Mip-Splatting: Alias-free 3D Gaussian Splatting
Zehao Yu1,2
1

Anpei Chen†,1,2

Binbin Huang3

Torsten Sattler4

Andreas Geiger1,2

2
3
University of TübingenTübingen AI Center
ShanghaiTech University
4
Czech Technical University in Prague

https://niujinshuchong.github.io/mip-splatting(a) Faithful Representation(b) Degenerate Representation

3D Object

3D Gaussian

FaithfulRendering

2D Gaussian

Image Plane(Screen Space)

FaithfulRendering

Dilated
2D Gaussian

5 Pixels
Camera Center(c) Zoom-out of (a)(d) Zoom-in of (b)Erosion(Brake cable
too thin)
Dilation(Spokes too thick due toscreen space dilation)

Brightening

Decreased
Focal length

Increased
Focal length

High frequency
artifacts due todegenerate (thin)
3D Gaussians

Figure 1. 3D Gaussian Splatting [18] renders images by representing 3D Objects as 3D Gaussians which are projected onto the image
plane followed by 2D Dilation in screen space as shown in (a). The method’s intrinsic shrinkage bias leads to degenerate 3D Gaussians
exceed sampling limit as illustrated by the δ function in (b) while rendering similarly to 2D due to the dilation operation. However, whenchanging the sampling rate (via the focal length or camera distance), we observe strong dilation effects (c) and high frequency artifacts (d).

Abstract
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 thisphenomenon 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 toconstrains the size of the 3D Gaussian primitives basedon the maximal sampling frequency induced by the input
views. It eliminates high-frequency artifacts when zooming
in. Moreover, replacing 2D dilation with a 2D Mip filter,
which simulates a 2D box filter, effectively mitigates aliasing and dilation issues. Our evaluation, including scenarios
such a training on single-scale images and testing on multiple scales, validates the effectiveness of our approach.
† Corresponding author.

1. Introduction
Novel View Synthesis (NVS) plays a critical role in computer graphics and computer vision, with various applications including virtual reality, cinematography, robotics,
and more. A particularly significant advancement in thisfield is the Neural Radiance Field (NeRF) [28], introducedby Mildenhall et al. in 2020. NeRF utilizes a multilayer perceptron (MLP) to represent geometry and viewdependent appearance effectively, demonstrating remarkable novel view rendering quality. Recently, 3D Gaussian
Splatting (3DGS) [18] has gained attention as an appealing
alternative to both MLP [28] and feature grid-based representations [4, 11, 24, 32, 46]. 3DGS stands out for its impressive novel view synthesis results, while achieving realtime rendering at high resolutions. This effectiveness andefficiency, coupled with the potential integration into thestandard rasterization pipeline of GPUs represents a significant step towards practical usage of NVS methods.
Specifically, 3DGS represents complex scenes as a set

8× Resolution
Full Resolution
1/4 Resolutionof 3D Gaussians, which are rendered to screen space
through splatting-based rasterization. The attributes of each
3D Gaussian, i.e., position, size, orientation, opacity, andcolor, are optimized through a multi-view photometric loss.
Thereafter, a 2D dilation operation is applied in screen
space for low-pass filtering. Although 3DGS has demonstrated impressive NVS results, it produces artifacts whencamera views diverge from those seen during training, suchas zoom in and zoom out, as illustrated in Figure 1. 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 causes erosion artifacts since the projected 2D Gaussians expand, yet dilation
remains constant, causing erosion and resulting in incorrect
gaps between Gaussians in the 2D projection.
To resolve these issues, we propose to regularize the 3D
representation in 3D space. Our key insight is that the highest frequency that can be reconstructed of a 3D scene isinherently constrained by the sampling rates of the input
images. We first derive the multi-view frequency bounds ofeach Gaussian primitive based on the training views according to the Nyquist-Shannon Sampling Theorem [33, 45].
By applying a low-pass filter to the 3D Gaussian primitives
in 3D space during the optimization, we effectively restrict
the maximal frequency of the 3D representation to meet the
Nyquist limit. Post-training, this filter becomes an intrinsic
part of the scene representation, remaining constant regardless of viewpoint changes. Consequently, our method eliminates the artifacts presents in 3DGS [18] when zooming in,
as shown in the 8× higher resolution image in Figure 2.
Nonetheless, rendering the reconstructed scene at lower
sampling rates (e.g., zooming out) results in aliasing. Previous work [1–3, 17] address aliasing by employing cone
tracing and applying pre-filtering to the input positional orfeature encoding, which is not applicable to 3DGS. Thus,
we introduce a 2D Mip filter (à la “mipmap”) specificallydesigned to ensure alias-free reconstruction and rendering across different scales. Our 2D Mip filter mimics the
2D box filter inherent to the actual physical imaging process [29, 37, 48], by approximating it with a 2D Gaussian
low pass filter. In contrast to previous work [1–3, 17] that
rely on the MLP’s ability to interpolate multi-scale signals
during training with multi-scale images, our closed-form
modification to the 3D Gaussian representation results inexcellent out-of-distribution generalization: Training at asingle sampling rate enables faithful rendering at various
sampling rates different from those used during training as
demonstrated by the 1/4× down-sampled image in Figure 2.
In summary, we make the following contributions:• We analyze and identify the root of 3DGS’s artefacts

