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One Ring to Rule Them All: Certifiably Robust Geometric Perception with Outliers
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the sparse moment relaxation with a reduced monomial basis | TLS geometric perception · SRA, SA, PCR, and MR with N=20 | relative duality gap: <10^{-3} | Helped |
| Use the DRS dual certifier instead of solving the sparse relaxation SDP | TLS geometric perception · SRA, SA, PCR, and MR at increasing N | runtime: SRA N=100: ** -> 8.35; SA N=100: >10^5 -> 37.44; PCR N=100: ** -> 357.48; MR N=100: ** -> 165.87 | Helped |
| Run DRS certification after GNC proposes a candidate | GNC estimates · SRA, SA, PCR, and MR with N=100 | classification of correct versus incorrect solutions: suboptimality below 1%; incorrect estimates above 10% | Helped |
| Use chordal-sparse SOS initialization for DRS | DRS dual certifier · TLS geometric perception | convergence speed | Helped |
| Use alternative correlative-sparsity variants of Lasserre's hierarchy instead of the proposed basis reduction (ablation) | TLS geometric perception · Minimum relaxation order | relaxation tightness | Hurt |
| Use the more restrictive chordal-sparse SOS program as the final certificate instead of refining with DRS (ablation) | Dual optimality certification · TLS geometric perception | certification strength | Hurt |
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