Recently, 3D Gaussian Splatting has demonstrated impressive novel view synthesis results, reaching high fidelity and efficiency. However, strong artifacts can be observed when changing the sampling rate, e.g., by changing focal length or camera distance. We find that the source for this phenomenon can be attributed to the lack of 3D frequency constraints and the usage of a 2D dilation filter. To address this problem, we introduce a 3D smoothing filter which constrains the size of the 3D Gaussian primitives based on the maximal sampling frequency induced by the input views, eliminating high-frequency artifacts when zooming in. Moreover, replacing 2D dilation with a 2D Mip filter, which effectively approximates a box filter for mipmap-style rendering, allows us to antialias and remove dilation artifacts simultaneously. Our evaluation on both standard benchmarks and out-of-distribution test conditions demonstrates the effectiveness of our approach on scenes with multiple sampling rates.

Novel view synthesis (NVS) plays a critical role in computer graphics and computer vision, with various applications including virtual reality, cinematography, robotics, and more. Neural Radiance Fields (NeRF) represented a significant advancement, but 3D Gaussian Splatting (3DGS) has emerged as an appealing alternative, offering impressive novel view synthesis results, while achieving real-time rendering at high resolutions. This effectiveness and efficiency, coupled with the potential integration into the standard rasterization pipeline of GPUs, represents a significant step towards practical usage of NVS methods.

However, 3DGS produces artifacts when camera views diverge from training views. We find that the source for this phenomenon can be attributed to the lack of 3D frequency constraints and the usage of a 2D dilation filter. Specifically, zooming out leads to a reduced size of the projected 2D Gaussians in screen space, while applying the same amount of dilation results in dilation artifacts. Conversely, zooming in reveals high-frequency artifacts because the optimization systematically underestimates the scale parameter of 3D Gaussians due to the implicit shrinkage bias introduced by the dilation operation.

Our key insight is that the highest frequency that can be reconstructed of a 3D scene is inherently constrained by the sampling rates of the input images. Based on this, we derive multi-view frequency bounds of each Gaussian primitive according to the Nyquist-Shannon Sampling Theorem and introduce a 3D smoothing filter that constrains Gaussian sizes accordingly. For rendering at lower sampling rates, we further introduce a 2D Mip filter specifically designed to ensure alias-free reconstruction and rendering across different scales. Our closed-form modification to the 3D Gaussian representation results in excellent out-of-distribution generalization: training at a single sampling rate enables faithful rendering at various sampling rates.

NeRF utilizes multilayer perceptrons (MLPs) to model scenes as continuous functions, which, despite their compact representation, impede rendering speed due to the expensive MLP evaluation required for each ray point. Subsequent work has focused on improving the training and rendering of NeRF with advanced scene representations. 3D Gaussian Splatting (3DGS) demonstrated impressive novel view synthesis results while achieving real-time rendering at high-definition resolutions. Importantly, 3DGS represents the scene explicitly as a collection of 3D Gaussians and uses rasterization instead of ray tracing. Nevertheless, 3DGS focuses on in-distribution evaluation where training and testing are conducted at similar sampling rates.

There are two principal strategies to combat aliasing: super-sampling, which increases the number of samples, and prefiltering, which applies low-pass filtering to the signal to meet the Nyquist limit. While Mip-NeRF and Tri-MipRF have addressed aliasing in NeRF-based methods, these approaches require multi-scale images for supervision. In contrast, our approach is based on 3DGS and determines the necessary low-pass filter size based on pixel size, allowing for alias-free rendering at scales unobserved during training. While our band-limited filter shares similarities with the EWA filter, their underlying principles are distinct: the EWA filter's role is to limit the frequency signal's bandwidth with an empirically chosen filter size, whereas our Mip filter is designed to replicate the box filter in the imaging process, targeting an exact approximation of a single pixel.

The Nyquist-Shannon Sampling Theorem is a fundamental concept in signal processing that describes the conditions under which a continuous signal can be accurately represented or reconstructed from its discrete samples. Two conditions must be met: Condition 1 — the continuous signal must be band-limited and may not contain any frequency components above a certain maximum frequency; Condition 2 — the sampling rate must be at least twice the highest frequency present in the continuous signal. To satisfy these constraints when reconstructing a signal from discrete samples, a low-pass or anti-aliasing filter is applied to the signal before sampling.

