We quantify the uncertainty in 3D Gaussian Splatting by deviating Gaussians to construction model space samples and learn with variational inference.
Recently, 3D Gaussian Splatting (3DGS) has become popular in reconstructing dense 3D representations of appearance and geometry. However, the learning pipeline in 3DGS inherently lacks the ability to quantify uncertainty, which is an important factor in applications like robotics mapping and navigation. In this paper, we propose an uncertainty estimation method built upon the Bayesian inference framework. Specifically, we propose a method to build variational multi-scale 3D Gaussians, where we leverage explicit scale information in 3DGS parameters to construct diversified parameter space samples. We develop an offset table technique to draw local multi-scale samples efficiently by offsetting selected attributes and sharing other base attributes. Then, the offset table is learned by variational inference with multi-scale prior. The learned offset posterior can quantify the uncertainty of each individual Gaussian component, and be used in the forward pass to infer the predictive uncertainty. Extensive experimental results on various benchmark datasets show that the proposed method provides well-aligned calibration performance on estimated uncertainty and better rendering quality compared with the previous methods that enable uncertainty quantification with view synthesis. Besides, by leveraging the model parameter uncertainty estimated by our method, we can remove noisy Gaussians automatically, thereby obtaining a high-fidelity part of the reconstructed scene, which is of great help in improving the visual quality.
We proposed an watermarking method for protecting the models generated by 3D Gaussian Splatting and use uncertainty to improve invisibility.
3D Gaussian Splatting (3DGS) has become a crucial method for acquiring 3D assets. To protect the copyright of these assets, digital watermarking techniques can be applied to embed ownership information discreetly within 3DGS mod- els. However, existing watermarking methods for meshes, point clouds, and implicit radiance fields cannot be directly applied to 3DGS models, as 3DGS models use explicit 3D Gaussians with distinct structures and do not rely on neural networks. Naively embedding the watermark on a pre-trained 3DGS can cause obvious distortion in rendered images. In our work, we propose an uncertainty- based method that constrains the perturbation of model parameters to achieve invisible watermarking for 3DGS. At the message decoding stage, the copyright messages can be reliably extracted from both 3D Gaussians and 2D rendered im- ages even under various forms of 3D and 2D distortions. We conduct extensive experiments on the Blender, LLFF, and MipNeRF-360 datasets to validate the effectiveness of our proposed method, demonstrating state-of-the-art performance on both message decoding accuracy and view synthesis quality.