3DGS [18]3DGS + EWA [59]Mip-Splatting

Reference

Figure 2. We trained all the models on single-scale (full resolution here) images and rendered images with different resolutions
by changing focal length. While all methods show similar performance at training scale, we observe strong artifacts in previous
work [18, 59] when changing the sampling rate. By contrast, our
Mip-Splatting renders faithful images across different scales.

when changing sampling rates.
• We introduce a 3D smoothing filter for 3DGS to effectively regularize the maximum frequency of 3D Gaussian primitives, resolving the artifacts observed in out-ofdistribution renderings of prior methods [18, 59].
• We replace the 2D dilation filter with a 2D Mip filter toaddress aliasing and dilation artifacts.
• Experiments on challenging benchmark datasets [2, 28]
demonstrate the effectiveness of Mip-Splatting whenmodifying the sampling rate.

2. Related Work
Novel View Synthesis: NVS is the process of generating
new images from viewpoints different from those of theoriginal captures [12, 22]. NeRF [28], which leverages volume rendering [10, 21, 25, 26], has become a standard technique in the field. NeRF utilizes MLPs [5, 27, 34] to model
scenes as continuous functions, which, despite their compact representation, impede rendering speed due to the expensive MLP evaluation that is required for each ray point.
Subsequent methods [16, 40, 41, 52, 54] distill a pretrained
NeRF into a sparse representation, enabling real-time rendering of NeRFs. Further advancements have been madeto improve the training and rendering of NeRF with advanced scene representations [4, 6, 11, 18, 19, 24, 32, 46,51]. In particular, 3D Gaussians Splatting (3DGS) [18]demonstrated impressive novel view synthesis results, whileachieving 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 (focal length/scene distance). In thispaper, we study the out-of-distribution generalization of
3DGS, training models at a single scale and evaluating it
across multiple scales.
Primitive-based Differentiable Rendering: Primitivebased rendering techniques, which rasterize geometricprimitives onto the image plane, have been explored extensively due to their efficiency [13, 14, 38, 44, 59, 60].
Differentiable point-based rendering methods [20, 36, 39,
43, 49, 53, 57] offer great flexibility in representing intricate structures and are thus well-suited for novel view
synthesis. Notably, Pulsar [20] stands out for its efficientsphere rasterization. The more recent 3D Gaussian Splatting (3DGS) work [18] utilizes anisotropic Gaussians [59]and introduces a tile-based sorting for rendering, achieving remarkable frame rates. Despite its impressive results,
3DGS exhibits strong artifacts when rendering at a different sampling rate. We address this issue by introducing a
3D smoothing filter to constrain the maximal frequencies of
the 3D Gaussian primitive representation, and a 2D Mip filter that approximates the box filter of the physical imaging
process for alias-free rendering.
Anti-aliasing in Rendering: There are two principal strategies to combat aliasing: super-sampling, which increases
the number of samples [7], and prefiltering, which applies low-pass filtering to the signal to meet the Nyquist
limit [8, 15, 31, 47, 50, 59]. For example, EWA splatting [59] applies a Gaussian low pass filter to the projected
2D Gaussian in screen space to produce a band limited output respecting the Nyquist frequency of the image. While
we also apply a band-limited filter to the Gaussian primitives, our band-limited filter is applied in 3D space and thefilter size is fully determined by the training images not theimages to be rendered. While our 2D Mip filter is also a
Gaussian low pass filter in screen space, it approximates thebox filter of the physical imaging process, approximating
a single pixel. Conversely, the EWA filter limits the frequency signal’s bandwidth to the rendered image, and thesize of the filter is chosen empirically. A critical difference to [59] is that we tackle the reconstruction problem,
optimizing the 3D Gaussian representation via inverse rendering while EWA splatting only considers the rendering
problem.
Recent neural rendering methods integrate pre-filtering
to mitigate aliasing [1–3, 17, 58]. Mip-NeRF [1], for instance, introduced an integrated position encoding (IPE) toattenuate high-frequency details. A similar idea is adapted
for feature grid-based representations [3, 17, 58]. Note thatthese approaches require multi-scale images extracted fromthe original data for supervision. In contrast, our approachis based on 3DGS [18] and determines the necessary lowpass filter size based on pixel size, allowing for alias-freerendering at scales unobserved during training.

