EntON: Eigenentropy-Optimized Neighborhood Densification in 3D Gaussian Splatting

TL;DR

A novel Eigenentropy-optimized neighboorhood densification strategy EntON in 3D Gaussian Splatting for geometrically accurate and high-quality rendered 3D reconstruction and achieves a favorable balance between geometric accuracy, rendering quality and efficiency by avoiding unnecessary scene expansion.

Abstract

We present a novel Eigenentropy-optimized neighboorhood densification strategy EntON in 3D Gaussian Splatting (3DGS) for geometrically accurate and high-quality rendered 3D reconstruction. While standard 3DGS produces Gaussians whose centers and surfaces are poorly aligned with the underlying object geometry, surface-focused reconstruction methods frequently sacrifice photometric accuracy. In contrast to the conventional densification strategy, which relies on the magnitude of the view-space position gradient, our approach introduces a geometry-aware strategy to guide adaptive splitting and pruning. Specifically, we compute the 3D shape feature Eigenentropy from the eigenvalues of the covariance matrix in the k-nearest neighborhood of each Gaussian center, which quantifies the local structural order. These Eigenentropy values are integrated into an alternating optimization framework: During the optimization process, the algorithm alternates between (i) standard gradient-based densification, which refines regions via view-space gradients, and (ii) Eigenentropy-aware densification, which preferentially densifies Gaussians in low-Eigenentropy (ordered, flat) neighborhoods to better capture fine geometric details on the object surface, and prunes those in high-Eigenentropy (disordered, spherical) regions. We provide quantitative and qualitative evaluations on two benchmark datasets: small-scale DTU dataset and large-scale TUM2TWIN dataset, covering man-made objects and urban scenes. Experiments demonstrate that our Eigenentropy-aware alternating densification strategy improves geometric accuracy by up to 33% and rendering quality by up to 7%, while reducing the number of Gaussians by up to 50% and training time by up to 23%. Overall, EnTON achieves a favorable balance between geometric accuracy, rendering quality and efficiency by avoiding unnecessary scene expansion.

Figures (12)

• Figure 1: Methodology EntON. Gaussians are adapted based on the Eigenentropy of their local neighborhood: low Eigenentropy leads to splitting, medium Eigenentropy results in unchanged Gaussians, and high Eigenentropy triggers pruning. In constrast, 3DGS triggers densification based on the view-space position gradient: small Gaussians are cloned, large Gaussians are splitted. EntON uses the level of Eigenentropy to focus densification on object surfaces, avoiding unnecessary scene expansion and thus efficiently compressing the information content of the scene representation.
• Figure 2: Representation of an ellipsoid from the neighborhood points represented by the Gaussian centers with the three eigenvectors ($\mathbf{\epsilon_1}, \mathbf{\epsilon_2}, \mathbf{\epsilon_3}$) and the corresponding eigenvalues ($\lambda_1, \lambda_2, \lambda_3$) in the three-dimensional coordinate system.
• Figure 3: Eigenentropy $E(\lambda_1, \lambda_2, \lambda_3)$ as a function of the largest normalized eigenvalue $\lambda_1$ (with $\lambda_1 \geq \lambda_2 \geq \lambda_3 \geq 0$, $\sum_{i=1}^3 \lambda_i = 1$). Curves represent different fixed values of $\lambda_3$ (ideal planar: $\lambda_3=0$; near-planar: $\lambda_3=0.1$; transitional between planar and spherical: $\lambda_3=1/6\approx0.1667$; and higher spherical distribution). Markers indicate minimum and maximum Eigenentropy for each case. The dashed line at $\ln 2 \approx 0.693$ corresponds to the ideal planar case ($\lambda_1 = \lambda_2 = 0.5$, $\lambda_3 = 0$).
• Figure 4: Low Eigenentropy leads to splitting, medium Eigenentropy results in unchanged Gaussians, and high Eigenentropy triggers pruning. Representation of the ellipsoids based on neighboring Gaussian centers with the three eigenvectors ($\mathbf{\epsilon_1}, \mathbf{\epsilon_2}, \mathbf{\epsilon_3}$) and the corresponding eigenvalues ($\lambda_1, \lambda_2, \lambda_3$) in the three-dimensional coordinate system.
• Figure 5: Trend of the mean Eigenentropy $\downarrow$ and mean cloud to cloud (C2C) distance $\downarrow$ of all DTU scenes during the training process. Comparison of 3DGS and EntON. As EntON starts at iteration 3000, C2C is first reported at iteration 2500.