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Version:
4.3a0.dev202505130056 ▾
|
"""
GTSAM Copyright 2010-2019, Georgia Tech Research Corporation,
Atlanta, Georgia 30332-0415
All Rights Reserved
See LICENSE for the license information
Unit tests to ensure backwards compatibility of the Python wrapper.
Author: Varun Agrawal
"""
import unittest
from typing import Iterable, List, Optional, Tuple, Union
import numpy as np
from gtsam.gtsfm import Keypoints
from gtsam.symbol_shorthand import X
from gtsam.utils.test_case import GtsamTestCase
import gtsam
from gtsam import (BetweenFactorPose2, Cal3_S2, Cal3Bundler, CameraSetCal3_S2,
CameraSetCal3Bundler, IndexPair, LevenbergMarquardtParams,
PinholeCameraCal3_S2, PinholeCameraCal3Bundler, Point2,
Point2Pairs, Point3, Pose2, Pose2Pairs, Pose3, Rot2, Rot3,
SfmTrack2d, ShonanAveraging2, ShonanAveragingParameters2,
Similarity2, Similarity3, TriangulationParameters,
TriangulationResult)
UPRIGHT = Rot3.Ypr(-np.pi / 2, 0.0, -np.pi / 2)
class TestBackwardsCompatibility(GtsamTestCase):
"""Tests for backwards compatibility of the Python wrapper."""
def setUp(self):
"""Setup test fixtures"""
p1 = [-1.0, 0.0, -1.0]
p2 = [1.0, 0.0, -1.0]
q1 = Rot3(1.0, 0.0, 0.0, 0.0)
q2 = Rot3(1.0, 0.0, 0.0, 0.0)
pose1 = Pose3(q1, p1)
pose2 = Pose3(q2, p2)
camera1 = gtsam.PinholeCameraCal3Fisheye(pose1)
camera2 = gtsam.PinholeCameraCal3Fisheye(pose2)
self.origin = np.array([0.0, 0.0, 0.0])
self.poses = gtsam.Pose3Vector([pose1, pose2])
self.fisheye_cameras = gtsam.CameraSetCal3Fisheye([camera1, camera2])
self.fisheye_measurements = gtsam.Point2Vector(
[k.project(self.origin) for k in self.fisheye_cameras])
fx, fy, s, u0, v0 = 2, 2, 0, 0, 0
k1, k2, p1, p2 = 0, 0, 0, 0
xi = 1
self.stereographic = gtsam.Cal3Unified(fx, fy, s, u0, v0, k1, k2, p1,
p2, xi)
camera1 = gtsam.PinholeCameraCal3Unified(pose1, self.stereographic)
camera2 = gtsam.PinholeCameraCal3Unified(pose2, self.stereographic)
self.unified_cameras = gtsam.CameraSetCal3Unified([camera1, camera2])
self.unified_measurements = gtsam.Point2Vector(
[k.project(self.origin) for k in self.unified_cameras])
## Set up two camera poses
# Looking along X-axis, 1 meter above ground plane (x-y)
pose1 = Pose3(UPRIGHT, Point3(0, 0, 1))
# create second camera 1 meter to the right of first camera
pose2 = pose1.compose(Pose3(Rot3(), Point3(1, 0, 0)))
# twoPoses
self.triangulation_poses = gtsam.Pose3Vector()
self.triangulation_poses.append(pose1)
self.triangulation_poses.append(pose2)
# landmark ~5 meters infront of camera
self.landmark = Point3(5, 0.5, 1.2)
def test_Cal3Fisheye_triangulation_rectify(self):
"""
Estimate spatial point from image measurements using
rectification from a Cal3Fisheye camera model.
"""
rectified = gtsam.Point2Vector([
k.calibration().calibrate(pt)
for k, pt in zip(self.fisheye_cameras, self.fisheye_measurements)
])
shared_cal = gtsam.Cal3_S2()
triangulated = gtsam.triangulatePoint3(self.poses,
shared_cal,
rectified,
rank_tol=1e-9,
optimize=False)
self.gtsamAssertEquals(triangulated, self.origin)
def test_Cal3Unified_triangulation_rectify(self):
"""
Estimate spatial point from image measurements using
rectification from a Cal3Unified camera model.
