GDGS: Gradient Domain Gaussian Splatting for Sparse Representation of Radiance Fields

TL;DR

The paper tackles the dense nature of 3D Gaussian splatting representations by introducing Gradient Domain Gaussian Splatting (GDGS), which models the Laplacian field rather than the signal itself. The method projects a sparse 3D Laplacian representation to 2D and recovers the view image by solving a Poisson equation, with a gradient-domain loss that emphasizes edges. Key contributions include showing substantial sparsity gains, improved PSNR (approximately 0.6–1 dB in reported experiments), and orders of magnitude reduction in particle count (often >100x) while maintaining or improving rendering quality. The approach enables efficient, edge-preserving view synthesis and holds promise for applications in human body modeling and indoor environments through scalable radiance-field representations.

Abstract

The 3D Gaussian splatting methods are getting popular. However, they work directly on the signal, leading to a dense representation of the signal. Even with some techniques such as pruning or distillation, the results are still dense. In this paper, we propose to model the gradient of the original signal. The gradients are much sparser than the original signal. Therefore, the gradients use much less Gaussian splats, leading to the more efficient storage and thus higher computational performance during both training and rendering. Thanks to the sparsity, during the view synthesis, only a small mount of pixels are needed, leading to much higher computational performance ($100\sim 1000\times$ faster). And the 2D image can be recovered from the gradients via solving a Poisson equation with linear computation complexity. Several experiments are performed to confirm the sparseness of the gradients and the computation performance of the proposed method. The method can be applied various applications, such as human body modeling and indoor environment modeling.

Figures (5)

• Figure 1: The relationship between the original signal (left) and the gradient domain representation (right). The gradient domain representation is sparse and thus only large gradients are needed. As a result, the 2D view gradient is also sparse and only a small part of pixels are rendered. And the final image is reconstructed via solving a Poisson equation.
• Figure 2: A 2D image (a) and its Laplace field (d). The middle and right columns show their probabilities and cumulative probabilities, respectively, where different color indicate color channels. The values are shifted with 128 but without scaling. As these figures shown, the Laplacian field is much sparser than the original image. Therefore, in the Laplacian field, we do not necessarily render all the pixels as in the 3D Gaussian splatting. Instead, only sparse edges are computed. Meanwhile, the rendered image can be recovered by its Laplacian field via solving a Poisson equation.
• Figure 3: The Cauchy parameter $\gamma$ in the intensity domain (a) and Laplacian domain (b), respectively. The smaller $\gamma$, the sparser the signal. The mean and median for (a) is 84.4 and 44.6. The mean and median for (b) is 3.1 and 2.8. The Laplacian field is much sparser. The different colors indicate the color channels in RGB images.
• Figure 4: The traditional Poisson solvers can accurately reconstruct the image as shown in (b). But they might generate artifacts when we force the more sparsity, as shown in (c).
• Figure 5: We use a U-Net structure to reconstruct the image from its Laplacian field. We add noise into the input to improve the robustness. We also use the mask in the input to improve the sparsity.