Calibration Method Portfolio

Calibrex supports multiple calibration methods behind one result and evidence contract. A method is not considered complete merely because it returns a matrix: it also needs typed inputs, provenance, observability diagnostics, holdout evaluation, and known-bad controls.

Implemented and In Progress

Method	Role	Status	Independent evaluation
Native fixed-trajectory LiDAR point-to-plane	LiDAR extrinsic refinement	Implemented	voxel-plane holdout and 6-DoF controls
Online motion-compensated LiDAR point-to-plane	Streaming LiDAR extrinsic refinement	Implemented	rolling holdout and adoption gates
Open3D RGB-D SLAC	External RGB-D trajectory/calibration adapter	Adapter boundary	Calibrex result/report metrics
OpenCV hand-eye / robot-world	External Tsai, Park, Horaud, Andreff, Daniilidis, Shah, and Li implementations	Apache-2.0 optional adapter	shared absolute-pose split and Calibrex holdout closure
Koide-style direct LiDAR-camera	External targetless baseline	Adapter boundary	projection, edge, depth-edge, and controls
Per-point Camera-LiDAR capture time	Asynchronous projection/deskew and scalar clock-offset evidence	Native solver + public adapter	17 ms synthetic truth, disjoint capture holdout, six time controls, TIERS real-data INCONCLUSIVE
Radar Doppler candidate consistency	Radar yaw evidence	Implemented	frame holdout, four yaw controls, sensor policy
Robust Radar ego velocity	Scan-wise motion estimation from Doppler	Native solver	synthetic truth, outliers, LOS rank diagnostics
Radar-to-trajectory yaw	Radar extrinsic rotation from paired velocities	Native solver	deterministic holdout, direction diversity, four yaw controls
Radar lever arm and clock offset	Translation/time from Radar and reference velocities	Native solver	profiled time grid, lever-arm spectrum, holdout, eight controls
Planar-board LiDAR-camera plane alignment	LiDAR-to-camera 6-DoF extrinsic	Native solver	capture holdout, normal/offset closure, normal-span diagnostics
Planar-board LiDAR-camera point+plane	Independent centre/normal 6-DoF baseline	Native solver	shared capture holdout, 6D joint spectrum, 12 known-bad controls, ACFR real data
Horn point-only Camera-LiDAR alignment	Normal-free centre-correspondence 6-DoF baseline	Native solver	shared capture holdout, quaternion eigengap, 6D spectrum, 12 controls, ACFR real data
Planar-board LiDAR-camera line+plane	One-pose-capable LiDAR-to-camera 6-DoF extrinsic	Native solver	plane/edge closure, separate rotation/translation spectra, edge-angle gate
Robust point-to-point ICP	Generic local 3D registration	Native solver	spatial-block holdout, mutual/trimmed matches, 3D-spread and frozen-pair diagnostics
Open3D Generalized ICP	Optional probabilistic registration baseline	MIT adapter	train-only source fit, common Calibrex spatial holdout/rematching metrics
PCL/Autoware NDT	External registration baseline	Subprocess/precomputed adapter	declared train isolation, common Calibrex spatial holdout/rematching metrics
Park-Martin motion hand-eye	Trajectory-derived AX = XB extrinsic	Native solver	motion holdout, axis spectrum, translation-system spectrum and closure
Tsai-Lenz motion hand-eye	Independent separable AX = XB baseline	Native solver	shared motion holdout, two system spectra, 12 known-bad controls
Daniilidis dual-quaternion hand-eye	Simultaneous AX = XB rotation/translation baseline	Native solver	shared holdout, 8D nullspace/Study diagnostics, 12 known-bad controls
Shah robot-world/hand-eye	Absolute-pose A_j X = Y B_j hand-eye and robot-world transforms	Native solver	separate holdout, dominant Kronecker gap, 6D translation rank, 24 controls
Li-Wang-Wu robot-world/hand-eye	Simultaneous absolute-pose A_j X = Z B_j 24-variable Kronecker baseline	Native solver	shared-with-Shah holdout, full rank/condition spectrum, SO(3) projection correction, 24 controls
Dornaika-Horaud robot-world/hand-eye	Unit-constrained absolute-pose A_j X = Z B_j quaternion closed form	Native solver	common absolute split, sign synchronization, closed-form width, 6D translation rank, 24 controls
Dornaika-Horaud nonlinear robot-world/hand-eye	Simultaneous 24-parameter A_j X = Z B_j refinement	Native analytic-Jacobian LM	paper penalties, data-Jacobian spectrum, convergence trace, SO(3) correction, 24 controls
LiDAR-IMU rotation consistency	Supplied rotation evaluation	Implemented	held-out angular-rate and gravity evidence
Anchored temporal offset	One-dimensional time calibration evidence	Implemented	injected offsets and adapted/anchored comparison
Backend-neutral joint SLAC graph	Coupled trajectory/extrinsic/time optimization	Native graph core + typed Schur LM	grouped holdout, robust LM, 48→8 TUM pose elimination, joint spectrum, per-block controls

