Anti-Aliased 2D Gaussian Splatting

We thank the reviewer for their time and feedback. We appreciate their positive comments on the paper's clarity, results, and organization. We will correct any missing references, formatting issues, or other minor points in the final version of the paper.

We would like to address the main weaknesses and questions raised, as we believe they stem from a few key misunderstandings of our work's motivation and technical novelty.

On the Purpose and Significance of Anti-Aliasing for 2DGS

The reviewer questions the purpose of our work, suggesting we should have focused on improving mesh quality and that "2DGS offers no substantial benefit over its 3D counterpart" for rendering. We are afraid this reflects a misunderstanding of our central motivation.

We would like to clarify a key point regarding the paper's goal for geometry, which appears to have been misinterpreted. The central claim is one of preservation, not improvement.

Our work is motivated by the fact that 2DGS possesses established geometric advantages over 3DGS, but its rendering limitations due to aliasing hinder its wider practical use and adoption. Therefore, our primary objective was to design an anti-aliasing solution that could be integrated into the pipeline without degrading this geometric fidelity. The DTU experiment (Table 4) was undertaken specifically to validate this claim of preservation. The results, showing our method performing on par with the strong baseline, should thus be interpreted as a success: we fixed the rendering problems while maintaining the geometric strengths.

2DGS is a vital and active research direction precisely because of its geometric accuracy. As we state in the introduction, 2DGS provides superior depth and normal reconstruction compared to 3DGS. This has led to a recent surge in follow-up work that builds upon the 2DGS representation for tasks where geometry is paramount and integral to rendering, such as in reflective scene modeling or physics based rendering where rendering is dependent on reflection direction (ie normal), e.g.:

• Ref-GS: Directional Factorization for 2D Gaussian Splatting. CVPR 25
• Ref-Gaussian Reflective Gaussian Splatting. ICLR 25

, sparse-view joint reconstruction and novel view synthesis, e.g.:

• MAtCha Gaussians: Atlas of Charts for High-Quality Geometry and Photorealism From Sparse Views, CVPR 25

, physics-based inverse rendering with ray tracing, e.g.:

• IRGS: Inter-Reflective Gaussian Splatting with 2D Gaussian Ray Tracing, CVPR 25

An anti-aliased 2DGS representation is highly impactful and beneficial for all such applications of 2DGS.

• The primary limitation of 2DGS is aliasing. Its inability to render well at different scales (e.g., camera zoom) prevents its widespread adoption despite its geometric advantages. Our work directly addresses this bottleneck.
• Our aim is a unified representation. We seek to create a single, robust representation that excels at both high-quality, multi-scale rendering and accurate surface reconstruction from a single training, combining the best of both worlds. The experiments were therefore designed to show that we significantly improve rendering while maintaining the state-of-the-art geometric performance of 2DGS.

This was also agreed on by other reviewers:

MET9 “This directly addresses a critical limitation of 2DGS, enhancing its practical applicability.”

oTXT “The paper is well-written and addresses an important problem: extending anti-aliasing to 2D Gaussian Splatting representations. This has the potential for significant impact given the widespread use of 2D GS.”

4K14 “The motivation and solution is clear. 2DGS has aliasing issues due to max operator”

On Novelty: Beyond a Simple Adaptation of Mip-Splatting

The reviewer characterizes our work as a simple adaptation of Mip-Splatting. We respectfully disagree and wish to highlight our novel technical contributions. Our framework consists of two distinct components, each addressing a different aspect of aliasing with a different level of innovation.

1. A Novel Framework is Required for the 2DGS Rendering Pipeline. The rendering mechanisms of 3DGS and 2DGS are fundamentally incompatible, precluding any direct application of 3DGS-based solutions.

• 3DGS projects 3D Gaussians to screen space, which is a well-defined affine transformation. Applying screen-space EWA filtering is a direct extension of existing literature.
• 2DGS does not project primitives. Instead, it computes a complex, non-linear ray-splat intersection (Eq. 5 and 6) to find a point in the planar splat’s local 2D space.

It is not at all trivial how to perform frequency-based band-limiting or pre-filtering in this context. Our "Object-Space Mip Filter" is a novel solution tailored specifically for this unique intersection-based rendering paradigm. It is a new mathematical derivation with broader impact.

Our technical approach is fundamentally different and more novel than that of Mip-Splatting. Mip-Splatting uses the standard screen-space EWA formulation and simply modifies the filter kernel size.

