DyGASR: Dynamic Generalized Exponential Splatting with Surface Alignment for Accelerated 3D Mesh Reconstruction

TL;DR

DASR, which utilizes generalized exponential function instead of traditional 3D Gaussian to decrease the number of particles and dynamically optimize the representation of the captured signal, surpasses existing 3DGS-based mesh reconstruction methods and demonstrates a 25% increase in speed and a 30% reduction in memory usage.

Abstract

Recent advancements in 3D Gaussian Splatting (3DGS), which lead to high-quality novel view synthesis and accelerated rendering, have remarkably improved the quality of radiance field reconstruction. However, the extraction of mesh from a massive number of minute 3D Gaussian points remains great challenge due to the large volume of Gaussians and difficulty of representation of sharp signals caused by their inherent low-pass characteristics. To address this issue, we propose DyGASR, which utilizes generalized exponential function instead of traditional 3D Gaussian to decrease the number of particles and dynamically optimize the representation of the captured signal. In addition, it is observed that reconstructing mesh with Generalized Exponential Splatting(GES) without modifications frequently leads to failures since the generalized exponential distribution centroids may not precisely align with the scene surface. To overcome this, we adopt Sugar's approach and introduce Generalized Surface Regularization (GSR), which reduces the smallest scaling vector of each point cloud to zero and ensures normal alignment perpendicular to the surface, facilitating subsequent Poisson surface mesh reconstruction. Additionally, we propose a dynamic resolution adjustment strategy that utilizes a cosine schedule to gradually increase image resolution from low to high during the training stage, thus avoiding constant full resolution, which significantly boosts the reconstruction speed. Our approach surpasses existing 3DGS-based mesh reconstruction methods, as evidenced by extensive evaluations on various scene datasets, demonstrating a 25\% increase in speed, and a 30\% reduction in memory usage.

Figures (5)

• Figure 1: Illustrates that our method, excels in both training time and reconstruction quality, achieving the highest performance.
• Figure 2: We verify the low-pass characteristics of 3D Gaussians. In (a), the GT image is shown on the left, and a rendering after 500 iterations of 3DGS on the right, both analyzed in the frequency domain via Fourier transform along the same horizontal line. The rendering appears in green and the GT image in blue, highlighting that the low-pass characteristics of 3DGS do not perfectly align with the scene's signal features. In (c), generalized exponential functions are displayed, where $\epsilon=1$ represents a scaled Laplace distribution, $\epsilon=2$, a scaled Gaussian distribution, along with other signal shapes such as triangles and squares. Here, $\epsilon$ serves as a parameter for each component in our method.
• Figure 3: Overview of Our Proposed Framework for Accelerated 3D Mesh Reconstruction.
• Figure 4: Qualitative Comparison of Three Scenes from the Mip-NeRF360 Dataset barron2021mip. The Last Column Displays Results from Our Rendering Method.
• Figure 5: Loss curves averaged from three random seeds in the bonsai scene. On the left are two types of losses in GSR, and on the right are training losses before and after the application of DRT.