ShonanAveraging - GTSAM Docs

Created by Codex.

Implement the common staircase relaxation and optimality-certificate machinery for Shonan rotation averaging.

Authors: Frank Dellaert, et al. (see THANKS for the full author list)

See LICENSE for the license information

Mathematical idea¶

Rotation averaging seeks absolute rotations whose relative rotations agree with measurements:

\min_{R_i\in\mathrm{SO}(d)}\sum_{(i,j)} \left\lVert R_iR_{ij}-R_j\right\rVert_F^2.

(1)

$\mathrm{SO}(d)$ is the special orthogonal group. Shonan averaging lifts the problem from $\mathrm{SO}(d)$ to successively larger $\mathrm{SO}(p)$ manifolds, searches for a certifiable optimum, and rounds the lifted solution back to dimension $d$ .

try:
    import google.colab
    %pip install --quiet gtsam-develop
except ImportError:
    pass

import gtsam
import numpy as np

from gtsam import symbol_shorthand

C = symbol_shorthand.C
K = symbol_shorthand.K
P = symbol_shorthand.P
S = symbol_shorthand.S
X = symbol_shorthand.X

Purpose and availability¶

ShonanAveraging<d> is the templated C++ implementation shared by the concrete ShonanAveraging2 and ShonanAveraging3 interfaces. It builds and optimizes problems on increasing SO(p) levels, checks the minimum eigenvalue certificate, descends through a negative-curvature direction when needed, and rounds a lifted solution back to rotations.

Use the concrete classes in application code. The base template itself is not directly exposed in Python.

C++ sketch¶

#include <gtsam/sfm/ShonanAveraging.h>

using namespace gtsam;

ShonanAveragingParameters<3> parameters;
ShonanAveraging<3>::Measurements measurements = /* relative Rot3 edges */;
ShonanAveraging<3> shonan(measurements, parameters);

auto [rotations, certificate] = shonan.run(/* minP = */ 3,
                                           /* maxP = */ 10);

In ordinary code prefer ShonanAveraging3, which provides the same main API and stable explicit template instantiation.

Source¶

ShonanAveraging.h