In contrast, our work introduces a new mathematical derivation for an anti-aliasing filter that operates directly in the object space of each splat. The derivation proceeds as follows:

• The Mapping: We begin with the ray-splat intersection function $m(\mathbf{x}) = \mathbf{u}(\mathbf{x})$ on the splat (Eq. 5 and 6).
• The Core Innovation: We form a first-order Taylor approximation of this complex mapping around a pixel, defined by its Jacobian $\mathbf{J} = \frac{\partial \mathbf{u}}{\partial \mathbf{x}}$ (Eq. 12). This local affine approximation is the key insight that makes an analytical solution possible.
• Mapping to Screen Space: Using this affine mapping and a fundamental property of Gaussian functions, we can express how the local unit Gaussian behaves in screen space (Eq. 13).
• Filtering in Screen Space: We then mathematically convolve this transformed Gaussian with a screen-space Mip filter (a Gaussian with covariance $\sigma\mathbf{I}$) to obtain a filtered Gaussian with covariance $\mathbf{J}^{-1}\mathbf{J}^{-\top} + \sigma\mathbf{I}$ (Eq. 15).
• Mapping Back to Object Space: Finally, we use the same affine transform properties to map this filtered screen-space Gaussian back into the splat's local uv-space. This yields our final, novel result: the primitive can be evaluated as a single Gaussian in its local space with a new, dynamically computed covariance $\boldsymbol{\Sigma}_{\text{local}}' = \mathbf{I} + \sigma\mathbf{J}\mathbf{J}^\top$ (Eq. 17).

To our knowledge, this formulation—pre-filtering an intersection-based primitive by analytically deriving an equivalent object-space covariance from a screen-space filter—is a new contribution that has not been proposed before, not even in classical graphics literature on surface splatting, highlighting its novelty and potential impact beyond just 2DGS.

2. The World-Space Flat Smoothing Kernel: A Necessary and Non-Trivial Formulation for Planar Primitives.

Our second component addresses pre-aliasing by band-limiting the representation, conceptually inspired by the frequency analysis in Mip-Splatting. However, a 3D volumetric filter cannot be applied to a 2D planar primitive. Our contribution was to correctly formulate this regularization for a flattened representation by projecting the 3D isotropic smoothing kernel onto the 2D splat plane. This results in our effective planar covariance matrix ($\mathbf{V}_k^{\text{eff}}$ in Eq. 9) and corresponding opacity modulation (Eq. 10), which is a necessary step to complete the anti-aliasing framework for 2DGS, especially for the case of magnification.

3. We provide new insights into the limitations of the original 2DGS.

A key contribution of our work is the analysis and demonstration of the clamping heuristic's ineffectiveness in the original 2DGS. Prior work had not identified this as a critical source of artifacts. Our experiments (2DGS w/o Clamping in Tables 1-5, and in the Appendix) provides the first concrete evidence that this heuristic often exacerbates aliasing and damages performance, especially during minification. This insight itself is a valuable contribution to the understanding of the vanilla 2DGS method.

On Missing Qualitative Mesh Results & FPS Comparison

Mesh Visualizations: Our initial focus on quantitative metrics in Table 4 was to rigorously demonstrate that our method preserves the state-of-the-art geometric accuracy of 2DGS, which was our central claim for this aspect of our work. We deemed numerical results sufficient as they clearly show preservation of baseline performance. To the request of the reviewer, we will add mesh visualizations.

FPS Comparison: The reviewer states that a comparison on FPS is missing. This is a factual error. We explicitly report the overhead in Section 4.1, "Implementation Details":

"our approach incurs a slight overhead of 10-15% in rendering time compared to the original 2DGS implementation."

On Experimental Settings (Table 5)

The reviewer correctly notes that different methods on the Mip-NeRF 360 benchmark use specific resolution settings. We confirm we followed the standard protocol. As stated in Section 4.3 (Single-scale Training and Same-scale Testing):

"Indoor scenes are downsampled by a factor of 2 and outdoor by 4."

The reported numbers for other methods are taken from Mip-Splatting, which used the same standard setup, thus ensuring a fair comparison.

We hope these clarifications address the reviewer's concerns and underscore the novelty and significance of our contributions. We are confident that AA-2DGS is a valuable step forward in making a geometrically superior representation practical for high-quality, multi-scale rendering. We thank the reviewer again for their constructive feedback.