3D Gaussian Splatting uses a set of scaled 3D Gaussian primitives and renders an image using volume splatting. The geometry of each scaled 3D Gaussian is parameterized by an opacity alpha, center p, and covariance matrix Sigma defined in world space. To ensure valid covariance matrices, a semi-definite parameterization via rotation matrix and scale vector is used. The 3D Gaussians are first transformed into camera coordinates, then projected to ray space via a local affine transformation. 3DGS utilizes spherical harmonics to model view-dependent color and renders images via alpha blending according to the primitive's depth order. To avoid degenerate cases where projected 2D Gaussians are too small in screen space, the projected 2D Gaussians are dilated — this operator adjusts the scale of the 2D Gaussian while leaving its maximum unchanged.

We observe that this optimization suffers from ambiguities: in traditional forward splatting, the centers and colors of Gaussian primitives are predetermined, whereas the 3D Gaussian covariance are chosen empirically. Due to screen space dilation with a Gaussian kernel (size approximately 1 pixel), the degenerate 3D Gaussian represented by a Dirac delta function leads to a similar image. In practice, due to its implicit shrinkage bias, 3DGS indeed systematically underestimates the scale parameter of 3D Gaussians during optimization. This leads to erosion effects when zooming in — the dilated 2D Gaussians become smaller in screen space, and the rendered image exhibits high-frequency artifacts, rendering object structures thinner than they actually appear.

Screen space dilation also negatively affects rendering when decreasing the sampling rate: dilation spreads radiance in a physically incorrect way across pixels, resulting in visible dilation artifacts at lower resolutions. Simply discarding screen space dilation results in optimization challenges for complex scenes, such as those present in the Mip-NeRF 360 dataset, where a large number of small Gaussians are created by the density control mechanism. This creates a dilemma: the dilation operation is necessary for stable optimization, yet it introduces artifacts at non-training sampling rates.

3D radiance field reconstruction from multi-view observations is a well-known ill-posed problem as multiple distinctly different reconstructions can result in the same 2D projections. Our key insight is that the highest frequency of a reconstructed 3D scene is limited by the sampling rate defined by the training views. A pixel corresponds to a sampling interval; when this pixel interval is back-projected to the 3D world space, it results in a world space sampling interval at a given depth d, with sampling frequency as its inverse. Given samples drawn at this frequency, reconstruction algorithms are able to reconstruct components of the signal with frequencies up to half the sampling frequency, following the Nyquist limit.

Since the sampling rate of a primitive is depth-dependent and differs across cameras, we determine the maximal sampling rate for primitive k as the maximum across all cameras, considering an indicator function assessing visibility. Given the maximal sampling rate for a primitive, we aim to constrain the maximal frequency of the 3D representation. This is achieved by applying a Gaussian low-pass filter to each 3D Gaussian primitive before projecting it onto screen space. This operation is efficient as convolving two Gaussians results in another Gaussian with variance equal to the sum of the two covariance matrices. The 3D smoothing adds a scaled identity term to the original covariance, where the scale depends inversely on the maximal sampling rate. By employing 3D Gaussian smoothing, we ensure that the highest frequency component of any Gaussian does not exceed half of its maximal sampling rate. Note that the low-pass filter becomes an intrinsic part of the 3D representation, remaining constant post-training.

While our 3D smoothing filter effectively mitigates high-frequency artifacts, rendering the reconstructed scene at lower sampling rates would still lead to aliasing. We replicate the physical imaging process, where photons hitting a pixel on the camera sensor are integrated over the pixel's area. While an ideal model would use a 2D box filter in image space, we approximate it with a 2D Gaussian filter for efficiency. The 2D Mip filter is applied in screen space with parameter s chosen to cover a single pixel in screen space. A critical difference to EWA splatting is that we tackle the reconstruction problem, optimizing the 3D Gaussian representation via inverse rendering, while EWA splatting only considers the forward rendering problem.

