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Updated scaling factors for proper geometric representation of uncertainty ellipses #1067

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merged 4 commits into from
Apr 12, 2022
Merged

Updated scaling factors for proper geometric representation of uncertainty ellipses #1067

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d9a00de
Modified the scaling values for plotting uncertainty ellipses to prop…
magicbycalvin Jan 25, 2022
1b81776
Changed all instances of the Sigma value, k, to 5 for plotting the co…
magicbycalvin Jan 28, 2022
e524e28
Updated comments to reflect standard deviations instead of variances …
magicbycalvin Jan 28, 2022
df7fb47
Merge branch 'fix/ellipses' into develop
dellaert Apr 12, 2022
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41 changes: 33 additions & 8 deletions python/gtsam/utils/plot.py
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Original file line number Diff line number Diff line change
Expand Up @@ -82,8 +82,11 @@ def plot_covariance_ellipse_3d(axes,
Plots a Gaussian as an uncertainty ellipse

Based on Maybeck Vol 1, page 366
k=2.296 corresponds to 1 std, 68.26% of all probability
k=11.82 corresponds to 3 std, 99.74% of all probability
For the 3D case:
k = 1.878 corresponds to 1 std, 68.26% of all probability
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I would an argument k here and say
k = 1 corresponds to xx%
k = 2 corresponds to xx%
k = 2.5 (default) corresponds to xx%

k = 3.763 corresponds to 3 std, 99.74% of all probability

We choose k = 5 which corresponds to 99.99846% of all probability in 3D

Args:
axes (matplotlib.axes.Axes): Matplotlib axes.
Expand All @@ -94,7 +97,8 @@ def plot_covariance_ellipse_3d(axes,
n: Defines the granularity of the ellipse. Higher values indicate finer ellipses.
alpha: Transparency value for the plotted surface in the range [0, 1].
"""
k = 11.82
# Sigma value corresponding to the covariance ellipse
k = 5
U, S, _ = np.linalg.svd(P)

radii = k * np.sqrt(S)
Expand All @@ -120,7 +124,16 @@ def plot_point2_on_axes(axes,
linespec: str,
P: Optional[np.ndarray] = None) -> None:
"""
Plot a 2D point on given axis `axes` with given `linespec`.
Plot a 2D point and its corresponding uncertainty ellipse on given axis
`axes` with given `linespec`.

Based on Stochastic Models, Estimation, and Control Vol 1 by Maybeck,
page 366
For the 2D case:
k = 1.515 corresponds to 1 std, 68.26% of all probability
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I would an argument k here and say
k = 1 corresponds to xx%
k = 2 corresponds to xx%
k = 2.5 (default) corresponds to xx%

k = 3.438 corresponds to 3 std, 99.74% of all probability

We choose k = 5 which corresponds to 99.99963% of all probability for 2D.

Args:
axes (matplotlib.axes.Axes): Matplotlib axes.
Expand All @@ -136,9 +149,11 @@ def plot_point2_on_axes(axes,
k = 5.0

angle = np.arctan2(v[1, 0], v[0, 0])
# We multiply k by 2 since k corresponds to the radius but Ellipse uses
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Wow. I guess we were looking at the wrong ellipses all that time!

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On the bright side, your numbers would have still been correct!

The requested changes have been made. Please let me know if you need anything else.

Thanks!

# the diameter.
e1 = patches.Ellipse(point,
np.sqrt(w[0] * k),
np.sqrt(w[1] * k),
np.sqrt(w[0]) * 2 * k,
np.sqrt(w[1]) * 2 * k,
np.rad2deg(angle),
fill=False)
axes.add_patch(e1)
Expand Down Expand Up @@ -182,6 +197,14 @@ def plot_pose2_on_axes(axes,
"""
Plot a 2D pose on given axis `axes` with given `axis_length`.

Based on Stochastic Models, Estimation, and Control Vol 1 by Maybeck,
page 366
For the 2D case:
k = 1.515 corresponds to 1 std, 68.26% of all probability
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same

k = 3.438 corresponds to 3 std, 99.74% of all probability

We choose k = 5 which corresponds to 99.99963% of all probability for 2D.

Args:
axes (matplotlib.axes.Axes): Matplotlib axes.
pose: The pose to be plotted.
Expand Down Expand Up @@ -213,9 +236,11 @@ def plot_pose2_on_axes(axes,
k = 5.0

angle = np.arctan2(v[1, 0], v[0, 0])
# We multiply k by 2 since k corresponds to the radius but Ellipse uses
# the diameter.
e1 = patches.Ellipse(origin,
np.sqrt(w[0] * k),
np.sqrt(w[1] * k),
np.sqrt(w[0]) * 2 * k,
np.sqrt(w[1]) * 2 * k,
np.rad2deg(angle),
fill=False)
axes.add_patch(e1)
Expand Down