DARB-Splatting: Generalizing Splatting with Decaying Anisotropic Radial Basis Functions

Vishagar Arunan*, Saeedha Nazar*, Hashiru Pramuditha*, Vinasirajan Viruthshaan*, Ranga Rodrigo, Sameera Ramasinghe, Simon Lucey,
University of Moratuwa, Sri Lanka.
Australian Institute for Machine Learning (AIML), University of Adelaiede, Australia.
*Indicates Equal Contribution
Paper Supplementary Code arXiv
Descriptive Diagram

This figure compares two different splat functions—Gaussian and cosine (specifically, half-cosine squared)—initialized for the same 3D covariance matrix, \(\Sigma\). Cosine functions, defined as \(\cos\left(\frac{d^2_M}{\xi}\right)\) for \(d^2_M < \frac{\pi}{2}\) where \(\xi(> 0)\), have finite support and exhibit effective reconstruction performance comparable to Gaussians. Notably, the cosine-based approach enhances training speed by 34% and reduces memory usage by 15%, providing a more memory-efficient alternative.

Abstract

Splatting-based 3D reconstruction methods have gained popularity with the advent of 3D Gaussian Splatting, efficiently synthesizing high-quality novel views. These methods commonly resort to using exponential family functions, such as the Gaussian function, as reconstruction kernels due to their anisotropic nature, ease of projection, and differentiability in rasterization. However, the field remains restricted to variations within the exponential family, leaving generalized reconstruction kernels largely underexplored, partly due to the lack of easy integration in 3D to 2D projections. In this light, we show that a class of decaying anisotropic radial basis functions (DARBFs), which are non-negative functions of the Mahalanobis distance, supports splatting by approximating the Gaussian function’s closed-form integration advantage. With this fresh perspective, we demonstrate up to 34% faster convergence during training and a 15% reduction in memory consumption across various DARB reconstruction kernels, while maintaining comparable PSNR, SSIM, and LPIPS results. We will make the code available.

Descriptive Diagram

We use the standard optimization pipeline from 3DGS with modifications, introducing a correction factor (\(\psi\)) to obtain the projected 2D covariance matrix (\(\Sigma^{\prime}_{2\times2}\)) compatible with splatting for DARBFs within the existing framework. Our changes within the pipeline are highlighted in red text.

We present comparisons between our proposed methods (Raised cosine) and established baseline (3DGS) alongside their respective ground truth images. The displayed scenes are ordered as follows: TRUCK and TRAIN from Tanks&Temples dataset; COUNTER from Mip-NeRF360 dataset. We highlight subtle improvements in our approach, such as the appearance of a light bulb in the rendered image of the first row, which is absent in the splitting algorithm. Additionally, the edges of the train and the shadows of the rack in the images on the second and third rows, respectively, are noticeably sharper, whereas these details appear blurred in the original splitting algorithm. Note that in addition to improved reconstruction, we also achieve significantly better training and memory efficiency with these alternative primitives. Please refer our manuscript for further details.

Training loss and speed curves across different scenes reveal significant performance differences. Specifically, the superior convergence speed of half-cosine squared splatting stands out compared to other selected DARBFs, particularly the Gaussian function. Although all the selected functions exhibit similar loss curves, notable variations are observed in their respective training speed curves across various scenes. These differences can be attributed to the inherent characteristics of each scene, which influence the training dynamics of the functions.

BibTeX

@misc{arunan2025darbsplattinggeneralizingsplattingdecaying,
      title={DARB-Splatting: Generalizing Splatting with Decaying Anisotropic Radial Basis Functions}, 
      author={Vishagar Arunan and Saeedha Nazar and Hashiru Pramuditha and Vinasirajan Viruthshaan and Sameera Ramasinghe and Simon Lucey and Ranga Rodrigo},
      year={2025},
      eprint={2501.12369},
      archivePrefix={arXiv},
      primaryClass={cs.CV},
      url={https://arxiv.org/abs/2501.12369}, 
}