APG-GS: Adaptive Point-consistent Geometry for Interactive 3D Gaussian Splatting

Recent advances in 3D Gaussian Splatting (3DGS) have enabled high-resolution real-time rendering; however, the unstructured nature of 3DGS complicates dynamic deformation. Without inherent topology, 3DGS often suffers from structural tearing and visual artifacts during manipulation. We present APG-GS, a framework enabling semantically selective deformation while preventing non-physical interference between adjacent objects. To establish reliable topology, we construct a Gaussian Similarity Graph using a multi-attribute metric that integrates spatial distance, orientation, scale, and Spherical Harmonics. A Point-consistent ChainMail algorithm then propagates user-driven displacements through the graph to ensure interactive responsiveness. Furthermore, we maintain geometric consistency by estimating local deformation gradients, refined via polar decomposition, to adapt Gaussian covariance matrices in real time. Experimental results demonstrate that APG-GS effectively reduces visual artifacts and preserves structural coherence without sacrificing rendering efficiency. This approach extends 3DGS from static reconstruction to interactive, user-driven dynamic applications.