Unified Gaussian Primitives for Scene Representation and Rendering (2406.09733v2)

Abstract: Searching for a unified scene representation remains a research challenge in computer graphics. Traditional mesh-based representations are unsuitable for dense, fuzzy elements, and introduce additional complexity for filtering and differentiable rendering. Conversely, voxel-based representations struggle to model hard surfaces and suffer from intensive memory requirement. We propose a general-purpose rendering primitive based on 3D Gaussian distribution for unified scene representation, featuring versatile appearance ranging from glossy surfaces to fuzzy elements, as well as physically based scattering to enable accurate global illumination. We formulate the rendering theory for the primitive based on non-exponential transport and derive efficient rendering operations to be compatible with Monte Carlo path tracing. The new representation can be converted from different sources, including meshes and 3D Gaussian splatting, and further refined via transmittance optimization thanks to its differentiability. We demonstrate the versatility of our representation in various rendering applications such as global illumination and appearance editing, while supporting arbitrary lighting conditions by nature. Additionally, we compare our representation to existing volumetric representations, highlighting its efficiency to reproduce details.

• The paper introduces a novel 3D Gaussian-based volumetric primitive that represents both hard surfaces and fine aggregated details.
• The methodology employs efficient Monte Carlo operations with closed-form ray integral evaluations and advanced importance sampling.
• Its unified approach simplifies scene representation, enabling flexible appearance modeling and opening new avenues for inverse rendering.

Unified Gaussian Primitives for Scene Representation and Rendering

The paper "Unified Gaussian Primitives for Scene Representation and Rendering" by Yang Zhou, Songyin Wu, and Ling-Qi Yan, presents a novel approach to scene representation in computer graphics using a unified primitive based on 3D Gaussian distributions. This technique addresses fundamental issues with traditional scene representations, specifically mesh-based and voxel-based methods, by providing a more flexible and general-purpose solution that can adapt to various geometric configurations and material properties.

Key Contributions

The key contributions of this work are as follows:

1. Introduction of a novel 3D Gaussian-based volumetric rendering primitive capable of representing both hard surfaces and aggregated elements such as dense, stochastic details.
2. Efficient Monte Carlo operations tailored for this representation, thus enabling comprehensive Monte Carlo path tracing.
3. A flexible phase function that integrates both the normal distribution function (NDF) of aggregated elements and the base bidirectional scattering distribution function (BSDF) of each element, allowing for versatile appearance modeling.
4. Various applications of their representation including gradient-based transmittance optimization, demonstrating its differentiability and potential for future inverse rendering applications.

Technical Insights

Scene Representation and Non-Exponential Transport

Traditional mesh-based representations, although efficient for hard connected surfaces, struggle to handle complex, small-scale geometry like hair, fur, and foliage. Voxel-based representations, on the other hand, encounter limitations due to high memory requirements and difficulty in representing hard surfaces. The authors propose the use of anisotropic 3D Gaussian primitives, inspired by the success of 3D Gaussian splatting, which demonstrates superior adaptability to detailed and irregular geometries.

A pivotal aspect of the paper is the non-exponential transport model, which replaces the traditional exponential light transport. This new model enables linear transmittance, allowing the sum of individual Gaussian contributions to be directly used for light scattering calculations. This simplification is significant, as it avoids the non-linear complexities inherent in exponential models and supports the modeling of both surface-like and volumetric characteristics.

Monte Carlo Path Tracing with Gaussian Primitives

The paper outlines methods for efficient Monte Carlo operations, crucial for unbiased path tracing. These include:

• Ray Integral Evaluations: Closed-form solutions (utilizing error functions) are derived for evaluating integrals over Gaussian distributions along rays.
• Ray Sampling: CDF inversion techniques are employed to sample free-flight distributions along rays, even handling cases of overlapping Gaussians effectively.
• Bounding Shapes: Primitives are bounded within truncated ellipsoids to facilitate efficient spatial data structures such as kd-trees for acceleration of ray intersection tests.

Appearance Modeling

The appearance of Gaussian primitives is modeled using a phase function combining the effects of an NDF and a base surface BSDF. This design abstracts away sub-primitive level scattering interactions, simplifying the representation while maintaining versatility. An improved stochastic evaluation method is proposed, which effectively combines traditional VNDF sampling with importance sampling of the base BSDF, further refined using Multiple Importance Sampling (MIS) techniques.

Applications and Results

The authors demonstrate compelling rendering applications of their Gaussian primitives:

1. Complex Scene Representation with Global Illumination: They showcase scenes composed entirely of Gaussian primitives, highlighting the ability to represent hard surfaces, fibers, and aggregated elements under diverse lighting conditions, including full global illumination effects.
2. UV-less Texturing and Appearance Editing: Extending UV-less texturing techniques, the authors introduce extended triplanar mapping and procedural noise operations for editing the base BSDF and NDF of primitives, facilitating rich, detail-preserving appearance modifications.
3. Comparison to Voxel-based Representations: Through comparisons, they exhibit how Gaussian primitives surpass voxel grids in reconstructing fine details and sharp geometries, emphasizing the inadequacy of voxel-based methods for high-frequency detail preservation.
4. Re-rendering 3D Gaussian Splatting Scenes: Demonstrating the flexibility of their representation, scenes originally modeled as radiance fields using 3D Gaussian splatting are empirically converted to their representation, enabling the support of arbitrary new lighting conditions.

Implications and Future Work

This novel representation offers several practical and theoretical implications. Practically, it simplifies the integration of various types of geometry and material properties within a single framework, potentially reducing the need for multiple, specialized representations in graphics pipelines. Theoretically, it opens up new avenues for further research in non-exponential transport models and their applications in graphics.

Future developments could include:

• Addressing the reciprocity constraints within the non-exponential transmittance model.
• Extending the phase function definition to support refraction and subsurface scattering.
• Developing detailed tools for digital content creation with this representation.
• Implementing a GPU-based renderer to achieve greater performance gains.

The proposed unified scene representation marks a significant step in addressing the limitations of current graphics methodologies, balancing efficiency and flexibility while paving the way for more advanced rendering and inverse rendering tasks.