3DGS is an emerging and increasingly popular technology in the field of novel view synthesis. Its highly realistic rendering quality and real-time rendering capabilities make it promising for various applications. However, when applied to large-scale aerial urban scenes, 3DGS methods suffer from issues such as excessive memory consumption, slow training times, prolonged partitioning processes, and significant degradation in rendering quality due to the increased data volume. To tackle these challenges, we introduce \textbf{HUG}, a novel approach that enhances data partitioning and reconstruction quality by leveraging a hierarchical neural Gaussian representation. We first propose a visibility-based data partitioning method that is simple yet highly efficient, significantly outperforming existing methods in speed. Then, we introduce a novel hierarchical weighted training approach, combined with other optimization strategies, to substantially improve reconstruction quality. Our method achieves state-of-the-art results on one synthetic dataset and four real-world datasets.

Novel view synthesis for dynamic scenes presents a significant challenge in computer graphics. While recent 3D Gaussian splatting methods have achieved state-of-the-art quality and speed for static scenes, their direct extension to 4D dynamic scenes remains non-trivial. Existing approaches for dynamic scene novel view synthesis typically fall into two categories: either employing time-varying dynamic Gaussians, which often suffer from artifacts due to MLP limitations, or directly extending Gaussians to 4D, which, despite yielding high rendering quality, incurs substantial memory overhead. This paper introduces a novel 4D anchor-based framework that effectively leverages the stronger representational power of 4D Gaussians while crucially addressing their storage inefficiency. Our approach models dynamic scenes by binding Gaussians to strategically distributed anchor points. Furthermore, we propose a dynamic anchor control strategy to generate additional anchors in dynamic regions requiring detailed reconstruction. Additionally, we design an anchor stabilization strategy to fix the attributes of anchors in static regions during training, thereby preventing redundancy. Extensive experiments on various benchmarks, including N3DV and the Technicolor dataset, demonstrate the superior visual quality of our method.

The discrete Laplacian operator holds a crucial role in 3D geometry processing, yet it is still challenging to define it on point clouds. Previous works mainly focused on constructing a local triangulation around each point to approximate the underlying manifold for defining the Laplacian operator, which may not be robust or accurate. In contrast, we simply use the K- nearest neighbors (KNN) graph constructed from the input point cloud and learn the Laplacian operator on the KNN graph with graph neural networks (GNNs). However, the ground-truth Laplacian operator is defined on a manifold mesh with a different connectivity from the KNN graph and thus cannot be directly used for training. To train the GNN, we propose a novel training scheme by imitating the behavior of the ground-truth Laplacian operator on a set of probe functions so that the learned Laplacian operator behaves similarly to the ground-truth Laplacian operator. We train our network on a subset of ShapeNet and evaluate it across a variety of point clouds. Compared with previous methods, our method reduces the error by an order of magnitude and excels in handling sparse point clouds with thin structures or sharp features. Our method also demonstrates a strong generalization ability to unseen shapes. With our learned Laplacian operator, we further apply a series of Laplacian-based geometry processing algorithms directly to point clouds and achieve accurate results, enabling many exciting possibilities for geometry processing on point clouds. The code and trained models are available at https://github.com/IntelligentGeometry/NeLo.