# Towards Monocular Shape from Refraction

arXiv: https://arxiv.org/abs/2305.19743 · HTML: https://mlsanity.com/paper/2305.19743/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 24 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 1 of 1)

- [Full 3D Reconstruction of Transparent Objects](https://mlsanity.com/paper/1805.03482/) (2018)

## Built on by (most cited first, 3 of 3)

- [TransNormal: Dense Visual Semantics for Diffusion-based Transparent Object Normal Estimation](https://mlsanity.com/paper/2602.00839/) (2026)
- [Looking Into the Water by Unsupervised Learning of the Surface Shape](https://mlsanity.com/paper/2603.07614/) (2026)
- [TransNormal-2: Geometry-Grounded Rectified Flow with Edge-Aware Decoding for Precise Normal Estimation](https://mlsanity.com/paper/2609.06665/) (2026)

## Abstract (arXiv)

Refraction is a common physical phenomenon and has long been researched in computer vision. Objects imaged through a refractive object appear distorted in the image as a function of the shape of the interface between the media. This hinders many computer vision applications, but can be utilized for obtaining the geometry of the refractive interface. Previous approaches for refractive surface recovery largely relied on various priors or additional information like multiple images of the analyzed surface. In contrast, we claim that a simple energy function based on Snell's law enables the reconstruction of an arbitrary refractive surface geometry using just a single image and known background texture and geometry. In the case of a single point, Snell's law has two degrees of freedom, therefore to estimate a surface depth, we need additional information. We show that solving for an entire surface at once introduces implicit parameter-free spatial regularization and yields convincing results when an intelligent initial guess is provided. We demonstrate our approach through simulations and real-world experiments, where the reconstruction shows encouraging results in the single-frame monocular setting.