiable Euler Characteristic Transforms for Shape Classification](https://mlsanity.com/paper/2310.07630/) (2023)
- [Geometry-Informed Neural Networks](https://mlsanity.com/paper/2402.14009/) (2024)
- [Point Cloud Synthesis Using Inner Product Transforms](https://mlsanity.com/paper/2410.18987/) (2024)
- [Reconstruction of three-dimensional shapes of normal and disease-related erythrocytes from partial observations using multi-fidelity neural networks](https://mlsanity.com/paper/2511.14962/) (2025)
- [Encoding the Euler Characteristic Transform](https://mlsanity.com/paper/2606.10824/) (2026)

## Abstract (arXiv)

The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which may lead to poor reconstructions as they ignore the structural properties of the shape. To tackle this, we propose a novel topological loss function based on the Euler Characteristic Transform. This loss can be used as an inductive bias to aid the optimization of any neural network toward better reconstructions in the regime of limited data. We show the effectiveness of the proposed loss function by incorporating it into SHAPR, a state-of-the-art shape reconstruction model, and test it on two benchmark datasets, viz., Red Blood Cells and Nuclei datasets. We also show a favourable property, namely injectivity and discuss the stability of the topological loss function based on the Euler Characteristic Transform.