MaGS: Reconstructing and Simulating Dynamic 3D Objects with Mesh-adsorbed Gaussian Splatting (2406.01593v2)

Abstract: 3D reconstruction and simulation, although interrelated, have distinct objectives: reconstruction requires a flexible 3D representation that can adapt to diverse scenes, while simulation needs a structured representation to model motion principles effectively. This paper introduces the Mesh-adsorbed Gaussian Splatting (MaGS) method to address this challenge. MaGS constrains 3D Gaussians to roam near the mesh, creating a mutually adsorbed mesh-Gaussian 3D representation. Such representation harnesses both the rendering flexibility of 3D Gaussians and the structured property of meshes. To achieve this, we introduce RMD-Net, a network that learns motion priors from video data to refine mesh deformations, alongside RGD-Net, which models the relative displacement between the mesh and Gaussians to enhance rendering fidelity under mesh constraints. To generalize to novel, user-defined deformations beyond input video without reliance on temporal data, we propose MPE-Net, which leverages inherent mesh information to bootstrap RMD-Net and RGD-Net. Due to the universality of meshes, MaGS is compatible with various deformation priors such as ARAP, SMPL, and soft physics simulation. Extensive experiments on the D-NeRF, DG-Mesh, and PeopleSnapshot datasets demonstrate that MaGS achieves state-of-the-art performance in both reconstruction and simulation.

• The paper introduces a mesh-adsorbed Gaussian representation that combines 3D Gaussian flexibility with mesh spatial coherence for improved dynamic reconstruction.
• It employs a learnable Relative Deformation Field to precisely capture motion details and ensure realistic mesh deformations.
• Evaluations on D-NeRF and NeRF-DS datasets show that MaGS outperforms previous methods in PSNR and SSIM, enabling high-quality interactive simulations.

Overview of the Mesh-adsorbed Gaussian Splatting (MaGS) Method for Dynamic 3D Reconstruction and Simulation

The paper "Reconstructing and Simulating Dynamic 3D Objects with Mesh-adsorbed Gaussian Splatting" introduces a novel method, Mesh-adsorbed Gaussian Splatting (MaGS), aimed at addressing the dual challenges of 3D reconstruction and simulation from monocular video input. This framework unifies these two tasks by leveraging a new representation that integrates 3D Gaussians with a mesh-based approach, thereby attaining substantial improvements in rendering accuracy and deformation realism.

Key Contributions

1. Mesh-adsorbed 3D Gaussian Representation: The MaGS representation constrains 3D Gaussians to hover on the mesh surface rather than being fixed to mesh facets. This design allows the combination of the rendering flexibility of 3D Gaussians with the spatial coherence of meshes, facilitating a unified approach for both reconstruction and simulation tasks.
2. Relative Deformation Field (RDF): MaGS introduces a learnable RDF that models the relative displacement between the mesh and 3D Gaussians. This extends traditional mesh-driven deformation paradigms, capturing the motion of each 3D Gaussian with greater precision and improving the coherence of complex deformations.

Methodological Insights

Stage I: Mesh Extraction and Deformation Field Estimation

In the initial stage, the approach focuses on coarse shape modeling and deformation estimation. Randomly initialized 3D Gaussians are used to form a deformation field through a multi-layer perceptron (DF-MLP). The optimization of this field enables the system to predict the changes across different frames, forming a basis for the subsequent mesh extraction.

Stage II: Mesh-adsorbed Gaussian Splatting

The second stage involves fine-tuning the representation:

• Mesh-adsorbed Gaussians: Gaussians are initialized on the mesh surface and allowed to hover rather than be rigidly fixed. This flexibility results in better optimization during deformation, preventing artifacts common in other methods.
• Local-Rigid Deformation via ARAP: The use of As-Rigid-As-Possible (ARAP) energy minimization exploits local rigidity, ensuring smooth and realistic mesh deformation.
• 3D Gaussian Splatting for Rendering: Finally, the deformed Mesh-adsorbed Gaussians are rendered using a differentiable renderer, allowing high-quality visualization.

Experimental Evaluation

The method was rigorously tested on the D-NeRF and NeRF-DS datasets, signaling notable advancements over existing techniques. Key metrics used include PSNR, SSIM, MS-SSIM, and LPIPS. The results demonstrated:

• Superior Quantitative Performance: MaGS outperformed existing state-of-the-art methods in terms of PSNR and SSIM across all tested scenes.
• Robust Detail Preservation: The method excelled in maintaining high visual quality by preserving intricate details in dynamic scenarios, thereby significantly reducing floating points and artifacts.

Simulation Capabilities

MaGS also facilitates user-interactive simulations, such as mesh dragging, by directly manipulating the mesh and adjusting the 3D Gaussians accordingly. This feature underscores the practical applicability of MaGS in scenarios requiring real-time and flexible object deformation.

Implications and Future Directions

The MaGS method contributes to both theoretical and practical aspects of computer vision by providing a coherent framework for integrating 3D reconstruction and dynamic simulation. It pushes the boundaries of how we can utilize mesh and point cloud representations in a unified manner to achieve superior rendering and realistic deformation.

Future Developments:

• Enhanced Initial Mesh Quality: Since the success of the MaGS method hinges significantly on the accuracy of the initial mesh, future research could focus on improving mesh extraction techniques, especially for low-resolution inputs.
• Extension to Various Domains: Incremental improvements and adaptations could extend MaGS to applications in virtual reality, medical imaging, and robotics, where accurate and dynamic 3D modeling is crucial.
• Deepfake Mitigation: Given the potential misuse of advanced 3D simulation methods, developing robust detection mechanisms and ethical guidelines will be vital for responsible deployment.

In summation, the Mesh-adsorbed Gaussian Splatting (MaGS) method represents a significant stride in the concurrent fields of 3D reconstruction and simulation, offering a versatile and effective solution backed by solid experimental validation. The adaptability and accuracy of this method highlight its potential broad applicability and room for future enhancements.