The native Radar ego-velocity solver uses Huber IRLS on d_i = -u_i^T v. It reports rank and condition diagnostics from the LOS normal matrix and refuses a 3D result when the scan geometry does not span three velocity directions. Automotive scans may therefore be valid only for a future planar or yaw-specific stage; Calibrex must not silently promote them to full 3D support.

Next Native Methods

1. Analytic/manifold factor Jacobians and sparse block storage behind the joint graph contract.
2. Sliding-window marginalization with explicit gauge and consistency diagnostics.
3. Additional primary-paper baselines and continuous-time motion adapters.

Optional Adapter Methods

• Open3D Generalized ICP
• PCL or Autoware NDT through a subprocess boundary
• Kalibr spatiotemporal camera-IMU calibration
• AprilTag or ChArUco observation extraction
• external visual and LiDAR odometry producers for hand-eye calibration

External implementations remain optional adapters. Their version, command, license boundary, input digests, and output role must be recorded. GPL or license-uncertain code must not be copied into src/calibrex.

Research Sequence

The intended sequence is compositional:

Radar Doppler returns
  → robust scan velocity
  → Radar-to-trajectory rotation
  → angular-rate-excited lever arm
  → joint spatial/temporal evidence

Likewise, target-based LiDAR-camera calibration supplies an independently checkable reference for later edge and mutual-information targetless methods. Every new optimizer must use a train split and be judged on an unchanged holdout split with explicit perturbation controls.

Planar-board LiDAR-camera research basis

The native plane-only solver follows the geometric contract introduced by Zhang and Pless (IROS 2004): an oriented camera plane corresponds to an oriented LiDAR plane. For p_camera = R p_lidar + t, the constraints are n_camera = R n_lidar and n_camera^T t = d_lidar - d_camera. Rotation is estimated by weighted orthogonal Procrustes and translation by weighted least squares. Robust IRLS weights whole captures, so a dense plane cannot silently dominate merely by containing more points.

Plane count alone is not an observability test. The camera-plane normal matrix must have rank three for full translation, and near-parallel normals remain ill-conditioned. This agrees with the explicit observability analysis of Fu et al. and the minimum three-pose plane/centre method evaluated by Verma et al.. Calibrex therefore reports the singular spectrum, rank, condition number, capture split, and every normal sign selected using the supplied initial transform.

An additional normal-free baseline follows Horn's unit-quaternion absolute orientation method. It aligns corresponding 3D board centres with scale fixed to one, reports the quaternion maximum eigengap and a local six-DoF Jacobian spectrum, and rejects collinear centre geometry. The RMS scale ratio is retained only as a unit diagnostic. It uses the exact same ACFR capture IDs and train/holdout split as the plane-only and centre+normal methods, so their transform deltas are comparable without split leakage.

Plane-only calibration does not claim one-shot observability. A finite board's boundary lines supply the missing in-plane constraints. The implemented line-plus-plane method follows Zhou, Li, and Kaess and can be observable from one pose when two non-parallel board edges are reliably measured. Plane plus one edge, or two parallel edges, remains rank five because translation along the shared edge direction is unobservable. Calibrex reports separate rotation and translation singular spectra and rejects weak edge-angle geometry. LCE-Calib likewise combines point-to-plane and point-to-line refinement (Jiao et al.).

The closed-form initializer assumes the extractor supplies stable edge IDs and consistent oriented directions. An unlabeled rectangle has a 180-degree permutation ambiguity, and a square can additionally admit 90-degree permutations. These discrete hypotheses are not silently resolved; the policy is recorded in provenance and such inputs require a labeled checkerboard, fiducial, or an adapter that enumerates and evaluates permutations.

Feature extraction stays outside the native core. GPL implementations such as FAST-Calib, plycal, and several ROS checkerboard packages may only be invoked through optional adapters; their code is not copied into src/calibrex.

Native robust point-to-point ICP

The native ICP follows the refreshed nearest-neighbour loop of Besl and McKay and the fixed-overlap trimming principle of Chetverikov et al.. Each iteration transforms the source, recomputes nearest neighbours, optionally retains only mutual pairs, applies a distance gate and stable distance-ranked trim, then solves the retained rigid alignment by an SO(3)-corrected SVD. This is a local registration method; the result does not claim global convergence.

