# NeST: Neural Stress Tensor Tomography by leveraging 3D Photoelasticity

arXiv: https://arxiv.org/abs/2406.10212 · HTML: https://mlsanity.com/paper/2406.10212/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 108 references that are in the map.
- First posted on arXiv 14 Jun 2024.

## Builds on (most cited first, 25 of 25)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [ObjectFolder: A Dataset of Objects with Implicit Visual, Auditory, and Tactile Representations](https://mlsanity.com/paper/2109.07991/) (2021)
- [MedNeRF: Medical Neural Radiance Fields for Reconstructing 3D-aware CT-Projections from a Single X-ray](https://mlsanity.com/paper/2202.01020/) (2022)
- [Reconstructing continuous distributions of 3D protein structure from cryo-EM images](https://mlsanity.com/paper/1909.05215/) (2019)
- [Deep Polarization Imaging for 3D shape and SVBRDF Acquisition](https://mlsanity.com/paper/2105.02875/) (2021)
- [Shape from Polarization for Complex Scenes in the Wild](https://mlsanity.com/paper/2112.11377/) (2021)
- [PANDORA: Polarization-Aided Neural Decomposition Of Radiance](https://mlsanity.com/paper/2203.13458/) (2022)
- [Ultra-NeRF: Neural Radiance Fields for Ultrasound Imaging](https://mlsanity.com/paper/2301.10520/) (2023)
- [Neural Volumetric Reconstruction for Coherent Synthetic Aperture Sonar](https://mlsanity.com/paper/2306.09909/) (2023)
- [Perspective Phase Angle Model for Polarimetric 3D Reconstruction](https://mlsanity.com/paper/2207.09629/) (2022)
- [Linear Differential Constraints for Photo-polarimetric Height Estimation](https://mlsanity.com/paper/1708.07718/) (2017)
- [Spectral and Polarization Vision: Spectro-polarimetric Real-world Dataset](https://mlsanity.com/paper/2311.17396/) (2023)
- [Implicit Neural Representations for Deconvolving SAS Images](https://mlsanity.com/paper/2112.08539/) (2021)
- [Sparse Ellipsometry: Portable Acquisition of Polarimetric SVBRDF and Shape with Unstructured Flash Photography](https://mlsanity.com/paper/2207.04236/) (2022)
- [Orbital Polarimetric Tomography of a Flare Near the Sagittarius A* Supermassive Black Hole](https://mlsanity.com/paper/2310.07687/) (2023)
- [Geodesy of irregular small bodies via neural density fields: geodesyNets](https://mlsanity.com/paper/2105.13031/) (2021)
- [3D-TSV: The 3D Trajectory-based Stress Visualizer](https://mlsanity.com/paper/2112.09202/) (2021)
- [Event-based Shape from Polarization with Spiking Neural Networks](https://mlsanity.com/paper/2312.16071/) (2023)

## Built on by (most cited first, 2 of 2)

- [Event Ellipsometer: Event-based Mueller-Matrix Video Imaging](https://mlsanity.com/paper/2411.17313/) (2024)
- [End-to-End Optimization of Polarimetric Measurement and Material Classifier](https://mlsanity.com/paper/2603.20519/) (2026)

## Abstract (arXiv)

Photoelasticity enables full-field stress analysis in transparent objects through stress-induced birefringence. Existing techniques are limited to 2D slices and require destructively slicing the object. Recovering the internal 3D stress distribution of the entire object is challenging as it involves solving a tensor tomography problem and handling phase wrapping ambiguities. We introduce NeST, an analysis-by-synthesis approach for reconstructing 3D stress tensor fields as neural implicit representations from polarization measurements. Our key insight is to jointly handle phase unwrapping and tensor tomography using a differentiable forward model based on Jones calculus. Our non-linear model faithfully matches real captures, unlike prior linear approximations. We develop an experimental multi-axis polariscope setup to capture 3D photoelasticity and experimentally demonstrate that NeST reconstructs the internal stress distribution for objects with varying shape and force conditions. Additionally, we showcase novel applications in stress analysis, such as visualizing photoelastic fringes by virtually slicing the object and viewing photoelastic fringes from unseen viewpoints. NeST paves the way for scalable non-destructive 3D photoelastic analysis.