Manyi Li

This supplementary material provides comprehensive experimental details and results to complement our main paper. We present: (1) motivation for this paper; (2) the qualitative results of our method in the LAB color space; (3) a detailed introduction to our network architecture, including a specific description of the cubic B-spline interpolation; (4) explorative abalation studies using the intermediate data and visualizations generated during the fine-tuning process; (5) quantitative results using different parameters and numbers of control points; (6) computation performance comparisons with training and testing time; (7) details about our interactive visualization tool; and (8) a detailed explanation of the stimuli in our perceptual study. Our full experimental datasets implementation code and trained models are available at https://osf.io/gb2tx/?view_only = 4d2a269b59bc4144b2806ec2d1a34e11.

Point cloud denoising task aims to recover the clean point cloud from the scanned data coupled with different levels or patterns of noise. The recent state-of-the-art methods often train deep neural networks to update the point locations towards the clean point cloud, and empirically repeat the denoising process several times in order to obtain the denoised results. It is not clear how to efficiently arrange the iterative denoising processes to deal with different levels or patterns of noise. In this paper, we propose an adaptive and iterative point cloud denoising method based on the score-based diffusion model. For a given noisy point cloud, we first estimate the noise variation and determine an adaptive denoising schedule with appropriate step sizes, then invoke the trained network iteratively to update point clouds following the adaptive schedule. To facilitate this adaptive and iterative denoising process, we design the network architecture and a two-stage sampling strategy for the network training to enable feature fusion and gradient fusion for iterative denoising. Compared to the state-of-the-art point cloud denoising methods, our approach obtains clean and smooth denoised point clouds, while preserving the shape boundary and details better. Our results not only outperform the other methods both qualitatively and quantitatively, but also are preferable on the synthetic dataset with different patterns of noises, as well as the real-scanned dataset.

3D Gaussian Splatting (3DGS) has witnessed exponential adoption across diverse applications, driving a critical need for semantic-aware 3D Gaussian representations to enable scene understanding and editing tasks. Existing approaches typically attach semantic features to a collection of free Gaussians and distill the features via differentiable rendering, leading to noisy segmentation and a messy selection of Gaussians. In this paper, we introduce AG$^2$aussian, a novel framework that leverages an anchor-graph structure to organize semantic features and regulate Gaussian primitives. Our anchor-graph structure not only promotes compact and instance-aware Gaussian distributions, but also facilitates graph-based propagation, achieving a clean and accurate instance-level Gaussian selection. Extensive validation across four applications, i.e. interactive click-based query, open-vocabulary text-driven query, object removal editing, and physics simulation, demonstrates the advantages of our approach and its benefits to various applications. The experiments and ablation studies further evaluate the effectiveness of the key designs of our approach.

Point cloud denoising task aims to recover the clean point cloud from the scanned data coupled with different levels or patterns of noise. The recent state‐of‐the‐art methods often train deep neural networks to update the point locations towards the clean point cloud, and empirically repeat the denoising process several times in order to obtain the denoised results. It is not clear how to efficiently arrange the iterative denoising processes to deal with different levels or patterns of noise. In this paper, we propose an adaptive and iterative point cloud denoising method based on the score‐based diffusion model. For a given noisy point cloud, we first estimate the noise variation and determine an adaptive denoising schedule with appropriate step sizes, then invoke the trained network iteratively to update point clouds following the adaptive schedule. To facilitate this adaptive and iterative denoising process, we design the network architecture and a two‐stage sampling strategy for the network training to enable feature fusion and gradient fusion for iterative denoising. Compared to the state‐of‐the‐art point cloud denoising methods, our approach obtains clean and smooth denoised point clouds, while preserving the shape boundary and details better. Our results not only outperform the other methods both qualitatively and quantitatively, but also are preferable on the synthetic dataset with different patterns of noises, as well as the real‐scanned dataset.

Indoor scene synthesis aims to automatically produce plausible, realistic, and diverse 3D indoor scenes, especially given arbitrary user requirements. Recently, the promising generalization ability of pre-trained large language models (LLM) assist in open-vocabulary indoor scene synthesis. However, the challenge lies in converting the LLM-generated outputs into reasonable and physically feasible scene layouts. In this paper, we propose to generate hierarchically structured scene descriptions with LLM and then compute the scene layouts. Specifically, we train a hierarchy-aware network to infer the fine-grained relative positions between objects and design a divide-and-conquer optimization to solve for scene layouts. The advantages of using hierarchically structured scene representation are two-fold. First, the hierarchical structure provides a rough grounding for object arrangement, which alleviates contradictory placements with dense relations and enhances the generalization ability of the network to infer fine-grained placements. Second, it naturally supports the divide-and-conquer optimization, by first arranging the sub-scenes and then the entire scene, to more effectively solve for a feasible layout. We conduct extensive comparison experiments and ablation studies with both qualitative and quantitative evaluations to validate the effectiveness of our key designs with the hierarchically structured scene representation. Our approach can generate more reasonable scene layouts while better aligned with the user requirements and LLM descriptions. We also present open-vocabulary scene synthesis and interactive scene design results to show the strength of our approach in the applications.