SD-GS: Gradient-Semantic Analysis Based on Multi-State Scene 3D Gaussian Splatting

By analyzing the semantic information of Direct Current (DC, the zeroth-order spherical harmonic coefficient) gradients during 3D Gaussian Splatting (3DGS) optimization, this paper achieves unsupervised state classification in scenes with discrete appearance states under the proposed State-Discovery Gaussian Splatting (SD-GS) framework via SVD dimensionality reduction and K-means clustering. To improve the stability of the clustering results, an appearance-difference-weighted refinement mechanism is further proposed to confirm high-confidence labels. To address the difficulty of distinguishing similar states when the number of states exceeds two, a sequential peeling strategy is proposed that decomposes a multi-class partition into several two-class separations. On four real-world scene datasets, SD-GS achieves 100% classification accuracy with reconstruction quality of 31.98–38.83 dB PSNR. Ablation studies validate the effectiveness of the gradient direction mode and the SVD dimensionality reduction strategy.