We sincerely thank the reviewer for their time and valuable feedback. We are pleased they found our paper’s motivation and writing to be clear and appreciate their positive assessment of our experimental validation. We would like to address the concerns raised regarding the work's originality and the scope of our evaluation to provide a clearer picture of our contributions.

On the Novelty of our Method Beyond a "Straightforward Adaptation"

We appreciate the reviewer's recognition that our work is inspired by Mip-Splatting. However, we wish to clarify that our method is not a "straightforward adaptation" but involves significant novel mathematical derivations necessitated by the fundamental rendering paradigm differences between 3DGS and 2DGS.

1. A Novel Framework is Required for the 2DGS Rendering Pipeline. The rendering mechanisms of 3DGS and 2DGS are fundamentally incompatible, precluding any direct application of 3DGS-based solutions.

• 3DGS projects 3D Gaussians to screen space, which is a well-defined affine transformation. Applying screen-space EWA filtering is a direct extension of existing literature.
• 2DGS does not project primitives. Instead, it computes a complex, non-linear ray-splat intersection (Eq. 5 and 6) to find a point in the planar splat’s local 2D space.

It is not at all trivial how to perform frequency-based band-limiting or pre-filtering in this context. Our "Object-Space Mip Filter" is a novel solution tailored specifically for this unique intersection-based rendering paradigm. It is a new mathematical derivation with broader impact.

The reviewer notes that our method is "straightforward adaptation of mip-splatting". However, our technical approach is fundamentally different and more novel than that of Mip-Splatting. Mip-Splatting uses the standard screen-space EWA formulation and simply modifies the filter kernel size.

In contrast, our work introduces a new mathematical derivation for an anti-aliasing filter that operates directly in the object space of each splat. The derivation proceeds as follows:

• The Mapping: We begin with the ray-splat intersection function $m(\mathbf{x}) = \mathbf{u}(\mathbf{x})$ on the splat (Eq. 5 and 6).
• The Core Innovation: We form a first-order Taylor approximation of this complex mapping around a pixel, defined by its Jacobian $\mathbf{J} = \frac{\partial \mathbf{u}}{\partial \mathbf{x}}$ (Eq. 12). This local affine approximation is the key insight that makes an analytical solution possible.
• Mapping to Screen Space: Using this affine mapping and a fundamental property of Gaussian functions, we can express how the local unit Gaussian behaves in screen space (Eq. 13).
• Filtering in Screen Space: We then mathematically convolve this transformed Gaussian with a screen-space Mip filter (a Gaussian with covariance $\sigma\mathbf{I}$) to obtain a filtered Gaussian with covariance $\mathbf{J}^{-1}\mathbf{J}^{-\top} + \sigma\mathbf{I}$ (Eq. 15).
• Mapping Back to Object Space: Finally, we use the same affine transform properties to map this filtered screen-space Gaussian back into the splat's local uv-space. This yields our final, novel result: the primitive can be evaluated as a single Gaussian in its local space with a new, dynamically computed covariance $\boldsymbol{\Sigma}_{\text{local}}' = \mathbf{I} + \sigma\mathbf{J}\mathbf{J}^\top$ (Eq. 17).

To our knowledge, this formulation—pre-filtering an intersection-based primitive by analytically deriving an equivalent object-space covariance from a screen-space filter—is a new contribution that has not been proposed before, not even in classical graphics literature on surface splatting, highlighting its novelty and potential impact beyond just 2DGS.

2. The World-Space Flat Smoothing Kernel: A Necessary and Non-Trivial Formulation for Planar Primitives.

Our second component addresses pre-aliasing by band-limiting the representation, conceptually inspired by the frequency analysis in Mip-Splatting. However, a 3D volumetric filter cannot be applied to a 2D planar primitive. Our contribution was to correctly formulate this regularization for a flattened representation by projecting the 3D isotropic smoothing kernel onto the 2D splat plane. This results in our effective planar covariance matrix ($\mathbf{V}_k^{\text{eff}}$ in Eq. 9) and corresponding opacity modulation (Eq. 10), which is a necessary step to complete the anti-aliasing framework for 2DGS, especially for the case of magnification.