3. Preliminaries
In this section, we first review the sampling theorem in Section 3.1, laying the foundation for understanding the aliasing problem. Subsequently, we introduce 3D Gaussian
Splatting (3DGS) [18] and its rendering process in Section 3.2.

3.1. Sampling Theorem
The Sampling Theorem, also known as the NyquistShannon Sampling Theorem [33, 45], is a fundamental concept in signal processing and digital communication that describes the conditions under which a continuous signal canbe accurately represented or reconstructed from its discrete
samples. To accurately reconstruct a continuous signal fromits discrete samples without loss of information, the following conditions must be met:
Condition 1 The continuous signal must be band-limited
and may not contain any frequency components above acertain maximum frequency ν.
Condition 2 The sampling rate ν̂ must be at least twice thehighest frequency present in the continuous signal: ν̂ ≥ 2ν.
In practice, to satisfy the constraints when reconstructing
a signal from discrete samples, a low-pass or anti-aliasing
filter is applied to the signal before sampling. The filter
eliminates any frequency components above ν̂2 and attenuates high-frequency content that could lead to aliasing.

3.2. 3D Gaussian Splatting
Prior works [18, 59] propose to represent a 3D scene as a setof scaled 3D Gaussian primitives {Gk |k = 1, · · · , K} andrender an image using volume splatting. The geometry ofeach scaled 3D Gaussian Gk is parameterized by an opacity (scale) αk ∈ [0, 1], center pk ∈ R3×1 and covariancematrix Σk ∈ R3×3 defined in world space:  \cG _k(\bx ) = e^{-\frac {1}{2} (\bx -\bp _k)^T \bSigma _k^{-1}(\bx -\bp _k)} (1)

To constrain Σk to the space of valid covariance matrices, asemi-definite parameterization Σk = Ok sk sTk OTk is used.
Here, s ∈ R3 is a scaling vector and O ∈ R3×3 is a rotation
matrix, parameterized by a quaternion [18].
To render an image for a given view point defined by rotation R ∈ R3×3 and translation t ∈ R3 , the 3D Gaussians{Gk } are first transformed into camera coordinates:  \bp '_k = \bR \, \bp _k + \bt , \quad \bSigma '_k = \bR \,\bSigma _k \, \bR ^T (2)

Afterwards, they are projected to ray space via a local affine
transformation
  \bSigma ''_k = \bJ _k\, \bSigma '_k \, \bJ _k^T (3)where the Jacobian matrix Jk is an affine approximation to
the projective transformation defined by the center of the 3D
Gaussian p′k . By skipping the third row and column of Σ′′k ,we obtain a 2D covariance matrix Σ2D
k in ray space, and we
use Gk2D to refer to the corresponding scaled 2D Gaussian,see [18] for details.
Finally, 3DGS [18] utilizes spherical harmonics to modelview-dependent color ck and renders image via alphablending according to the primitive’s depth order 1, . . . , K:  \bc (\bx ) = \sum ^K_{k=1} \bc _k\,\alpha _k\,\cG ^{2D}_k(\bx ) \prod _{j=1}^{k-1} (1 - \alpha _j\,\cG ^{2D}_j(\bx )) 

(4)

Dilation: To avoid degenerate cases where the projected 2D
Gaussians are too small in screen space, i.e., smaller than apixel, the projected 2D Gaussians are dilated as follows:
  \cG ^{2D}_k(\bx ) = e^{-\frac {1}{2} (\bx -\bp _k)^T \, {(\bSigma ^{2D}_k + \, s \, \bI )}^{-1} \, (\bx -\bp _k)} \label {eqn:dilation} (5)where I is a 2D identity matrix and s is a scalar dilation
hyperparameter. Note that this operator adjusts the scale ofthe 2D Gaussian while leaving its maximum unchanged. As
this effect is similar to that of dilation operators in morphology, we called it a 2D screen space dilation operation* .
Reconstruction: As the rendering process is fast and differentiable, the 3D Gaussian parameters can be efficiently
optimized using a multi-view loss. During optimization, 3D
Gaussians are adaptively added and deleted to better represent the scene. We refer the reader to [18] for details.

