Math

Challenge

Global localization and continuous frame tracking are fragile assumptions in real scenes, especially around occlusions, misalignment, and temporary tracking failure.

Contribution

Developed a SLAM architecture that is graph-based end to end: frontend and backend alike form graphs of relationships between direct observations — nothing is accumulated into an intermediate model, so every pose stays traceable to raw data. A real-time ICP tracking frontend feeds an async backend that selects keyframes and optimizes the pose graph: poses as nodes, measured relative motions as edges, refined jointly. Loop closure — recognizing an already-seen region and using it to cancel accumulated drift — lets reconstruction continue through a tracking break and reconnect later. Ground-truth replay showed the textbook consistency filter was rejecting precisely the corrective long-range closures; replaced it with an inlier-ratio gate, accepting a closure by the fraction of points that genuinely agree. The keyframe backbone — a covisibility graph linking frames that see the same surface, with keyframes chosen as a dominating set, a small subset guaranteed adjacent to every frame — traces to a first GPU implementation authored in 2023, whose design the production kernel still carries.

Outcome

Trajectory error fell from 3.16 mm — the floor set by frame-to-frame tracking alone — to 0.76 mm, validated against ground truth across an 18-recording corpus, and pose-graph optimization sped up 10× (16 s → 1.6 s) via a sparse direct solver whose factorization structure is computed once and reused — with a temporary tracking loss no longer the end of the scan.