triangulation

The triangulation API reconstructs 3D landmarks from multiple camera measurements. TriangulationParameters configures robust validity checks, while TriangulationResult distinguishes a valid point from geometric failure modes.

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

See LICENSE for the license information

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

import gtsam
import numpy as np

A two-view track¶

Build two calibrated cameras, project a known point, and place the cameras in a matching CameraSet. Real applications supply measured pixels rather than generating them this way.

K = gtsam.Cal3_S2(800.0, 800.0, 0.0, 320.0, 240.0)
camera0 = gtsam.PinholeCameraCal3_S2(gtsam.Pose3(), K)
camera1 = gtsam.PinholeCameraCal3_S2(
    gtsam.Pose3(gtsam.Rot3(), np.array([1.0, 0.0, 0.0])), K
)
point = np.array([0.2, -0.1, 5.0])
cameras = gtsam.CameraSetCal3_S2([camera0, camera1])
measurements = [camera.project(point) for camera in cameras]

`TriangulationParameters`¶

The parameters control rank tolerance, EPI correction, maximum landmark distance, dynamic outlier rejection, the LOST algorithm, and an optional measurement noise model. Negative distance/outlier thresholds disable those checks.

parameters = gtsam.TriangulationParameters(
    rankTolerance=1e-9,
    enableEPI=False,
    landmarkDistanceThreshold=10.0,
    dynamicOutlierRejectionThreshold=5.0,
    useLOST=False,
)
print("distance threshold:", parameters.landmarkDistanceThreshold)

`TriangulationResult`¶

triangulateSafe() returns a result rather than throwing for common geometric failures. Test valid() before calling get(). The predicates degenerate(), outlier(), farPoint(), and behindCamera() explain invalid results.

result = gtsam.triangulateSafe(cameras, measurements, parameters)
print("status:", result.status)
print("valid:", result.valid())
assert result.valid()
np.testing.assert_allclose(result.get(), point, atol=1e-8)

Other triangulation entry points¶

triangulatePoint3() performs linear triangulation with optional nonlinear refinement, while triangulateNonlinear() refines an initial point. Overloads accept shared calibrations, camera sets with individual calibrations, spherical cameras, and batches of tracks.

Source¶

triangulation.h

AI assistance caveat¶

AI was used to help draft this documentation, and inaccuracies could be present.