3D Skew-Normal Splatting

Abstract: 3D Gaussian Splatting (3DGS) has emerged as a leading representation for real-time novel view synthesis and has been widely adopted in various downstream applications. The core strength of 3DGS lies in its efficient kernel-based scene representation, where Gaussian primitives provide favorable mathematical and computational properties. However, under a finite primitive budget, the symmetric shape of each primitive directly affects representation compactness, especially near asymmetric structures such as object boundaries and one-sided surfaces. Recent works have explored more complex kernel distributions; however, they either remain within the elliptical family or rely on hard truncation, which limits continuous shape control and introduces distributional discontinuities. In this paper, we propose Skew-Normal Splatting (SNS), which adopts the Azzalini Skew-Normal distribution as the fundamental primitive. By introducing a learnable and bounded skewness parameter, SNS can continuously interpolate between symmetric Gaussians and Half-Gaussian-like shapes, enabling flexible modeling of both sharp boundaries and interior regions. Moreover, SNS preserves analytical tractability under affine transformations and marginalization. This property allows seamless integration into existing Gaussian Splatting rasterization pipelines. Furthermore, to address the strong coupling between scale, rotation, and skewness parameters, we introduce a decoupled parameterization and a block-wise optimization strategy to enhance training stability and accuracy. Extensive experiments on standard novel-view synthesis benchmarks show that SNS consistently improves reconstruction quality over Gaussian and recent non-Gaussian kernels, with clearer benefits on sharp boundaries and thin or one-sided structures.

• The paper introduces a novel Skew-Normal kernel that uses a learnable skewness parameter to adapt to asymmetric scene features.
• It integrates analytical projection and block-coordinate descent optimization to decouple and stabilize scale, rotation, and skewness parameters.
• The method achieves state-of-the-art PSNR improvements and superior rendering of sharp boundaries and thin structures across multiple datasets.

Skew-Normal Splatting for High-Fidelity 3D Scene Representation

Motivation and Context

3D Gaussian Splatting (3DGS) has established itself as a computationally efficient and mathematically tractable alternative to neural radiance fields (NeRF) for real-time novel view synthesis. However, the standard Gaussian kernel's inherent symmetry limits the compactness and expressivity of scene representations, particularly under constraints of finite primitive budgets. This limitation is most evident near boundaries and asymmetric structures, where multiple overlapping Gaussians are required to approximate sharp transitions, leading to redundancy and blurred reconstructions. Prior attempts to generalize the kernel framework to non-Gaussian forms have introduced elliptical or truncated distributions but fail to deliver continuous, flexible control of asymmetric primitive shapes without discontinuities.

Skew-Normal Splatting: Methodological Contributions

The paper introduces “Skew-Normal Splatting” (SNS), which leverages the multivariate Skew-Normal distribution (Azzalini) as the foundational kernel. The Skew-Normal kernel introduces a learnable, bounded skewness parameter, enabling a continuous interpolation between symmetric Gaussians and maximally skewed “Half-Gaussian” structures. This allows for superior adaptability to sharp boundaries, corners, and one-sided surfaces, while retaining the capacity to represent interior object regions efficiently.

Analytically, SNS preserves closure under affine transformations and marginalization. The authors derive closed-form expressions for projection and integration, facilitating seamless incorporation into existing 3DGS rasterization pipelines. Optimization is stabilized by decoupling scale, rotation, and skewness parameters via canonical reparameterization and block-wise alternating update schemes. Key advances include:

• Analytical projection of 3D Skew-Normal primitives to 2D screen space—critical for efficient splatting.
• Deterministic spatial offsets for bounding box localization, correcting for deviation between location parameter and spatial mean.
• Block-coordinate descent and k-decomposition to mitigate inter-parameter interference and optimize skewness independently from geometric attributes.

Experimental Evaluation

SNS is evaluated across multiple datasets (Mip-NeRF360, Tanks & Temples, Deep Blending) and compared against Gaussian and recent non-Gaussian splatting kernels (GES, SSS, 3D-HGS, etc.). Quantitative results indicate consistent improvements in PSNR, SSIM, and LPIPS, especially for scenes with pronounced boundary complexity and thin structures. For example:

• SNS achieves 30.17 PSNR on Mip-NeRF360 (best among tested methods), 25.08 on Tanks&Temples, and 30.30 on Deep Blending.
• Gains are most substantial on Tanks&Temples, with SNS outperforming SSS in both PSNR and perceptual similarity metrics.
• Per-scene analysis shows SNS delivers the most accurate and visually complete reconstructions in regions with sharp edges, as demonstrated by object completeness metrics and boundary preservation in qualitative comparisons.

Ablation studies confirm the complementary benefit of k-decomposition and alternating optimization, resulting in increased PSNR and improved perceptual metrics. The full SNS model consistently attains the highest average PSNR across all datasets.

Theoretical Implications

SNS extends explicit kernel-based splatting beyond the elliptical family into asymmetric forms while maintaining tractable closed-form renders. The bounded skewness prevents spatial footprint degeneracy, optimizing both representation compactness and computational load. Analytical reparameterization ensures gradient flow continuity, facilitating efficient backpropagation in deep learning architectures.

This work highlights the necessity of flexible kernel design in explicit scene representations, and demonstrates that introducing controlled asymmetry into primitives provides significant fidelity gains without compromising computational tractability.

Practical Impact and Limitations

For applications requiring real-time rendering or downstream manipulation—robotics, autonomous driving, cultural heritage preservation—SNS enables accurate reconstructions of environments containing sharp features, discontinuities, and one-sided elements. The method remains compatible with standard 3DGS pipelines and incurs comparable training overheads.

However, the reliance on numerically accurate CDF evaluation for Skew-Normal kernels introduces moderate rendering speed penalties. Moreover, SNS inherits limitations from the underlying 3DGS framework, notably challenges in rendering highly specular surfaces with SH-based representations. The optimization protocol, while robust, does not uniformly maximize all evaluation metrics, suggesting room for future refinement.

Future Directions

Potential directions include:

• Accelerating CDF computations via analytic approximations or hardware-specific optimizations.
• Integrating spatial hierarchy for adaptive kernel allocation, selectively deploying Skew-Normals at complex boundaries and Gaussians in homogeneous regions.
• Developing multi-objective optimization strategies to balance reconstruction fidelity and perceptual quality.
• Extending the kernel framework for hybrid rendering, scene editing, and open-vocabulary 3D scene understanding.

Conclusion

The Skew-Normal Splatting paradigm augments 3D Gaussian Splatting by introducing controllable, bounded asymmetry in primitive representation. Analytical tractability, continuous shape control, and optimization stability enable SNS to outperform both Gaussian and modern non-Gaussian kernels in high-fidelity 3D reconstruction tasks. This work advances explicit kernel-based rendering and suggests new avenues for efficient, expressive, and robust scene modeling (2605.15010).