SIGMA

Stage 1: Geometry-first motion masks

1. Extract SIFT keypoints from \(I_{t-1}, I_t\), match with FLANN + Lowe ratio, estimate \(F_{t-1,t}\) via RANSAC.
2. Compute dense optical flow \(u_{t-1,t}(p)\), warp \(I_{t-1}\) to \(\tilde I_{t-1}\), measure photometric residual \(r_{\text{photo}}(p)\).
3. Epipolar residual: \(r_{\text{epi}}(p) = \frac{|x_t^\top F_{t-1,t} x_{t-1}|}{\|(F x_{t-1})_{1:2}\|_2 + \|(F^\top x_t)_{1:2}\|_2 + \varepsilon}\).
4. Fuse cues: \(r(p) = \alpha r_{\text{epi}} + (1-\alpha) r_{\text{photo}}\); threshold to mask \(M_t\). Show RGB overlays.

Stage 2: Temporal inpainting

Use previous clean estimate \(\hat I_{t-1}\) as guidance: \(\hat I_t = \text{Inp}(I_t, M_t^{\text{rect}}, \hat I_{t-1})\). Implemented with SDXL inpainting + SDXL-Lightning LoRA (8-step sampling); rectangularized masks to reduce artifacts and preserve sky/ground seams. Show before/after triplets.

Stage 3: Streaming static reconstruction

Sliding-window VGGT: \(\{\mathbf{K}_t, \mathbf{R}_t, \mathbf{t}_t, \mathbf{D}_t, \mathcal{T}\}_{t=1}^T = \text{Recon}(\hat{\mathcal{I}}_{t-w:t})\). Fuse depths/tracks into a single static point cloud/mesh; visualize camera frusta + fused cloud. Incremental fusion keeps memory low.