4. Sensitivity to Sampling Rate
In traditional forward splatting, the centers pk and colors ck
of Gaussian primitives are predetermined, whereas the 3D
Gaussian covariance Σk are chosen empirically [42, 59].
In contrast, 3DGS [18], optimizes all parameters jointly
through an inverse rendering framework by backpropagating a multi-view photometric loss.
We observe that this optimization suffers from ambiguities as illustrated in Figure 1 which shows a simple example involving one object and an image sensor with 5 pixels.
Consider the 3D object in (a), its approximation by a 3D
Gaussian and its projection into screen space (blue pixel).
Due to screen space dilation (Eq. 5) with a Gaussian kernel(size ≈ 1 pixel), the degenerate 3D Gaussian represented bya Dirac δ function in (b) leads to a similar image. In order torepresent high frequency details in real world scenes, the dilated 2D Gaussians would become small, since the smaller* The dilation operation is not mentioned in original paper.

the Gaussian, the higher the frequency it represents, resulting in systematically underestimation of its scale.
While this does not affect rendering at similar sampling
rates (cf. Figure 1 (a) vs. (b)), it leads to erosion effects
when zooming in or moving the camera closer. This is because the dilated 2D Gaussians become smaller in screen
space. In this case, the rendered image exhibits highfrequency artifacts, rendering object structures thinner thanthey actually appear as illustrated in Figure 1 (d).
Conversely, screen space dilation also negatively affects
rendering when decreasing the sampling rate as illustrated
in Figure 1 (c) which shows a zoomed-out version of (a). In
this case, dilation spreads radiance in a physically incorrect
way across pixels. Note that in (c), the area covered by
the projection of the 3D object is smaller than a pixel, yet
the dilated Gaussian is not attenuated, accumulating more
light than what physically reaches the pixel. This leads toincreased brightness and dilation artifacts which strongly
degrade the appearance of the bicycle wheels’ spokes.
The aforementioned scale ambiguity becomes particularly problematic in representations involving millions ofGaussians. However, simply discarding screen space dilation results in optimization challenges for complex scenes,
such as those present in the Mip-NeRF 360 dataset [2],where a large number of small Gaussians are created by thedensity control mechanism [18], exceeding GPU capacity.
Moreover, even if a model can be successfully trained without dilation, decreasing the sampling rate results in aliasing
effects due to the lack of anti-aliasing [59].

5. Mip Gaussian Splatting
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 to below half the maximum sampling rate determined by the training images, eliminating high frequency
artifacts when zooming in. Moreover, we demonstrate that
replacing 2D screen space dilation with a 2D Mip filter,
which approximates the box filter inherent to the physicalimaging process, effectively mitigates aliasing and dilation
issues. In combination, Mip-Splatting enables alias-freerenderings† across various sampling rates. We now discuss
the the 3D smoothing and the 2D Mip filters in detail.

5.1. 3D Smoothing Filter
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 [2, 55, 56]. Our key insight is that the highest frequency of a reconstructed 3D scene is limited by† Note that we use alias to refer to multiple artifacts discussed in thepaper, including dilation, erosion, oversmoothing, high-frequency artifacts
and aliasing itself.

Camera 4(smaller d)Camera 1

Camera 2(smaller f)

Camera 3(larger f)

Camera 5(larger d)Figure 3. Sampling limits. A pixel corresponds to sampling interval T̂ . We band-limit the 3D Gaussians by the maximal sampling
rate (i.e., minimal sampling interval) among all observations. This
example shows 5 cameras at different depths d and with different
focal lengths f . Here, camera 3 determines the minimal T̂ andhence the maximal sampling rate ν̂.

