# OReX: Object Reconstruction from Planar Cross-sections Using Neural Fields

arXiv: https://arxiv.org/abs/2211.12886 · HTML: https://mlsanity.com/paper/2211.12886/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 23 Nov 2022.

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [ReStyle: A Residual-Based StyleGAN Encoder via Iterative Refinement](https://mlsanity.com/paper/2104.02699/) (2021)
- [NeRF: Neural Radiance Field in 3D Vision: A Comprehensive Review (Updated Post-Gaussian Splatting)](https://mlsanity.com/paper/2210.00379/) (2022)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [ACORN: Adaptive Coordinate Networks for Neural Scene Representation](https://mlsanity.com/paper/2105.02788/) (2021)
- [Point2Mesh: A Self-Prior for Deformable Meshes](https://mlsanity.com/paper/2005.11084/) (2020)
- [Multiresolution Deep Implicit Functions for 3D Shape Representation](https://mlsanity.com/paper/2109.05591/) (2021)
- [Neural-IMLS: Self-supervised Implicit Moving Least-Squares Network for Surface Reconstruction](https://mlsanity.com/paper/2109.04398/) (2021)
- [Cut-and-Approximate: 3D Shape Reconstruction from Planar Cross-sections with Deep Reinforcement Learning](https://mlsanity.com/paper/2210.12509/) (2022)

## Built on by (most cited first, 7 of 7)

- [Slice3D: Multi-Slice, Occlusion-Revealing, Single View 3D Reconstruction](https://mlsanity.com/paper/2312.02221/) (2023)
- [SweepNet: Unsupervised Learning Shape Abstraction via Neural Sweepers](https://mlsanity.com/paper/2407.06305/) (2024)
- [CrossSDF: 3D Reconstruction of Thin Structures From Cross-Sections](https://mlsanity.com/paper/2412.04120/) (2024)
- [3D Heart Reconstruction from Sparse Pose-agnostic 2D Echocardiographic Slices](https://mlsanity.com/paper/2507.02411/) (2025)
- [LiverUSRecon: Automatic 3D Reconstruction and Volumetry of the Liver with a Few Partial Ultrasound Scans](https://mlsanity.com/paper/2406.19336/) (2024)
- [SBP-Net: Learning Thin Structure Reconstruction with Sliding-Box Projections](https://mlsanity.com/paper/2606.04251/) (2026)
- [SILSA: Sliding-Window Slice Latents for Topology-Preserving High-Resolution 3D Generation](https://mlsanity.com/paper/2610.02201/) (2026)

## Abstract (arXiv)

Reconstructing 3D shapes from planar cross-sections is a challenge inspired by downstream applications like medical imaging and geographic informatics. The input is an in/out indicator function fully defined on a sparse collection of planes in space, and the output is an interpolation of the indicator function to the entire volume. Previous works addressing this sparse and ill-posed problem either produce low quality results, or rely on additional priors such as target topology, appearance information, or input normal directions. In this paper, we present OReX, a method for 3D shape reconstruction from slices alone, featuring a Neural Field as the interpolation prior. A modest neural network is trained on the input planes to return an inside/outside estimate for a given 3D coordinate, yielding a powerful prior that induces smoothness and self-similarities. The main challenge for this approach is high-frequency details, as the neural prior is overly smoothing. To alleviate this, we offer an iterative estimation architecture and a hierarchical input sampling scheme that encourage coarse-to-fine training, allowing the training process to focus on high frequencies at later stages. In addition, we identify and analyze a ripple-like effect stemming from the mesh extraction step. We mitigate it by regularizing the spatial gradients of the indicator function around input in/out boundaries during network training, tackling the problem at the root. Through extensive qualitative and quantitative experimentation, we demonstrate our method is robust, accurate, and scales well with the size of the input. We report state-of-the-art results compared to previous approaches and recent potential solutions, and demonstrate the benefit of our individual contributions through analysis and ablation studies.