# Generation of Synthetic Non-Homogeneous Fog by Discretized Radiative Transfer Equation

## TL;DR

This paper introduces a physics-based method for generating realistic, non-uniform fog in images, outperforming traditional techniques in realism and accuracy.

## Contribution

A novel fog synthesis approach using the discretized Radiative Transfer Equation to model inhomogeneous fog and anisotropic scattering.

## Key findings

- The method achieves a 10% and 42% lower Fréchet Inception Distance compared to Koschmieder and CycleGAN baselines.
- It shows a 4% and 21% higher Pearson correlation, indicating better structural fidelity.
- The method's high memory usage due to tensor computations limits its real-time or large-scale deployment.

## Abstract

The synthesis of realistic fog in images is critical for applications such as autonomous navigation, augmented reality, and visual effects. Traditional methods based on Koschmieder’s law or GAN-based image translation typically assume homogeneous fog distributions and rely on oversimplified scattering models, limiting their physical realism. In this paper, we propose a physics-driven approach to fog synthesis by discretizing the Radiative Transfer Equation (RTE). Our method models spatially inhomogeneous fog and anisotropic multi-scattering, enabling the generation of structurally consistent and perceptually plausible fog effects. To evaluate performance, we construct a dataset of real-world foggy, cloudy, and sunny images and compare our results against both Koschmieder-based and GAN-based baselines. Experimental results show that our method achieves a lower Fréchet Inception Distance (−10% vs. Koschmieder, −42% vs. CycleGAN) and a higher Pearson correlation (+4% and +21%, respectively), highlighting its superiority in both feature space and structural fidelity. These findings highlight the potential of RTE-based fog synthesis for physically consistent image augmentation under challenging visibility conditions. However, the method’s practical deployment may be constrained by high memory requirements due to tensor-based computations, which must be addressed for large-scale or real-time applications.