we recompute the maximal sampling rate of each Gaussianprimitive every m iterations as we found the 3D Gaussians
centers remain relatively stable throughout the training.
3D Smoothing: Given the maximal sampling rate ν̂k for aprimitive, we aim to constrain the maximal frequency of the
3D representation. This is achieved by applying a Gaussian
low-pass filter Glow to each 3D Gaussian primitive Gk before
projecting it onto screen space:  \cG _k(\bx )_{\text {reg}} = (\cG _k \otimes \cG _{\text {low}})(\bx ) \label {eqn:filter_3d_simple}(8)This operation is efficient as convolving two Gaussians withcovariance matrices Σ1 and Σ2 results in another Gaussianwith variance Σ1 + Σ2 . Hence,
  \cG _k(\bx )_\text {reg} = \sqrt {\frac {|\bSigma _k|}{|\bSigma _k + \frac {s}{\hat {\nu }_k^2} \cdot \bI |}} \, \, e^{-\frac {1}{2} (\bx -\bp _k)^T \, (\bSigma _k + \frac {s}{\hat {\nu }_k^2} \cdot \bI )^{-1} \, (\bx -\bp _k)} \label {eqn:filter_3d_full} the sampling rate defined by the training views. Following
Nyquist’s theorem 3.1, we aim to constrain the maximum
frequency of the 3D representation during optimization.
Multiview Frequency Bounds: Multi-view images are 2D
projections of a continuous 3D scene. The discrete image
grid determines where we sample points from the continuous 3D signal. This sampling rate is intrinsically related tothe image resolution, camera focal length, and the scene’s
distance from the camera. For an image with focal length
f in pixel units, the sampling interval in screen space is 1.
When this pixel interval is back-projected to the 3D worldspace, it results in a world space sampling interval T̂ at agiven depth d, with sampling frequency ν̂ as its inverse:  \hat {T} = \frac {1}{\hat {\nu }} = \frac {d}{f} \label {eqn:sampling_rate} (6)As posited by Nyquist’s theorem Section 3.1, given samples
drawn at frequency ν̂, reconstruction algorithms are able toreconstruct components of the signal with frequencies up tofν̂
2 , or 2d . Consequently, a primitive smaller than 2T̂ may
result in aliasing artifacts during the splatting process, since
its size is below twice the sampling interval.
To simplify, we approximate depth d using the center ofthe primitive pk , and disregard the impact of occlusion forsampling interval estimation. Since the sampling rate of aprimitive is depth-dependent and differs across cameras, we
determine the maximal sampling rate for primitive k as  \hat {\nu }_k = \text {max}\left (\left \{ \mathds {1}_n(\bp _k) \cdot \frac {f_n}{d_n}\right \}^{N}_{n=1}\right ) (7)

where N is the total number of images, 1n (p) is an indicator function that assesses the visibility of a primitive. It
is true if the Gaussian center pk falls within the view frustum of the n-th camera. Intuitively, we choose the sampling
rate such that there exists at least one camera that is able
to reconstruct the respective primitive. This process is illustrated in Figure 3 for N = 5. In our implementation,(9)Here, s is a scalar hyperparameter to control the size of thefilter. Note that the scale ν̂sk of the 3D filters for each primitive are different as they depend on the training views inwhich they are visible. By employing 3D Gaussian smoothing, we ensure that the highest frequency component of any
Gaussian does not exceed half of its maximal sampling rate
for at least one camera. Note that Glow becomes an intrinsic part of the 3D representation, remaining constant posttraining.

5.2. 2D Mip Filter
While our 3D smoothing filter effectively mitigates highfrequency artifacts [18, 59], rendering the reconstructedscene at lower sampling rates (e.g., zooming out or moving the camera further away) would still lead to aliasing. To
overcome this, we replace the screen space dilation filter of
3DGS by a 2D Mip filter.
More specifically, we replicate the physical imaging process [37, Section 8], where photons hitting a pixel on thecamera sensor are integrated over the pixel’s area. While anideal model would use a 2D box filter in image space, we
approximate it with a 2D Gaussian filter for efficiency
  \cG ^{2D}_k(\bx )_{\text {mip}} = \sqrt {\frac {|\bSigma ^{2D}_k|}{|\bSigma ^{2D}_k + s \bI |}} \, \, e^{-\frac {1}{2} (\bx -\bp _k)^T \, (\bSigma ^{2D}_k + s \bI )^{-1} \, (\bx -\bp _k)} \label {eqn:ewa_filter} (10)where s is chosen to cover a single pixel in screen space.
While our Mip filter shares similarities with the EWA
filter [59], their underlying principles are distinct. Our Mip
filter is designed to replicate the box filter in the imaging
process, targeting an exact approximation of a single pixel.
Conversely, the EWA filter’s role is to limit the frequency
signal’s bandwidth, and the size of the filter is chosen empirically. The EWA paper [15, 59] even advocates for an identity covariance matrix, effectively occupying a 3x3 pixel region on the screen. However, this approach leads to overlyPSNR ↑
SSIM ↑LPIPS ↓
Full Res. 1/2 Res. 1/4 Res. 1/8 Res. Avg. Full Res. 1/2 Res. 1/4 Res. 1/8 Res. Avg. Full Res. 1/2 Res. 1/4 Res. 1/8 Res Avg.
NeRF w/o  \mathcal {L}_\text {area}  [1, 28] 31.20 30.65 26.25 22.53 27.66 0.950 0.956 0.930 0.871 0.927 0.055 0.034 0.043 0.075 0.052
NeRF [28]29.90 32.13 33.40 29.47 31.23 0.938 0.959 0.973 0.962 0.958 0.074 0.040 0.024 0.039 0.044
MipNeRF [1]32.63 34.34 35.47 35.60 34.51 0.958 0.970 0.979 0.983 0.973 0.047 0.026 0.017 0.012 0.026
Plenoxels [11]31.60 32.85 30.26 26.63 30.34 0.956 0.967 0.961 0.936 0.955 0.052 0.032 0.045 0.077 0.051
TensoRF [4]32.11 33.03 30.45 26.80 30.60 0.956 0.966 0.962 0.939 0.956 0.056 0.038 0.047 0.076 0.054
30.00 32.15 33.31 29.35 31.20 0.939 0.961 0.974 0.963 0.959 0.079 0.043 0.026 0.040 0.047
Instant-NGP [32]Tri-MipRF [17]*32.65 34.24 35.02 35.53 34.36 0.958 0.971 0.980 0.987 0.974 0.047 0.027 0.018 0.012 0.026
3DGS [18]28.79 30.66 31.64 27.98 29.77 0.943 0.962 0.972 0.960 0.960 0.065 0.038 0.025 0.031 0.040
3DGS [18] + EWA [59] 31.54 33.26 33.78 33.48 33.01 0.961 0.973 0.979 0.983 0.974 0.043 0.026 0.021 0.019 0.027
Mip-Splatting (ours)
32.81 34.49 35.45 35.50 34.56 0.967 0.977 0.983 0.988 0.979 0.035 0.019 0.013 0.010 0.019

