# TensoIS: A Step Towards Feed-Forward Tensorial Inverse Subsurface Scattering for Perlin Distributed Heterogeneous Media

arXiv: https://arxiv.org/abs/2509.04047 · HTML: https://mlsanity.com/paper/2509.04047/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 58 references that are in the map.
- First posted on arXiv 4 Sep 2025.

## Builds on (most cited first, 8 of 8)

- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [TensoIR: Tensorial Inverse Rendering](https://mlsanity.com/paper/2304.12461/) (2023)
- [SeaThru-NeRF: Neural Radiance Fields in Scattering Media](https://mlsanity.com/paper/2304.07743/) (2023)
- [Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representations](https://mlsanity.com/paper/2205.02825/) (2022)
- [NeMF: Inverse Volume Rendering with Neural Microflake Field](https://mlsanity.com/paper/2304.00782/) (2023)
- [ScatterNeRF: Seeing Through Fog with Physically-Based Inverse Neural Rendering](https://mlsanity.com/paper/2305.02103/) (2023)
- [Inverse Rendering of Translucent Objects using Physical and Neural Renderers](https://mlsanity.com/paper/2305.08336/) (2023)
- [Deep Polarization Cues for Single-shot Shape and Subsurface Scattering Estimation](https://mlsanity.com/paper/2407.08149/) (2024)

## Abstract (arXiv)

Estimating scattering parameters of heterogeneous media from images is a severely under-constrained and challenging problem. Most of the existing approaches model BSSRDF either through an analysis-by-synthesis approach, approximating complex path integrals, or using differentiable volume rendering techniques to account for heterogeneity. However, only a few studies have applied learning-based methods to estimate subsurface scattering parameters, but they assume homogeneous media. Interestingly, no specific distribution is known to us that can explicitly model the heterogeneous scattering parameters in the real world. Notably, procedural noise models such as Perlin and Fractal Perlin noise have been effective in representing intricate heterogeneities of natural, organic, and inorganic surfaces. Leveraging this, we first create HeteroSynth, a synthetic dataset comprising photorealistic images of heterogeneous media whose scattering parameters are modeled using Fractal Perlin noise. Furthermore, we propose Tensorial Inverse Scattering (TensoIS), a learning-based feed-forward framework to estimate these Perlin-distributed heterogeneous scattering parameters from sparse multi-view image observations. Instead of directly predicting the 3D scattering parameter volume, TensoIS uses learnable low-rank tensor components to represent the scattering volume. We evaluate TensoIS on unseen heterogeneous variations over shapes from the HeteroSynth test set, smoke and cloud geometries obtained from open-source realistic volumetric simulations, and some real-world samples to establish its effectiveness for inverse scattering. Overall, this study is an attempt to explore Perlin noise distribution, given the lack of any such well-defined distribution in literature, to potentially model real-world heterogeneous scattering in a feed-forward manner.