Point holdout is spatial rather than an independent random-point split. Source points are grouped into deterministic voxels before train/holdout selection so neighbouring samples of the same surface do not trivially leak across the evaluation boundary. Held-out source points are evaluated with fresh target nearest neighbours.

The solver reports the fixed-pair six-dimensional information spectrum, but it does not interpret its inverse as calibration covariance. As shown by Bonnabel, Barczyk, and Goulette, ordinary point-to-point fixed-correspondence Hessians can be misleading when ICP rematches points. The native solver therefore conservatively rejects collinear and planar retained geometry instead of reporting full confidence from a formally rank-six frozen-pair Jacobian.

Effective diagnostics now perturb all six transform directions and rerun the complete nearest/mutual/gate/trim correspondence policy. They report rematched black-box objective curvature and correspondence-pair Jaccard stability, not a covariance matrix. Six independent initialization probes additionally flag a distinct transform with equivalent spatial holdout error as a symmetry ambiguity. Local curvature and global multi-start falsification remain separate diagnostics because either can pass while the other fails.

Segal-Haehnel-Thrun GICP and Biber-Strasser NDT are optional adapters with distinct method IDs. Their library-specific fitness values are retained as raw provenance, not treated as directly comparable metrics; Calibrex recomputes common spatial holdout, inlier, rematching curvature, and correspondence-Jaccard metrics for cross-backend comparisons. An external NDT result that does not declare train/holdout isolation is explicitly warned.

Motion hand-eye calibration

The native hand-eye solver implements the separable Lie-algebra construction of Park and Martin. Inputs are typed relative-motion pairs that explicitly satisfy A X = X B. With alpha = Log(R_A) and beta = Log(R_B), rotation is the weighted orthogonal Procrustes map alpha = R_X beta. Translation is then solved from (R_A - I)t_X = R_X t_B - t_A.

Motion count is not used as a substitute for observability. One rotation-axis family leaves the hand-eye twist about that axis ambiguous, while the stacked translation system also leaves translation along the shared axis unobservable. The solver requires at least two independent rotation-axis directions and rank three in stack(R_A - I). It rejects identity and sub-threshold rotations and reports separate rotation-axis and translation singular spectra, rank, and translation condition number.

Evaluation compares A X and X B without refitting and reports rotation geodesic and translation closure on train and holdout motions. If relative motions were derived from absolute trajectories, the upstream builder must split disjoint absolute pose or temporal blocks before constructing pairs; randomly splitting a dense all-pairs motion set would leak the same poses into both sets. That builder remains separate from the core solver so eye-in-hand, eye-to-hand, and robot-world/hand-eye conventions cannot be mixed implicitly.

Tsai and Lenz is implemented as an independent modified-Rodrigues/linear-translation baseline with the same typed motion split and closure evaluation as Park-Martin. The simultaneous dual-quaternion method of Daniilidis is also implemented as an independent 8D nullspace solver. It enforces unit and Study constraints, reports the full singular spectrum and nullspace separation, and selects real constrained candidates by train closure. OpenCV calibrateHandEye is suitable for an optional adapter; Kalibr is a distinct camera-IMU spatiotemporal workflow and is not labeled as this native AX = XB method.

Shah is implemented separately for the absolute-pose robot-world/hand-eye equation A_j X = Y B_j. Its Kronecker SVD returns both X and Y, followed by a rank-six joint translation solve. The adapter preserves a separate absolute-pose split and reports dominant-singular width, SO(3) projection correction, held-out closure, and signed controls for both estimated transforms. Li, Wang, and Wu provide an independent simultaneous absolute-pose comparison: their equations (17)-(19) solve vec(R_X), vec(R_Z), t_X, and t_Z in one rank-gated 24-variable system. Calibrex preserves the paper method's non-recomputed translations after SO(3) projection and exposes the resulting correction and held-out closure rather than treating the linear estimate as automatically physical. None of the absolute-pose baselines is relabeled as relative-motion AX=XB evidence.

Dornaika and Horaud add a third independent absolute-pose estimator. It directly enforces two unit-quaternion constraints in the paper's positive quadratic closed form, then conditionally solves six translations. Calibrex records quaternion double-cover sign synchronization, the four-value spectrum and minimum width, unit errors, held-out closure, and 24 controls. The paper's separate nonlinear method is also implemented as a 24-parameter analytic-Jacobian LM refinement. Its convergence trace, data-Jacobian width, orthogonality penalty, SO(3) correction, and mixed-unit weighting limitation remain explicit.