Table 1. Multi-scale Training and Multi-scale Testing on the Blender dataset [28]. Our approach achieves state-of-the-art performancein most metrics. It significantly outperforms 3DGS [18] and 3DGS + EWA [59]. ∗ indicates that we retrain the model.

smooth results when zooming out as we will show in our
experiments.

6. Experiments
We first present the implementation details of MipSplatting. We then assess its performance on the Blenderdataset [28] and the challenging Mip-NeRF 360 dataset [2].
Finally, we discuss the limitations of our approach.

6.1. Implementation
We build our method upon the popular open-source 3DGS
code base [18]‡ . Following [18], we train our models for
30K iterations across all scenes and use the same loss function, Gaussian density control strategy, schedule and hyperparameters. For efficiency, we recompute the sampling rateof each 3D Gaussian every m = 100 iterations. We choose
the variance of our 2D Mip filter as 0.1, approximating asingle pixel, and the variance of our 3D smoothing filter as
0.2, totaling 0.3 for a fair comparison with 3DGS [18] and3DGS + EWA [59] which replaces the dilation of 3DGS
with the EWA filter.

6.2. Evaluation on the Blender Dataset
Multi-scale Training and Multi-scale Testing: Following
previous work [1, 17], we train our model with multi-scaledata and evaluate on multi-scale data. Similar to [1, 17]
where rays of full resolution images are sampled more frequently compared to lower resolution images, we sample
40 percent of full resolution images and 20 percent fromother image resolutions each. Our quantitative evaluationis shown in Table 1. Our approach attains comparable orsuperior performance compared to state-of-the-art methods
such as Mip-NeRF [1] and Tri-MipRF [17]. Notably, ourmethod outperforms 3DGS [18] and 3DGS + EWA [59] bya substantial margin, owing to its 2D Mip filter.
Single-scale Training and Multi-scale Testing: Contrary
to prior work that evaluates models trained on single-scaledata at the same scale, we consider an important new setting‡ https://github.com/graphdeco-inria/gaussian-splattingthat involves training on full-resolution images and rendering at various resolutions (i.e. 1×, 1/2, 1/4, and 1/8) to mimic
zoom-out effects. In the absence of a public benchmark
for this setting, we trained all baseline methods ourselves.
We use NeRFAcc [23]’s implementation for NeRF [28],Instant-NGP [32], and TensoRF [4] for its efficiency. Official implementations were employed for Mip-NeRF [1],Tri-MipRF [17], and 3DGS [18]. The quantitative results,
as presented in Table 2, indicate that our method significantly outperforms all existing state-of-the-art methods. A
qualitative comparison is provided in Figure 4. Methods
based on 3DGS [18] capture fine details more effectively
than Mip-NeRF [1] and Tri-MipRF [17], but only at theoriginal training scale. Notably, our method surpasses both
3DGS [18] and 3DGS + EWA [59] in rendering quality atlower resolutions. In particular, 3DGS [18] exhibits dilation artifacts. EWA splatting [59] uses a large low pass filter
to limit the frequency of the rendered images, resulting inoversmoothed images, which becomes particularly apparent
at lower resolutions.

