Certifiably Globally Optimal Extrinsic Calibration From Per-Sensor Egomotion
Bibliographic record
Abstract
We present a certifiably globally optimal algorithm for determining the extrinsic calibration between two sensors that are capable of producing independent egomotion estimates. This problem has been previously solved using a variety of techniques, including local optimization approaches that have no formal global optimality guarantees. We use a quadratic objective function to formulate calibration as a quadratically constrained quadratic program (QCQP). By leveraging recent advances in the optimization of QCQPs, we are able to use existing semidefinite program solvers to obtain a certifiably global optimum via the Lagrangian dual problem. Our problem formulation can be globally optimized by existing general-purpose solvers in less than a second, regardless of the number of measurements available and the noise level. This enables a variety of robotic platforms to rapidly and robustly compute and certify a globally optimal set of calibration parameters without a prior estimate or operator intervention. We compare the performance of our approach with a local solver on extensive simulations and multiple real datasets. Finally, we present necessary observability conditions that connect our approach to recent theoretical results and analytically support the empirical performance of our system.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".