3D Student Splatting and Scooping

TL;DR

This paper introduces Student Splatting and Scooping (SSS), a non-monotonic, unnormalized mixture model for 3D radiance fields that replaces Gaussians with learnable Student's t distributions and incorporates both positive (splatting) and negative (scooping) components. By employing SGHMC for optimization and enabling careful component management (adding, recycling, and sign-aware density control), SSS achieves higher rendering quality and substantially improved parameter efficiency, often matching or surpassing state-of-the-art methods with far fewer components. The approach is demonstrated across diverse datasets (Mip-NeRF 360, Tanks & Temples, Deep Blending), showing superior quantitative metrics (PSNR, SSIM, LPIPS) and qualitative detail, with ablations validating the benefits of t-distribution expressivity and principled sampling. Overall, SSS provides a robust, more expressive alternative to 3DGS that reduces model complexity while preserving or enhancing reconstruction fidelity and visual quality, enabling more efficient neural rendering pipelines.

Abstract

Recently, 3D Gaussian Splatting (3DGS) provides a new framework for novel view synthesis, and has spiked a new wave of research in neural rendering and related applications. As 3DGS is becoming a foundational component of many models, any improvement on 3DGS itself can bring huge benefits. To this end, we aim to improve the fundamental paradigm and formulation of 3DGS. We argue that as an unnormalized mixture model, it needs to be neither Gaussians nor splatting. We subsequently propose a new mixture model consisting of flexible Student's t distributions, with both positive (splatting) and negative (scooping) densities. We name our model Student Splatting and Scooping, or SSS. When providing better expressivity, SSS also poses new challenges in learning. Therefore, we also propose a new principled sampling approach for optimization. Through exhaustive evaluation and comparison, across multiple datasets, settings, and metrics, we demonstrate that SSS outperforms existing methods in terms of quality and parameter efficiency, e.g. achieving matching or better quality with similar numbers of components, and obtaining comparable results while reducing the component number by as much as 82%.

Figures (9)

• Figure 1: Student's t with varying degrees of freedom $\nu$. (standard deviation is 5).
• Figure 1: Visual comparison. (a) SSS restores the best details inside the metal bowl. (b) SSS is the only one that can reconstruct the details of the chair refracted in the transparent cup. (c) The reconstruction of the wall edge (bright blue box) and the font were both done best by SSS. (d) SSS's details on the distant woods and the reconstruction of the sky are the best. (e) The reconstruction of the pattern on the wall is SSS at its best.
• Figure 2: High parameter efficiency by negative components. We use a torus with only ambient lighting and frontal views (a), where the challenge is to capture the shape topology with as few components as possible. We initialize the component means near the center. Only using positive densities either underfits if two components are used (b), or requires at least 5 components to capture the topology correctly (c). In contrast, in (d), we only need two components (one positive and one negative), to capture the topology of the shape. Both components are co-located at the center of the torus. The positive component covers the torus but also the hole, while the negative component subtracts densities in the middle to make a hole.
• Figure 2: Visual results of all methods with varying component numbers of room scene from Mip-NeRF 360. Only 3DGS-MCMC and SSS can restore the details of the carpet, but the result of SSS obviously has a more realistic carpet texture.
• Figure 3: Visual comparison Zoom-in for better visualization. (a) SSS restores better the indentations of the box lid; (b) SSS is the best at detailing windows in the upper center; (c) Only the image rendered by SSS contains the green track detail in the upper right corner; (d) SSS is the best at restoring the reflection in the front window of the truck; (e) SSS perfectly restores the light switch next to the stairs.