6.3. Evaluation on the Mip-NeRF 360 Dataset
Single-scale Training and Multi-scale Testing: To simulate zoom-in effects, we train models on data downsampled
by a factor of 8 and rendered at successively higher resolutions (1×, 2×, 4×, and 8×). In the absence of a publicbenchmark for this setting, we trained all baseline methods ourselves. We use the official implementation for MipNeRF 360 [1] and 3DGS [18] and use a community reimplementation for Zip-NeRF [3]§ as the code is not available. The results in Table 3 show that our method performs
comparable to prior work at the training scale (1×) and significantly exceeds all state-of-the-art methods at higher resolutions. As depicted in Figure 5, our method generates
high fidelity imagery without high-frequency artifacts. Notably, both Mip-NeRF 360 [2] and Zip-NeRF [3] exhibit
subpar performance at increased resolutions, likely due totheir MLPs’ inability to extrapolate to out-of-distribution
frequencies. While 3DGS [18] introduces notable erosion§ https://github.com/SuLvXiangXin/zipnerf-pytorch

Full
1/2
1/4
1/8

Full
1/2
1/4
1/8

Full
1/2
1/4
1/8

Mip-NeRF [1]Tri-MipRF [17]3DGS [18]3DGS [18] + EWA [59]Mip-Splatting (ours)

GT

Figure 4. Single-scale Training and Multi-scale Testing on the Blender Dataset [28]. All methods are trained at full resolution andevaluated at different (smaller) resolutions to mimic zoom-out. Methods based on 3DGS capture fine details better than Mip-NeRF [1] andTri-MipRF [17] at training resolution. Mip-Splatting surpasses both 3DGS [18] and 3DGS + EWA [59] at lower resolutions.
PSNR ↑
SSIM ↑LPIPS ↓
Full Res. 1/2 Res. 1/4 Res. 1/8 Res. Avg. Full Res. 1/2 Res. 1/4 Res. 1/8 Res. Avg. Full Res. 1/2 Res. 1/4 Res. 1/8 Res Avg.
NeRF [28]31.48 32.43 30.29 26.70 30.23 0.949 0.962 0.964 0.951 0.956 0.061 0.041 0.044 0.067 0.053
MipNeRF [1]33.08 33.31 30.91 27.97 31.31 0.961 0.970 0.969 0.961 0.965 0.045 0.031 0.036 0.052 0.041
TensoRF [4]32.53 32.91 30.01 26.45 30.48 0.960 0.969 0.965 0.948 0.961 0.044 0.031 0.044 0.073 0.048
Instant-NGP [32]33.09 33.00 29.84 26.33 30.57 0.962 0.969 0.964 0.947 0.961 0.044 0.033 0.046 0.075 0.049
Tri-MipRF [17]32.89 32.84 28.29 23.87 29.47 0.958 0.967 0.951 0.913 0.947 0.046 0.033 0.046 0.075 0.050
3DGS [18]33.33 26.95 21.38 17.69 24.84 0.969 0.949 0.875 0.766 0.890 0.030 0.032 0.066 0.121 0.063
3DGS [18] + EWA [59] 33.51 31.66 27.82 24.63 29.40 0.969 0.971 0.959 0.940 0.960 0.032 0.024 0.033 0.047 0.034
Mip-Splatting (ours)
33.36 34.00 31.85 28.67 31.97 0.969 0.977 0.978 0.973 0.974 0.031 0.019 0.019 0.026 0.024

Table 2. Single-scale Training and Multi-scale Testing on the Blender Dataset [28]. All methods are trained on full-resolution images
and evaluated at four different (smaller) resolutions, with lower resolutions simulating zoom-out effects. While Mip-Splatting yields
comparable results at training resolution, it significantly surpasses previous work at all other scales.

artifacts due to dilation operations, 3DGS + EWA [59] performs better while still yielding pronounced high-frequency
artifacts. In contrast, our method avoids such artifacts,yielding aesthetically pleasing images that more closely resemble ground truth. It’s important to remark that rendering
at higher resolutions is a super-resolution task, and models
should not hallucinate high-frequency details absent fromthe training data.
Single-scale Training and Same-scale Testing: We further
evaluate our method on the Mip-NeRF 360 dataset [2] following the widely used setting, where models are trained
and tested at the same scale, with indoor scenes downsampled by a factor of two and outdoor scenes by four.
As shown in Table 4, our method performs on par with
3DGS [18] and 3DGS + EWA [59] in this challenging
benchmark, without any decrease in performance. This con-firms our method’s effectiveness to handle various settings.

