ShonanGaugeFactor - GTSAM Docs

Created by Codex.

Remove the stabilizer gauge directions introduced by a lifted Shonan variable.

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

See LICENSE for the license information

Mathematical idea¶

Only the first $d$ columns of $Q\in\mathrm{SO}(p)$ affect the lifted rotation. Right actions in the remaining $p-d$ dimensions therefore form an $\mathrm{SO}(p-d)$ stabilizer with

\frac{(p-d)(p-d-1)}{2}

(1)

unobservable tangent directions. ShonanGaugeFactor constrains exactly this linearized null space without adding a nonlinear residual.

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¶

An SO(p) relaxation contains SO(p-d) directions that do not alter its projected Stiefel frame. ShonanGaugeFactor contributes a constant Jacobian on precisely those tangent directions. Its nonlinear error is always zero; its role appears during linearization.

This implementation class is currently C++-only. ShonanAveraging adds it internally when configured with gauge weight.

C++ example¶

#include <gtsam/sfm/ShonanGaugeFactor.h>

using namespace gtsam;

const Key key = Symbol('Q', 0);
const size_t p = 6;
const size_t d = 3;
ShonanGaugeFactor factor(key, p, d, 1e3);  // optional precision gamma

Values values;
values.insert(key, SOn::FromMatrix(Matrix::Identity(p, p)));
const auto linear = factor.linearize(values);

The constructor requires p >= d. For p-d < 2, the stabilizer has zero dimension and the factor contributes no rows.

Source¶

ShonanGaugeFactor.h