GES: Generalized Exponential Splatting for Efficient Radiance Field Rendering (2402.10128v2)

Abstract: Advancements in 3D Gaussian Splatting have significantly accelerated 3D reconstruction and generation. However, it may require a large number of Gaussians, which creates a substantial memory footprint. This paper introduces GES (Generalized Exponential Splatting), a novel representation that employs Generalized Exponential Function (GEF) to model 3D scenes, requiring far fewer particles to represent a scene and thus significantly outperforming Gaussian Splatting methods in efficiency with a plug-and-play replacement ability for Gaussian-based utilities. GES is validated theoretically and empirically in both principled 1D setup and realistic 3D scenes. It is shown to represent signals with sharp edges more accurately, which are typically challenging for Gaussians due to their inherent low-pass characteristics. Our empirical analysis demonstrates that GEF outperforms Gaussians in fitting natural-occurring signals (e.g. squares, triangles, and parabolic signals), thereby reducing the need for extensive splitting operations that increase the memory footprint of Gaussian Splatting. With the aid of a frequency-modulated loss, GES achieves competitive performance in novel-view synthesis benchmarks while requiring less than half the memory storage of Gaussian Splatting and increasing the rendering speed by up to 39%. The code is available on the project website https://abdullahamdi.com/ges .

• The paper introduces GES, replacing Gaussian with Generalized Exponential Functions to enhance rendering speed and reduce memory usage.
• It details a differentiable rasterization method and frequency-modulated image loss to accurately capture both low- and high-frequency details.
• Evaluations on benchmarks demonstrate competitive view synthesis quality with significantly lower memory footprint and faster frame rates.

Generalized Exponential Splatting for Efficient Radiance Field Rendering

The paper "GES: Generalized Exponential Splatting for Efficient Radiance Field Rendering" introduces a novel representation technique for 3D scene modeling, known as Generalized Exponential Splatting (GES). By leveraging Generalized Exponential Functions (GEF) instead of Gaussian functions, GES offers significant improvements in memory efficiency and rendering speed, while maintaining competitive performance on novel view synthesis tasks.

Introduction

The motivation for this work stems from the limitations of 3D Gaussian Splatting (GS) in modeling high-frequency details in 3D scenes. Gaussian functions possess inherent low-pass characteristics, which constrain their ability to accurately represent signals with sharp features. As a result, GS often requires a large number of small Gaussians to approximate such scenes, leading to increased memory consumption and computational load.

To address these issues, the authors propose GES, a method that uses GEF to model 3D scenes more efficiently. GES retains the benefits of fast differentiable rendering, essential for real-time applications, while significantly reducing memory footprint and enhancing rendering speed.

Methodology

Generalized Exponential Function (GEF)

The core of GES is the GEF, defined by:

$$f(x | \mu, \alpha, \beta, A) = A \exp\left(-\left(\frac{|x - \mu|}{\alpha}\right)^\beta\right)$$

where $\mu$ is the location parameter, $\alpha$ is the scale parameter, $\beta$ is the shape parameter, and $A$ is the amplitude. By adjusting $\beta$, GEF can adapt to various signal shapes, providing a more flexible modeling capability compared to Gaussian functions.

Differentiable GES Formulation

GES maintains a similar framework to GS but introduces the shape parameter $\beta$ for each splat, which modifies the focus and sharpness of the splats. This modification allows for better representation of sharp edges and high-frequency details.

The authors approximate the effect of $\beta$ on the covariance of each component using a modification function $\phi(\beta)$. This function ensures that the variance of each splat is adjusted appropriately, maintaining the efficiency of the rasterization process.

Fast Differentiable Rasterizer

GES leverages an approximate rasterization technique, which avoids direct computation of the exponent $\beta$. Instead, it simulates the effect of $\beta$ by scaling the variance of each component. This approach preserves the fast rendering capabilities of GS while benefiting from the enhanced modeling flexibility of GEF.

Frequency-Modulated Image Loss

To guide the optimization process, the authors introduce a frequency-modulated image loss $\mathcal{L}_{\omega}$, which emphasizes different frequency bands at various stages of training. This loss is implemented using a Difference of Gaussians (DoG) filter to create edge-aware masks, ensuring that GES captures both low-frequency and high-frequency details effectively.

Results

Numerical Simulations

The authors demonstrate the superiority of GEF over Gaussian mixtures through numerical simulations on 1D signals. The results show that GEF consistently achieves lower approximation errors for various signal types, particularly those with high-frequency components.

Novel View Synthesis

GES is evaluated on several benchmark datasets, including Mip-NeRF360, Tanks and Temples, and Deep Blending. The results indicate that GES achieves competitive performance (e.g., PSNR, SSIM, LPIPS) while requiring significantly less memory and providing faster rendering speeds compared to GS and other contemporary methods.

For instance, on the Mip-NeRF360 dataset, GES achieves a PSNR of 26.91, a SSIM of 0.794, and an LPIPS of 0.250 with a memory footprint of only 377MB and a rendering speed of 186 FPS. These results highlight the efficiency of GES in balancing performance and computational cost.

Ablation Studies

The paper includes ablation studies to analyze the impact of various components of GES, such as the frequency-modulated image loss and the shape parameter $\beta$. The studies confirm that these components contribute significantly to the performance and efficiency of GES.

Implications and Future Work

GES represents a significant advancement in 3D scene modeling, offering a more memory-efficient and faster alternative to Gaussian-based methods. The ability to model high-frequency details more accurately is particularly beneficial for applications in gaming, cinema, and virtual reality, where real-time rendering and high visual fidelity are crucial.

Future research could explore further optimization of GES for dynamic and complex environments, as well as its integration with other advanced 3D modeling techniques. Additionally, investigating the potential of GES in other domains, such as medical imaging and remote sensing, could open new avenues for its application.

The paper "GES: Generalized Exponential Splatting for Efficient Radiance Field Rendering" provides a comprehensive and well-founded approach to enhancing the efficiency and accuracy of 3D scene modeling, paving the way for more immersive and computationally feasible virtual experiences.