SA-GS: Scale-Adaptive Gaussian Splatting for Training-Free Anti-Aliasing

In this paper, we present a Scale-adaptive method for Anti-aliasing Gaussian Splatting (SA-GS). While the state-of-the-art method Mip-Splatting needs modifying the training procedure of Gaussian splatting, our method functions at test-time and is training-free. Specifically, SA-GS can be applied to any pretrained Gaussian splatting field as a plugin to significantly improve the field's anti-alising performance. The core technique is to apply 2D scale-adaptive filters to each Gaussian during test time. As pointed out by Mip-Splatting, observing Gaussians at different frequencies leads to mismatches between the Gaussian scales during training and testing. Mip-Splatting resolves this issue using 3D smoothing and 2D Mip filters, which are unfortunately not aware of testing frequency. In this work, we show that a 2D scale-adaptive filter that is informed of testing frequency can effectively match the Gaussian scale, thus making the Gaussian primitive distribution remain consistent across different testing frequencies. When scale inconsistency is eliminated, sampling rates smaller than the scene frequency result in conventional jaggedness, and we propose to integrate the projected 2D Gaussian within each pixel during testing. This integration is actually a limiting case of super-sampling, which significantly improves anti-aliasing performance over vanilla Gaussian Splatting. Through extensive experiments using various settings and both bounded and unbounded scenes, we show SA-GS performs comparably with or better than Mip-Splatting. Note that super-sampling and integration are only effective when our scale-adaptive filtering is activated. Our codes, data and models are available at https://github.com/zsy1987/SA-GS.

SlimmeRF: Slimmable Radiance Fields

Neural Radiance Field (NeRF) and its variants have recently emerged as successful methods for novel view synthesis and 3D scene reconstruction. However, most current NeRF models either achieve high accuracy using large model sizes, or achieve high memory-efficiency by trading off accuracy. This limits the applicable scope of any single model, since high-accuracy models might not fit in low-memory devices, and memory-efficient models might not satisfy high-quality requirements. To this end, we present SlimmeRF, a model that allows for instant test-time trade-offs between model size and accuracy through slimming, thus making the model simultaneously suitable for scenarios with different computing budgets. We achieve this through a newly proposed algorithm named Tensorial Rank Incrementation (TRaIn) which increases the rank of the model's tensorial representation gradually during training. We also observe that our model allows for more effective trade-offs in sparse-view scenarios, at times even achieving higher accuracy after being slimmed. We credit this to the fact that erroneous information such as floaters tend to be stored in components corresponding to higher ranks. Our implementation is available at https://github.com/Shiran-Yuan/SlimmeRF.

Low-Rank Tensor Completion With Generalized CP Decomposition and Nonnegative Integer Tensor Completion

The problem of tensor completion is important to many areas such as computer vision, data analysis, signal processing, etc. Previously, a category of methods known as low-rank tensor completion has been proposed and developed, involving the enforcement of low-rank structures on completed tensors. While such methods have been constantly improved, none have previously considered exploiting the numerical properties of tensor elements. This work attempts to construct a new methodological framework called GCDTC (Generalized CP Decomposition Tensor Completion) based on these properties. In this newly introduced framework, the CP Decomposition is reformulated as a Maximum Likelihood Estimate (MLE) problem, and generalized via the introduction of differing loss functions. The generalized decomposition is subsequently applied to low-rank tensor completion. Such loss functions can also be easily adjusted to consider additional factors in completion, such as smoothness, standardization, etc. An example of nonnegative integer tensor decomposition via the Poisson CP Decomposition is given to demonstrate the new methodology's potentials. Through experimentation with real-life data, it is confirmed that this method could produce results superior to current state-of-the-art methodologies. It is expected that the proposed notion would inspire a new set of tensor completion methods based on the generalization of decompositions, thus contributing to related fields.