Visualize uncertainty and covariance

Covariance ellipsoids in 3D

Use Ellipsoids3D. To draw a 3×3 covariance matrix, take its eigendecomposition:

• the half sizes of the ellipsoid are k * sqrt(eigenvalues), where k is the number of standard deviations,
• the rotation is the matrix of eigenvectors (one eigenvector per column).

Put the rotation and the mean in a Transform3D on the same entity:

import numpy as np
import rerun as rr

rr.init("rerun_example_covariance_ellipsoid", spawn=True)

mean = np.array([1.0, 2.0, 0.5])
covariance = np.array([
    [0.40, 0.10, 0.00],
    [0.10, 0.20, 0.05],
    [0.00, 0.05, 0.10],
])

eigenvalues, eigenvectors = np.linalg.eigh(covariance)
k = 2.0  # Two standard deviations

rr.log("estimate/covariance", rr.Transform3D(translation=mean, mat3x3=eigenvectors))
rr.log("estimate/covariance", rr.Ellipsoids3D(half_sizes=[k * np.sqrt(eigenvalues)]))

To draw many ellipsoids in one entity, pass centers and one rotation per ellipsoid with quaternions instead. You can convert a rotation matrix to a quaternion with, for example, scipy.spatial.transform.Rotation.from_matrix(eigenvectors).as_quat() (which returns xyzw). If np.linalg.det(eigenvectors) is negative, flip the sign of one column first, so that the matrix is a rotation.

Covariance ellipses in 2D

Ellipses2D draws ellipses aligned with the X and Y axes. It has no rotation, so for a 2×2 covariance with correlation, draw the outline as a LineStrips2D:

mean = np.array([50.0, 40.0])
covariance = np.array([[30.0, 12.0], [12.0, 10.0]])
k = 2.0

eigenvalues, eigenvectors = np.linalg.eigh(covariance)
angles = np.linspace(0.0, 2.0 * np.pi, 64)
unit_circle = np.stack([np.cos(angles), np.sin(angles)])
outline = mean + (eigenvectors @ (k * np.sqrt(eigenvalues)[:, None] * unit_circle)).T

rr.log("estimate/covariance_2d", rr.LineStrips2D([outline]))

Error bands in plots

For one-dimensional values over time, Measurements logs each value together with its variance. The time series view draws a band of one standard deviation around the line. Measurements is unstable: its data format may change in future releases.

"""Log scalar measurements with variances over time."""

import math

import rerun as rr

rr.init("rerun_example_measurements_simple", spawn=True)

# Two parallel pressure sensors (in Pa), each with slowly drifting variance.
for step in range(64):
    rr.set_time("step", sequence=step)
    pressures = [
        101_325.0 + 50.0 * math.sin(step / 10.0),
        101_300.0 + 30.0 * math.cos(step / 8.0),
    ]
    variances = [
        100.0 + 25.0 * math.sin(step / 7.0),
        80.0 + 15.0 * math.cos(step / 11.0),
    ]
    rr.log(
        "pressure",
        rr.Measurements(values=pressures, variances=variances, units="Pa"),
    )

Gaussian splats

GaussianSplats3D draws 3D Gaussians with a center, per-axis scales (standard deviations), a rotation, and a color with opacity. It is meant for 3D Gaussian Splatting (3DGS) reconstructions, but you can also use it to show many probability distributions at once. GaussianSplats3D is unstable: its data format may change in future releases.

3DGS .ply files are loaded as GaussianSplats3D when you open them in the Viewer, or log them with rr.log_file_from_path.