Monte-Carlo neural rendering

Recent advances in neural rendering have achieved high-quality photorealistic scene reconstruction, yet some computational challenges remain. Neural Radiance Fields are slow to train, while 3D Gaussian Splatting depends on heuristic rules, is sensitive to initialization, and fixes rendering quality regardless of computational constraints. This thesis addresses these limitations through sampling-based methods and probabilistic reformulations. First, we present soft mining, an importance sampling approach that accelerates neural field training by focusing computation on regions with higher reconstruction error. Using Langevin Monte Carlo, sampling probabilities adapt dynamically during training, improving both convergence speed and final rendering quality. Second, we reformulate 3DGS as a Markov Chain Monte Carlo process, interpreting Gaussians as probabilistic samples rather than relying on manual splitting and pruning. By introducing stochastic updates via Stochastic Gradient Langevin Dynamics, we remove the dependence on heuristic density control and good initialization, resulting in a more robust optimization process. Finally, we introduce an order-independent stochastic transparency method for Gaussian-based rendering, eliminating the costly sorting step in traditional pipelines. This technique integrates seamlessly with hardware rasterization, improves rendering efficiency, avoids popping artifacts, and ensures compatibility across GPU architectures. Collectively, these contributions make scene reconstruction faster, more robust, and more computationally efficient, advancing the practical deployment of neural rendering in real-world applications.