Softmax-GS: Generalized Gaussians Learning When to Blend or Bound

2026-04-30

AI Summary

This work addresses the view inconsistency and boundary blurriness in 3D Gaussian Splatting (3D GS) caused by overlapping Gaussians. To resolve these issues, the authors propose Softmax-GS, which introduces a learnable softmax-based competition mechanism into 3D GS for the first time. This approach enables continuous control over the transition from smooth blending to sharp boundaries while preserving permutation invariance and transmittance consistency. By employing a learnable parameter to modulate the softmax fusion strategy, Softmax-GS effectively balances rendering continuity with edge sharpness. Experiments on real-world scene benchmarks demonstrate that the method significantly improves reconstruction quality and parameter efficiency, and ablation studies confirm the contribution of each component.

Abstract

3D Gaussian Splatting (3D GS) is widely adopted for novel view synthesis due to its high training and rendering efficiency. However, its efficiency relies on the key assumption that Gaussians do not overlap in the 3D space, which leads to noticeable artifacts and view inconsistencies. In addition, the inherently diffuse boundaries of Gaussians hinder accurate reconstruction of sharp object edges. We propose Softmax-GS, a unified solution that addresses both the view-inconsistency and the diffuse-boundary problem by enforcing a softmax-based competition in overlapping regions between two Gaussians. With learnable parameters controlling the strength of the competition, it enables a continuous spectrum from smooth color blending to crisp, well-defined boundaries. Our formulation explicitly preserves order invariance for any two overlapping Gaussians and ensures that the output transmittance remains unchanged irrespective of the extent of overlapping, preventing undesirable discontinuities in the rendered output. Ablation experiments on simple geometries demonstrate the effectiveness of each component of Softmax-GS, and evaluations on real-world benchmarks show that it achieves state-of-the-art performance, improving both reconstruction quality and parameter efficiency.

Problem

• 3D Gaussian Splatting
• view inconsistency
• diffuse boundaries
• overlapping Gaussians
• novel view synthesis

Innovation

• Softmax-GS
• 3D Gaussian Splatting
• view consistency
• sharp boundaries
• order invariance