Motion Is Not Projection: View-Consistent Attribution in Dynamic Gaussian Splatting

Dynamic novel-view synthesis reconstructs time-varying scenes from videos and renders novel views at unobserved viewpoints. Existing Gaussian optimization entangles geometry with training-view information, rendering them non-identifiable from 2D projection errors alone. In this paper, we investigate a fundamental question: can image-space errors be attributed to 3D Gaussian geometry in an identifiable and viewpoint-invariant manner? We first prove that position and shape respond differently to viewpoint changes, inducing view-dependent projection bias that can be compensated by normal-direction shrinkage. Subsequently, we propose MoProGS (Motion-Projection Factorized Gaussian Splatting), which factorizes dynamic deformation from view-dependent projection. Specifically, we separately model the geometric responses of Gaussian position and covariance, and derive a geometry-view coupling factor to boundedly adjust the projected support before rasterization. This balances the relative contributions of geometric parameters to forward projection and backward gradients, yielding viewpoint-consistent geometric error attribution. Experiments on D-NeRF, HyperNeRF, and Neu3D show that MoProGS consistently improves novel-view synthesis quality. Controlled studies further verify the distinct projection sensitivities of position and shape parameters, and clarify the roles of camera conditioning and individual components.