At each time step ROAMing receives a posed RGB-D frame and updates its surfel map in two stages. It first warps every existing surfel, visible or hidden, with a predicted 3D motion, and only then fuses the new depth image. Because the map is moved before association, moving objects do not corrupt data association, and surfaces that pass behind an occluder keep travelling with their neighbours instead of being frozen or discarded.
Geometric prior. Forward optical flow between frames t−1 and t (RAFT in the fast configuration, WAFT in the accurate one) is lifted to 3D with depth and the camera poses. This supplies motion wherever a valid correspondence exists; hidden surfels and rejected correspondences receive a zero prior, so the prior alone can never move hidden geometry.
Visibility-aware refinement. A local-relative transformer, in the spirit of Point Transformer and RAFT’s iterative refinement, predicts a residual displacement for every surfel. Tokens encode the prior, its magnitude, visibility and k-nearest-neighbour distance; attention encodes relative offsets rather than absolute positions. Each of three iterations attends over a fixed source graph (k = 16), warps the centres by the current estimate, rebuilds a warped graph (k = 32) and attends again. A hidden surfel remains a token even with a zero prior, so motion propagates through partially observed local structure without any segmentation. Motion below 2 mm is zeroed to suppress drift on static geometry.
Surfel fusion. Established projective surfel fusion is applied to the propagated map: an information filter combines depth-consistent associations, uncovered measurements spawn new surfels, free-space contradictions prune stale ones, and occluded or out-of-frustum surfels persist.