3. We provide new insights into the limitations of the original 2DGS.

A key contribution of our work is the analysis and demonstration of the clamping heuristic's ineffectiveness in the original 2DGS. Prior work had not identified this as a critical source of artifacts. Our experiments (2DGS w/o Clamping in Tables 1-5, and in the Appendix) provides the first concrete evidence that this heuristic often exacerbates aliasing and damages performance, especially during minification. This insight itself is a valuable contribution to the understanding of the vanilla 2DGS method.

On the Surface Reconstruction Evaluation

We thank the reviewer for their question regarding surface reconstruction on other datasets. We would like to gently point to Section 4.5 and Table 4, where we evaluate our method on the standard DTU surface reconstruction benchmark precisely to address this concern.

The purpose of this experiment was to demonstrate that our anti-aliasing solution preserves the state-of-the-art geometric accuracy that is a major strength of 2DGS. The results in Table 4, showing our method is on par with the original 2DGS confirm that our framework successfully integrates advanced anti-aliasing without degrading this crucial capability. We believe the comprehensive DTU benchmark is sufficient to robustly support this claim.

Our paper introduces a novel, non-trivial method for 2DGS anti-aliasing, provides new insights into the limitations of the original 2DGS, and validates that our approach preserves its key geometric strengths. We hope these clarifications help the reviewer better appreciate the originality and significance of our contributions.

Thank you again for your time and consideration.

We sincerely thank the reviewer for their time and for providing a thoughtful and positive assessment of our work. We are grateful for the "excellent" ratings in Quality, Clarity, and Significance and for the recognition that our paper addresses an important problem with a clear derivation and state-of-the-art results.

We would like to address the minor weaknesses pointed out by the reviewer, which we believe will further strengthen our paper.

1. Regarding the Discussion of Limitations:

   The reviewer noted that "The paper lacks a discussion of its limitations." We would like to respectfully clarify that we included a dedicated "Limitations" section (Section C) in the Appendix.

   In this section, we discuss:

   • The inherent trade-off between antialiasing and preserving high-frequency detail, a common challenge for all such methods.
   • The fundamental limitations stemming from the use of 2D planar primitives, including the "needle-like" artifacts that can appear at grazing angles during magnification.
   • The specific trade-offs of our two-part solution, where the Object-Space Mip filter primarily addresses minification (zoom-out) and the Flat Smoothing Kernel targets magnification (zoom-in).

   We acknowledge that this section is in the appendix, which may have been overlooked due to this placement. We believe this discussion thoroughly contextualizes the scope and applicability of our method as requested.

2. Regarding Additional Visualizations (Depth, Normals, Meshes):

   We thank the reviewer for this constructive suggestion. Our evaluation was centered on showcasing the primary contributions: significant improvements in anti-aliased rendering at multiple scales, while numerically demonstrating the preservation of 2DGS's geometric fidelity on the DTU benchmark. We will happily include additional visualizations in the revision. As the reviewer intuits, the benefits of our anti-aliasing are not confined to RGB output but naturally extend to all rendered buffers.

We thank the reviewer for their positive and constructive feedback. We are pleased that they found our method to be "highly successful", "computationally efficient" and "well-written". We appreciate the opportunity to address the remaining concerns regarding novelty and the comparison to HDGS.

On Novelty and Contribution

We respectfully wish to clarify that our work introduces a novel algorithmic framework derived from a signal-processing analysis of the unique 2DGS rendering pipeline and the planar nature of its primitives. This required deriving a first-of-its-kind Object-Space Mip Filter and a non-trivial adaptation of band-limiting for planar primitives with the World-Space Flat Smoothing Kernel, as direct adaptation of prior art is not possible.

1. A Novel Framework is Required for the 2DGS Rendering Pipeline. The rendering mechanisms of 3DGS and 2DGS are fundamentally incompatible, precluding any direct application of 3DGS-based solutions.

• 3DGS projects 3D Gaussians to screen space, which is a well-defined affine transformation. Applying screen-space EWA filtering is a direct extension of existing literature.
• 2DGS does not project primitives. Instead, it computes a non-linear ray-splat intersection (Eq. 5 and 6) to find a point in the planar splat’s local 2D space.

It is not at all trivial how to perform frequency-based band-limiting or pre-filtering in this context. Our "Object-Space Mip Filter" is a novel solution tailored specifically for this unique intersection-based rendering paradigm. It is a new mathematical derivation with broader impact.

