Global pose estimation¶

Code under src/theia/sfm/global_pose_estimation implements rotation averaging and global camera position solvers used by the global SfM pipeline. They fuse pairwise geometric constraints from a view graph into a consistent set of absolute camera orientations and positions.

This is not two-view minimal estimation (see Estimators); inputs are already aggregated TwoViewInfo edges between views (relative rotation and translation direction, etc.). The high-level global SfM flow is described in SfM — Global SfM Pipeline.

Problem shape¶

Global rotations: From relative rotations \(R_{ij}\) on edges \((i,j)\), estimate an angle-axis (or equivalent) global orientation per view so that constraints like \(R_{ij} \approx R_j R_i^\top\) are satisfied in a robust way.
Global positions: Given fixed global rotations and pairwise translation directions (from TwoViewInfo), estimate camera centers up to the usual gauge (translation + scale; global SfM fixes this in later bundle adjustment).

Several position methods also use view triplets and/or tracks from a Reconstruction (linear triplet / LiGT / nonlinear with point priors).

Base interfaces (C++)¶

`RotationEstimator`¶

Header: rotation_estimator.h

virtual bool EstimateRotations(
    const std::unordered_map<ViewIdPair, TwoViewInfo>& view_pairs,
    std::unordered_map<ViewId, Eigen::Vector3d>* rotations) = 0;

pyTheia: abstract base pt.sfm.RotationEstimator; concrete classes expose EstimateRotations / EstimateRotationsWrapper (see below). Most solvers need a reasonable initial guess for global orientations (e.g. spanning tree).

`PositionEstimator`¶

Header: position_estimator.h

virtual bool EstimatePositions(
    const std::unordered_map<ViewIdPair, TwoViewInfo>& view_pairs,
    const std::unordered_map<ViewId, Eigen::Vector3d>& orientation,
    std::unordered_map<ViewId, Eigen::Vector3d>* positions) = 0;

pyTheia: abstract base pt.sfm.PositionEstimator; subclasses take a Reconstruction in the constructor when they need tracks / triplets.

Global rotation averaging¶

Implementations derive from RotationEstimator. In ReconstructionEstimatorOptions, the enum GlobalRotationEstimatorType (pt.sfm.GlobalRotationEstimatorType) selects which one the global pipeline uses.

Python / C++ class	`GlobalRotationEstimatorType`	Summary
`RobustRotationEstimator`	`ROBUST_L1L2` (default)	L1 then IRLS; Efficient and Large Scale Rotation Averaging, Chatterjee & Govindu (ICCV 2013).
`NonlinearRotationEstimator`	`NONLINEAR`	Ceres + robust loss on rotation manifold.
`LinearRotationEstimator`	`LINEAR`	Linearized system + projection to SO(3); Martinec & Pajdla (CVPR 2007). Optional `AddRelativeRotationConstraint` for multiple constraints per pair (Zhu et al., arXiv 2017).
`LagrangeDualRotationEstimator`	`LAGRANGE_DUAL`	SDP / Lagrange dual rotation averaging (Eriksson et al., CVPR 2018 / PAMI 2019).
`HybridRotationEstimator`	`HYBRID`	Combines Lagrange-dual estimation with IRLS local refinement (`irls_rotation_local_refiner.h`).

RobustRotationEstimator (pyTheia) also exposes AddRelativeRotationConstraint and SetFixedGlobalRotations for specialized setups.

Global camera positions¶

Implementations derive from PositionEstimator. GlobalPositionEstimatorType (pt.sfm.GlobalPositionEstimatorType) selects the solver in the global pipeline.

Python / C++ class	`GlobalPositionEstimatorType`	Summary
`NonlinearPositionEstimator`	`NONLINEAR` (default)	Robust nonlinear alignment to pairwise translation directions; Robust Global Translations with 1DSfM, Wilson & Snavely (ECCV 2014). Uses `Reconstruction` for optional point–camera constraints.
`LinearPositionEstimator`	`LINEAR_TRIPLET`	Linear system from view triplets and baseline ratios; Jiang et al. (ICCV 2013).
`LeastUnsquaredDeviationPositionEstimator`	`LEAST_UNSQUARED_DEVIATION`	L1-style via IRLS / ADMM; Ozyesil & Singer (CVPR 2015).
`LiGTPositionEstimator`	`LIGT`	Linear formulation using pose-only / triplet constraints (Cai et al., arXiv:2103.01530). Requires `Reconstruction`.

Triplet baseline helper¶

`ComputeTripletBaselineRatios`¶

Header: compute_triplet_baseline_ratios.h

pyTheia: pt.sfm.ComputeTripletBaselineRatios(triplet, features1, features2, features3) → (success, baselines) where baselines is a 3-vector: scale of baseline between views 1–2, 1–3, and 2–3, from triangulated depths of aligned feature triplets.

Used when turning triplet geometry into constraints for linear / LiGT-style position solvers.

Supporting and C++-only sources¶

These files support the estimators above (Ceres costs, internal IRLS / L1 blocks, tests). They are not separate top-level pyTheia APIs:

Pairwise residuals: pairwise_rotation_error.{h,cc}, pairwise_translation_error.{h,cc}, pairwise_translation_and_scale_error.{h,cc}
Rotation building blocks: l1_rotation_global_estimator.*, irls_rotation_local_refiner.*, rotation_estimator_util.h
C++-only position variant: bata_position_estimator.h (revised least-unsquared / BATA-style formulation; not exposed in pybind as of this writing)

Python/C++ bridge for triplet baselines: global_pose_estimation_wrapper.cc.

pyTheia usage notes¶

Configure the global pipeline via ReconstructionEstimatorOptions.global_rotation_estimator_type and global_position_estimator_type (see SfM).
To call estimators directly, construct the concrete Options struct (RobustRotationEstimatorOptions, LinearPositionEstimatorOptions, …), build the view_pairs map and orientation / position maps, then call EstimateRotationsWrapper / EstimatePositionsWrapper where provided (signatures match the C++ EstimateRotations / EstimatePositions but return or mutate maps in a pybind-friendly way).