Native I2I performance and recovery plan¶
This note records the July 2026 performance change to the native Pandey-style Camera-LiDAR mutual-information solver and the evidence required before making an accuracy claim.
Implemented change¶
The Gaussian smoothing of the finite 2D MI histogram previously iterated over
every output bin in Python. It now creates a NumPy sliding-window view and
contracts every window with the same kernel in one einsum. A scalar-reference
unit test requires agreement at 1e-13 relative and absolute tolerance.
On the development host, 100 repetitions on a 32 x 32 histogram measured:
| Implementation | Mean time per convolution |
|---|---|
| Scalar Python windows | 10.71 ms |
| Vectorized NumPy contraction | 0.78 ms |
This local microbenchmark is approximately 13.8 times faster for the isolated kernel. It is not a claim that complete calibration is 13.8 times faster; projection, numerical gradients, probes, and curvature evaluation remain in the end-to-end runtime.
Coarse-to-fine initializer¶
The optional initializer performs deterministic signed coordinate searches at fixed translation and rotation resolutions. Search and validation frames are separate subsets of the solver's training partition. A proposed initialization is accepted only when it does not reduce either aggregate training MI or the internal validation MI. The local optimizer is also run from the original initial estimate. The coarse-started endpoint replaces that baseline endpoint only when aggregate and every per-frame training MI are non-decreasing. The final benchmark holdout remains untouched.
The default solver behavior remains the versioned
pandey_mutual_information_bb_ascent/v0.1 path. Coarse search must be enabled
explicitly and records every level, evaluation count, proposed transform,
validation score, and acceptance decision in provenance.
KITTI recovery protocol¶
calibrex kitti benchmark-i2i consumes the digest-locked 20-frame KITTI raw
input artifact and compares:
- the scalar Gaussian-convolution reference with native I2I numerical-gradient/Barzilai-Borwein optimization;
- vectorized Gaussian convolution with deterministic, safety-gated coarse-to-fine initialization and the same local optimizer.
Both methods receive the same six +0.10 m or +10 deg single-axis
perturbations, seeded fit/holdout split, iteration budget, and point sample.
The schema-valid benchmark retains translation error, rotation error, held-out
normalized MI, recovery rate, failures, runtime, input digest, and producer
provenance.
Official KITTI raw result¶
The 31 July 2026 run used the KITTI-hosted
2011_09_26_drive_0005_sync.zip, selected the preregistered frame indices
0:154:8, and locked 44 files under aggregate input SHA-256
80987aa55ee30c53134607bd0d5562e002fa963fd6d2028e61f0cda47acae9db.
The run used Python 3.12.3, NumPy 2.5.1, and an Intel Core i5-1145G7. Each
method used 2,000 deterministically sampled points per frame and 20 local
iterations.
| Metric | Scalar reference | Vectorized safe coarse | Change |
|---|---|---|---|
| Mean runtime per trial | 4.4674 s | 2.5990 s | 1.719x faster |
| Mean translation error | 0.0740715 m | 0.0740715 m | 0 |
| Mean rotation error | 5.1457413 deg | 5.1457413 deg | 0 |
| Mean holdout normalized MI | 0.0123131 | 0.0123131 | 0 |
| Recovery rate at 0.05 m / 1 deg | 0/6 | 0/6 | 0 |
All six paired trials produced identical transform-error, holdout-MI, and recovery metrics. The optimized path therefore passes the preregistered non-degradation and runtime gates. The result establishes a performance improvement, not a solver-accuracy improvement: neither method recovered any of the six large perturbations under the strict threshold. This poor capture range is the reason coarse search remains opt-in and why a geometry-based D2D objective is the next accuracy item.
The generated benchmark definition and aggregate are schema-valid and record the input digest, complete executed Python-source digest (including uncommitted changes), config/output hashes, execution host, Python/NumPy versions, and coarse acceptance decisions.
Research basis and boundaries¶
- Borer et al., From Chaos to Calibration, motivates a future geometry-based D2D objective and initialization-recovery evaluation.
- Koide et al., General, Single-shot, Target-less, and Automatic LiDAR-Camera Extrinsic Calibration Toolbox, motivates multi-frame direct registration and an external MIT-licensed baseline.
- Liu et al.,
adaptive-voxelization implementation,
motivates correspondence acceleration. Its GPL-2.0 code must not enter
src/calibrex; only an independent implementation or subprocess adapter is acceptable.
The next accuracy change should add a solver-neutral depth-map input contract and D2D MI objective. Learned depth estimation remains an external adapter with model/version/weight-digest/license provenance.