6.4. Limitations
Our method employs a Gaussian filter as an approximation
to a box filter for efficiency. However, this approximation
introduces errors, particularly when the Gaussian is smallin screen space. This issue correlates with our experimental findings, where increased zooming out leads to larger
errors, as evidenced in Table 2. Additionally, there is aslight increase in training overhead as the sampling rate foreach 3D Gaussian must be calculated every m = 100 iterations. Currently, this computation is performed using
PyTorch [35] and a more efficient CUDA implementation
could potentially reduce this overhead. Designing a betterdata structure for precomputing and storing the sampling
rate, as it depends solely on the camera poses and intrin-Mip-NeRF 360 [2]Zip-NeRF [3]3DGS [18]3DGS [18] + EWA [59]Mip-Splatting (ours)

GT

Figure 5. Single-scale Training and Multi-scale Testing on the Mip-NeRF 360 Dataset [2]. All models are trained on images downsampled by a factor of eight and rendered at full resolution to demonstrate zoom-in/moving closer effects. In contrast to prior work,
Mip-Splatting renders images that closely approximate ground truth. Please also note the high-frequency artifacts of 3DGS + EWA [59].
PSNR ↑
SSIM ↑LPIPS ↓
1× Res. 2× Res. 4× Res. 8× Res. Avg. 1× Res. 2× Res. 4× Res. 8× Res. Avg. 1× Res. 2× Res. 4× Res. 8× Res. Avg.
Instant-NGP [32]26.79 24.76 24.27 24.27 25.02 0.746 0.639 0.626 0.698 0.677 0.239 0.367 0.445 0.475 0.382
mip-NeRF 360 [2]29.26 25.18 24.16 24.10 25.67 0.860 0.727 0.670 0.706 0.741 0.122 0.260 0.370 0.428 0.295
zip-NeRF [3]29.66 23.27 20.87 20.27 23.52 0.875 0.696 0.565 0.559 0.674 0.097 0.257 0.421 0.494 0.318
3DGS [18]29.19 23.50 20.71 19.59 23.25 0.880 0.740 0.619 0.619 0.715 0.107 0.243 0.394 0.476 0.305
3DGS [18] + EWA [59] 29.30 25.90 23.70 22.81 25.43 0.880 0.775 0.667 0.643 0.741 0.114 0.236 0.369 0.449 0.292
Mip-Splatting (ours)
29.39 27.39 26.47 26.22 27.37 0.884 0.808 0.754 0.765 0.803 0.108 0.205 0.305 0.392 0.252

Table 3. Single-scale Training and Multi-scale Testing on the Mip-NeRF 360 Dataset [2]. All methods are trained on the smallest scale(1×) and evaluated across four scales (1×, 2×, 4×, and 8×), with evaluations at higher sampling rates simulating zoom-in effects. While
our method yields comparable results at the training resolution, it significantly surpasses all previous work at all other scales.

NeRF [9, 28]
mip-NeRF [1]
NeRF++ [56]Plenoxels [11]Instant NGP [32, 52]
mip-NeRF 360 [2, 30]
Zip-NeRF [3]3DGS [18]3DGS [18]*3DGS [18] + EWA [59]Mip-Splatting (ours)

PSNR ↑ SSIM ↑ LPIPS ↓
23.85
0.605
0.451
24.04
0.616
0.441
25.11
0.676
0.375
23.08
0.626
0.463
25.68
0.705
0.302
27.57
0.793
0.234
28.54
0.828
0.189
27.21
0.815
0.214
27.70
0.826
0.202
27.77
0.826
0.206
27.79
0.827
0.203

Table 4. Single-scale Training and Same-scale Testing on the
Mip-NeRF 360 dataset [2]. In the standard in-distribution setting, our approach demonstrates performance on par with many
established techniques. ∗ indicates that we retrain the model.

7. Conclusion
We introduced Mip-Splatting, a technique improving 3DGS
with a 3D smoothing filter and a 2D Mip filter for aliasfree rendering at any scale. Our 3D smoothing filter effectively limits the maximal frequency of Gaussian primitives
to match the sampling constraints imposed by the training
images, while the 2D Mip filter approximates the box filter to simulate the physical imaging process. Mip-Splatting
significantly outperforms state-of-the-art methods in out-ofdistribution scenarios, when testing at sampling rates different from training, resulting in better generalization to outof-distribution camera poses and zoom factors.

Acknowledgement
sics, is an avenue for future work. As mentioned before,
the sampling rate computation is the only prerequisite during training and the 3D smoothing filter can be fused with
the Gaussian primitives per Eq. 9, thereby eliminating any
additional overhead during rendering.

ZY, AC and AG are supported by the ERC Starting Grant
LEGO-3D (850533) and DFG EXC number 2064/1 project number 390727645. TS is supported by a Czech
Science Foundation (GACR) EXPRO grant (UNI-3D, grantno. 23-07973X). We also thank Christian Reiser for insightful discussions during the preparation of the draft.

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