To overcome these challenges, we make two modifications to the original 3DGS model. In particular, we introduce a 3D smoothing filter that limits the frequency of the 3D representation and replace the 2D dilation with a 2D Mip filter that approximates box filtering in the physical imaging process. The 3D smoothing filter resolves the scale ambiguity by ensuring Gaussian primitives maintain physically meaningful sizes constrained by the Nyquist frequency of the training views. The 2D Mip filter, meanwhile, replaces the ad-hoc dilation with a principled anti-aliasing mechanism that adapts to the target rendering resolution. Together, these principled and simple modifications require only few changes to the original 3DGS code, making our approach easy to adopt.

We build our method upon the popular open-source 3DGS code base. Following 3DGS, we train our models for 30K iterations across all scenes and use the same loss function, Gaussian density control strategy, schedule and hyperparameters. For the multi-scale training setting on the Blender dataset, our approach attains comparable or superior performance compared to state-of-the-art methods such as Mip-NeRF and Tri-MipRF. Notably, our method outperforms 3DGS and 3DGS + EWA by a substantial margin. For the single-scale training and multi-scale testing — a novel evaluation protocol proposed in this work — our method significantly outperforms all existing state-of-the-art methods.

On the Mip-NeRF 360 dataset, we evaluate in two setups. First, following the standard approach where models are trained and evaluated at the same scale, with indoor scenes downsampled by a factor of two and outdoor scenes by four. In this in-distribution setting, Mip-Splatting maintains competitive performance with the original 3DGS. Second, models are trained on data downsampled by a factor of 8 and rendered at successively higher resolutions to simulate zoom-in effects. Qualitative results demonstrate that Mip-Splatting effectively eliminates high-frequency artifacts, yielding high quality renderings that more closely resemble ground truth. Methods based on 3DGS capture fine details more effectively than Mip-NeRF and Tri-MipRF, but only at the original training scale — 3DGS exhibits dilation artifacts at lower resolutions, while EWA splatting uses a large low-pass filter, resulting in oversmoothed images.

In the absence of a public benchmark for the single-scale training and multi-scale testing setting, we trained all baseline methods ourselves. The quantitative results indicate that our method significantly outperforms all existing state-of-the-art methods in this challenging evaluation. Notably, our method surpasses both 3DGS and 3DGS + EWA in rendering quality at lower resolutions. In particular, 3DGS exhibits dilation artifacts, while EWA splatting uses a large low-pass filter to limit the frequency of the rendered images, resulting in oversmoothed images. Our approach achieves the best balance between artifact removal and detail preservation across all tested scales.

To evaluate the effectiveness of the 3D smoothing filter, we conduct an ablation with the single-scale training and multi-scale testing setting to simulate zoom-in effects in the Mip-NeRF 360 dataset. Omitting the 3D smoothing filter results in high-frequency artifacts when rendering higher resolution images. Excluding the 2D Mip filter causes a slight decline in performance as this filter's role is mainly for mitigating zoom-out artifacts. The absence of both filters leads to an excessive generation of small Gaussian primitives, due to the density control mechanism, resulting in out-of-memory errors.

The ablation further demonstrates the complementary nature of the two filters. While the 3D smoothing filter is critical for zoom-in scenarios by preventing overly sharp Gaussian primitives, the 2D Mip filter provides benefits primarily for zoom-out operations by properly integrating multiple Gaussians within a single pixel's footprint. We choose the variance of our 2D Mip filter as 0.1, approximating a single pixel, and the variance of our 3D smoothing filter as 0.2, totaling 0.3 for a fair comparison with the EWA filter. These hyperparameters remain fixed across all experiments, demonstrating the robustness of our approach.

We have presented Mip-Splatting, which addresses the aliasing and dilation artifacts of 3D Gaussian Splatting when the sampling rate changes. Our approach introduces two principled modifications: a 3D smoothing filter that constrains the maximum frequency of Gaussian primitives based on the Nyquist-Shannon Sampling Theorem, and a 2D Mip filter that replaces the ad-hoc dilation with a physically motivated anti-aliasing mechanism. These modifications are closed-form, computationally efficient, and require only minimal changes to the original 3DGS implementation. Experiments demonstrate that training at a single sampling rate enables faithful rendering at various sampling rates, achieving state-of-the-art results on both in-distribution and out-of-distribution evaluation benchmarks. Our work demonstrates the value of incorporating signal processing principles into modern neural rendering pipelines.