Laplacian Analysis Meets Dynamics Modelling: Gaussian Splatting for 4D Reconstruction

2025-08-06

AI Summary

Existing dynamic 3D Gaussian splatting methods suffer from motion blur and feature collision due to low-rank decomposition and high-dimensional grid sampling—rooted in a spectral conflict between motion detail preservation and deformation consistency. To address this, we propose a spectrum-aware 4D reconstruction framework. First, we design a Laplacian encoding architecture to explicitly model multi-scale motion spectra. Second, we introduce enhanced Gaussian dynamical attributes for hybrid explicit-implicit motion modeling. Third, we integrate KDTree-guided adaptive splitting with dynamic region queries to improve geometric and motion representation fidelity. Our method unifies hash encoding, photometric error compensation, and Laplacian feature encoding. Evaluated on multiple complex dynamic scenes, it achieves state-of-the-art reconstruction accuracy and visual quality, significantly enhancing spatiotemporal consistency and high-frequency motion detail recovery.

Technology Category

• Computer Vision: 3D Computer Vision
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Machine Learning: Feature Construction/Reformulation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

While 3D Gaussian Splatting (3DGS) excels in static scene modeling, its extension to dynamic scenes introduces significant challenges. Existing dynamic 3DGS methods suffer from either over-smoothing due to low-rank decomposition or feature collision from high-dimensional grid sampling. This is because of the inherent spectral conflicts between preserving motion details and maintaining deformation consistency at different frequency. To address these challenges, we propose a novel dynamic 3DGS framework with hybrid explicit-implicit functions. Our approach contains three key innovations: a spectral-aware Laplacian encoding architecture which merges Hash encoding and Laplacian-based module for flexible frequency motion control, an enhanced Gaussian dynamics attribute that compensates for photometric distortions caused by geometric deformation, and an adaptive Gaussian split strategy guided by KDTree-based primitive control to efficiently query and optimize dynamic areas. Through extensive experiments, our method demonstrates state-of-the-art performance in reconstructing complex dynamic scenes, achieving better reconstruction fidelity.

Problem

• Extending 3D Gaussian Splatting to dynamic scenes without over-smoothing or feature collision
• Balancing motion detail preservation and deformation consistency across frequencies
• Improving dynamic 3DGS with hybrid explicit-implicit functions for complex scene reconstruction

Innovation

• Spectral-aware Laplacian encoding for motion control
• Enhanced Gaussian dynamics attribute for distortion compensation
• Adaptive Gaussian split strategy for dynamic optimization