# Learning to Estimate Single-View Volumetric Flow Motions without 3D Supervision

## TL;DR

This paper introduces an unsupervised deep learning method to estimate 3D flow and volumetric densities from monocular videos without needing 3D ground truth, enabling stable long-term fluid motion predictions.

## Contribution

It presents a novel unsupervised training approach for 3D flow estimation from monocular videos, eliminating the need for volumetric supervision and using real-world data.

## Key findings

- Accurately estimates 3D flow from monocular videos.
- Stable long-term predictions of fluid motion.
- Works effectively on real-world data like smoke plumes.

## Abstract

We address the challenging problem of jointly inferring the 3D flow and volumetric densities moving in a fluid from a monocular input video with a deep neural network. Despite the complexity of this task, we show that it is possible to train the corresponding networks without requiring any 3D ground truth for training. In the absence of ground truth data we can train our model with observations from real-world capture setups instead of relying on synthetic reconstructions. We make this unsupervised training approach possible by first generating an initial prototype volume which is then moved and transported over time without the need for volumetric supervision. Our approach relies purely on image-based losses, an adversarial discriminator network, and regularization. Our method can estimate long-term sequences in a stable manner, while achieving closely matching targets for inputs such as rising smoke plumes.