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

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.