📄 Paper (arXiv) | 💻 Code (GitHub)
Gaussian Splatting has proven to be an effective algorithm for novel view synthesis and 3D reconstruction from multiview images. However, the underlying volumetric primitive – the ellipsoidal Gaussian– has limited expressive capabilities, leading to difficulties in 3D modelling (especially geometry such as edges, corners, and high curvature). To address this limitation, in this paper, we introduce Superquadric Splats (SQS), an extended class of volumetric primitives, as a super-set of Gaussian splats, to model more detailed geometry. We treat superquadrics as volumetric distance functions rather than level-set surfaces. A non-trivial differentiable rendering pipeline is developed to support this. Extensive experimental analysis on multiple datasets validates the effectiveness of the proposed SQS approach, showing both enhanced visual and geometric performance compared to Gaussian-based splatting (with more than 1dB in PSNR and prominent geometric improvement).
Superquadrics are a parametric family of three-dimensional shapes that generalize classical quadrics such as spheres, ellipsoids, cylinders, and cubes. By introducing shape exponents that control curvature and sharpness, superquadrics can smoothly interpolate between rounded and sharp geometries, enabling the representation of edges, corners, and flat faces within a single analytic formulation. In Gaussian Splatting, each primitive is modeled as an ellipsoidal Gaussian, which restricts the geometry to smooth, convex shapes. Superquadrics strictly generalize ellipsoids: when the shape exponents are set to specific values, the superquadric reduces exactly to a standard ellipsoid. In our formulation, we treat superquadrics as volumetric distance functions rather than explicit surface level sets. By varying the shape parameters, a wide range of geometries can be represented while preserving differentiability and compact parameterization. The interactive visualization illustrates several example superquadric shapes. The equation below defines the distance field of a superquadric.
Ellipsoidal Gaussians have limited expressive power: they are inherently smooth and cannot accurately represent sharp features such as corners, thin structures, edges, or high-curvature geometry. As a result, Gaussian splatting often struggles to faithfully reconstruct detailed surfaces, leading to blurred geometry and loss of structural fidelity. Superquadrics significantly expand the modeling capacity of each primitive. Their shape parameters allow anisotropic deformation and controllable sharpness, enabling a single splat to better approximate complex local geometry. This reduces the number of primitives required to represent fine structures and improves both geometric accuracy and visual sharpness. By replacing Gaussian primitives with Superquadric Splats (SQS), the reconstruction gains improved alignment to real scene geometry, yielding higher PSNR and visibly sharper surfaces, especially in regions containing edges, corners, and object boundaries.
We integrate superquadrics into the rendering pipeline by projecting their volumetric distance field onto the image plane, rather than rasterizing explicit surfaces. For each pixel, the projected distance is converted into intensity using an inverse exponential formulation, analogous to the opacity accumulation used in 3D Gaussian Splatting. This preserves the differentiable volumetric rendering framework while extending the primitive representation beyond ellipsoids. The entire pipeline remains fully differentiable, enabling end-to-end optimization of superquadric parameters directly from image supervision. Conceptually, the method follows the same rendering philosophy as 3DGS, but with a richer primitive model that allows more accurate spatial representation without sacrificing efficiency or optimization stability.
Below we present qualitative comparisons between standard 3D Gaussian Splatting (GS) and the proposed Superquadric Splats (SQS). The interactive sliders allow direct visual comparison of reconstructions across multiple scenes.
This project is partially supported by the Royal Society grants (SIF\R1\231009, IES\R3\223050), and is supported by the Amazon Research Award “PCo3D: Physically Plausible Controllable 3D Generative Models”. The computations in this research were supported by the Baskerville Tier 2 HPC service. Baskerville was funded by the EPSRC and UKRI through the World Class Labs scheme (EP\T022221\1) and the Digital Research Infrastructure programme (EP\W032244\1) and is operated by Advanced Research Computing at the University of Birmingham.
@inproceedings{macswayne2026_3dsqs,
title = {3D Superquadric Splatting (3DSQS)},
author = {MacSwayne, Daniel and Leonardis, Ales and Jiao, Jianbo},
booktitle = {Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision (WACV)},
year = {2026}
}