QuaST: Quasiconformal Jacobian-Guided Shape Transport for Stable Streaming 4D Gaussian Reconstruction

Streaming 4D Gaussian reconstruction calls for local motion and Gaussian shape to evolve coherently across frames, yet existing residual-based update methods do not explicitly guarantee this. We present QuaST, a quasiconformal Jacobian-guided shape transport framework that models relative center motion and covariance evolution through a shared local deformation map. QuaST constructs a persistent motion-domain graph and estimates rank-aware local Jacobians from relative center motion. A quasiconformal-inspired prior constrains anisotropic distortion within local neighborhoods. A stop-gradient interface lets neighborhood motion guide covariance transport while routing the transport loss only to current Gaussian scale and rotation. Furthermore, temporal shape control limits excessive anisotropic changes of individual Gaussians across consecutive frames. QuaST integrates these constraints into optimization while retaining standard Gaussian rendering, without a learned deformation field or motion-driving anchors. QuaST is strictly causal: the update at frame $t$ uses only the current training images and states stored from frames up to $t-1$, with no future-frame access. Experiments on DyNeRF and SelfCap show that QuaST improves novel-view reconstruction and maintains stable performance over extended captures of up to 1,200 frames.