The reviewer notes that our work adapts existing principles. However, our technical approach is fundamentally different and more novel than that of Mip-Splatting. Mip-Splatting uses the standard screen-space EWA formulation and simply modifies the filter kernel size.

In contrast, our work introduces a new mathematical derivation for an anti-aliasing filter that operates directly in the object space of each splat.

The derivation proceeds as follows:

• The Mapping: We begin with the ray-splat intersection function $m(\mathbf{x}) = \mathbf{u}(\mathbf{x})$ on the splat (Eq. 5 and 6).
• The Core Innovation: We form a first-order Taylor approximation of this complex mapping around a pixel, defined by its Jacobian $\mathbf{J} = \frac{\partial \mathbf{u}}{\partial \mathbf{x}}$ (Eq. 12). This local affine approximation is the key insight that makes an analytical solution possible.
• Mapping to Screen Space: Using this affine mapping and a fundamental property of Gaussian functions, we can express how the local unit Gaussian behaves in screen space (Eq. 13).
• Filtering in Screen Space: We then mathematically convolve this transformed Gaussian with a screen-space Mip filter (a Gaussian with covariance $\sigma\mathbf{I}$) to obtain a filtered Gaussian with covariance $\mathbf{J}^{-1}\mathbf{J}^{-\top} + \sigma\mathbf{I}$ (Eq. 15).
• Mapping Back to Object Space: Finally, we use the same affine transform properties to map this filtered screen-space Gaussian back into the splat's local uv-space. This yields our final, novel result: the primitive can be evaluated as a single Gaussian in its local space with a new, dynamically computed covariance $\boldsymbol{\Sigma}_{\text{local}}' = \mathbf{I} + \sigma\mathbf{J}\mathbf{J}^\top$ (Eq. 17).

To our knowledge, this formulation—pre-filtering an intersection-based primitive by analytically deriving an equivalent object-space covariance from a screen-space filter—is a new contribution that has not been proposed before, not even in classical graphics literature on surface splatting, highlighting its novelty and potential impact beyond just 2DGS.

2. The World-Space Flat Smoothing Kernel: A Necessary and Non-Trivial Formulation for Planar Primitives.

Our second component addresses pre-aliasing by band-limiting the representation, conceptually inspired by the frequency analysis in Mip-Splatting. However, a 3D volumetric filter cannot be applied to a 2D planar primitive. Our contribution was to correctly formulate this regularization for a flattened representation by projecting the 3D isotropic smoothing kernel onto the 2D splat plane. This results in our effective planar covariance matrix ($\mathbf{V}_k^{\text{eff}}$ in Eq. 9) and corresponding opacity modulation (Eq. 10), which is a necessary step to complete the anti-aliasing framework for 2DGS, especially for the case of magnification.

3. We provide new insights into the limitations of the original 2DGS.

A key contribution of our work is the analysis and demonstration of the clamping heuristic's ineffectiveness in the original 2DGS. Prior work had not identified this as a critical source of artifacts. Our experiments (2DGS w/o Clamping in Tables 1-5, and in the Appendix) provides the first concrete evidence that this heuristic often exacerbates aliasing and damages performance, especially during minification. This insight itself is a valuable contribution to the understanding of the vanilla 2DGS method.

Regarding the Comparison to HDGS

We thank the reviewer for bringing HDGS to our attention. We are happy to provide a direct comparison based on the results presented in both papers.

The HDGS paper includes a "Reduced resolution rendering on the NeRF synthetic dataset" experiment (Table 1 in HDGS), which directly corresponds to our "Single-scale Training and Multi-scale Testing on the Blender Dataset" experiment (Table 2 in our submission). A direct comparison of the average PSNR demonstrates the superiority of our approach:

• Our Method (AA-2DGS): 32.11 PSNR
• HDGS: 29.45 PSNR

Our method significantly outperforms HDGS on this benchmark by over 2.6 dB. We believe this substantial performance gap stems from the fundamental difference in our anti-aliasing strategies. HDGS employs a frustum-based super-sampling method. It treats each pixel as a frustum and casts 5 rays to average the result which is approximative and computationally more expensive. Differently, our method uses a principled analytical pre-filtering approach that mitigates aliasing more effectively and efficiently by directly addressing its signal-processing roots.

Finally, we will gladly correct any typos and formatting issues in the final version.

We hope these clarifications have addressed the reviewer's concerns and reinforced the novelty and significance of our contributions. We thank the reviewer again for their valuable time and feedback.