"""
rectified = gtsam.Point2Vector([
k.calibration().calibrate(pt)
for k, pt in zip(self.unified_cameras, self.unified_measurements)
])
shared_cal = gtsam.Cal3_S2()
triangulated = gtsam.triangulatePoint3(self.poses,
shared_cal,
rectified,
rank_tol=1e-9,
optimize=False)
self.gtsamAssertEquals(triangulated, self.origin)
def test_track_generation(self) -> None:
"""Ensures that DSF generates three tracks from measurements
in 3 images (H=200,W=400)."""
kps_i0 = Keypoints(np.array([[10.0, 20], [30, 40]]))
kps_i1 = Keypoints(np.array([[50.0, 60], [70, 80], [90, 100]]))
kps_i2 = Keypoints(np.array([[110.0, 120], [130, 140]]))
keypoints_list = gtsam.KeypointsVector()
keypoints_list.append(kps_i0)
keypoints_list.append(kps_i1)
keypoints_list.append(kps_i2)
# For each image pair (i1,i2), we provide a (K,2) matrix
# of corresponding image indices (k1,k2).
matches_dict = gtsam.MatchIndicesMap()
matches_dict[IndexPair(0, 1)] = np.array([[0, 0], [1, 1]])
matches_dict[IndexPair(1, 2)] = np.array([[2, 0], [1, 1]])
tracks = gtsam.gtsfm.tracksFromPairwiseMatches(
matches_dict,
keypoints_list,
verbose=False,
)
assert len(tracks) == 3
# Verify track 0.
track0 = tracks[0]
assert track0.numberMeasurements() == 2
np.testing.assert_allclose(track0.measurements[0][1], Point2(10, 20))
np.testing.assert_allclose(track0.measurements[1][1], Point2(50, 60))
assert track0.measurements[0][0] == 0
assert track0.measurements[1][0] == 1
np.testing.assert_allclose(
track0.measurementMatrix(),
[
[10, 20],
[50, 60],
],
)
np.testing.assert_allclose(track0.indexVector(), [0, 1])
# Verify track 1.
track1 = tracks[1]
np.testing.assert_allclose(
track1.measurementMatrix(),
[
[30, 40],
[70, 80],
[130, 140],
],
)
np.testing.assert_allclose(track1.indexVector(), [0, 1, 2])
# Verify track 2.
track2 = tracks[2]
np.testing.assert_allclose(
track2.measurementMatrix(),
[
[90, 100],
[110, 120],
],
)
np.testing.assert_allclose(track2.indexVector(), [1, 2])
def test_sfm_track_2d_constructor(self) -> None:
"""Test construction of 2D SfM track."""
measurements = gtsam.SfmMeasurementVector()
measurements.append((0, Point2(10, 20)))
track = SfmTrack2d(measurements=measurements)
track.measurement(0)
assert track.numberMeasurements() == 1
def test_FixedLagSmootherExample(self):
'''
Simple test that checks for equality between C++ example
file and the Python implementation. See
gtsam_unstable/examples/FixedLagSmootherExample.cpp
'''
# Define a batch fixed lag smoother, which uses
# Levenberg-Marquardt to perform the nonlinear optimization
lag = 2.0
smoother_batch = gtsam.BatchFixedLagSmoother(lag)
# Create containers to store the factors and linearization points
# that will be sent to the smoothers
new_factors = gtsam.NonlinearFactorGraph()
new_values = gtsam.Values()
new_timestamps = gtsam.FixedLagSmootherKeyTimestampMap()
# Create a prior on the first pose, placing it at the origin
prior_mean = Pose2(0, 0, 0)
prior_noise = gtsam.noiseModel.Diagonal.Sigmas(
np.array([0.3, 0.3, 0.1]))
X1 = 0
new_factors.push_back(
gtsam.PriorFactorPose2(X1, prior_mean, prior_noise))
new_values.insert(X1, prior_mean)
new_timestamps.insert((X1, 0.0))
delta_time = 0.25
time = 0.25
i = 0
ground_truth = [
Pose2(0.995821, 0.0231012, 0.0300001),
Pose2(1.49284, 0.0457247, 0.045),
Pose2(1.98981, 0.0758879, 0.06),
Pose2(2.48627, 0.113502, 0.075),
Pose2(2.98211, 0.158558, 0.09),
Pose2(3.47722, 0.211047, 0.105),
Pose2(3.97149, 0.270956, 0.12),
Pose2(4.4648, 0.338272, 0.135),
Pose2(4.95705, 0.41298, 0.15),
Pose2(5.44812, 0.495063, 0.165),
Pose2(5.9379, 0.584503, 0.18),
]
# Iterates from 0.25s to 3.0s, adding 0.25s each loop
# In each iteration, the agent moves at a constant speed
# and its two odometers measure the change. The smoothed
# result is then compared to the ground truth
while time <= 3.0:
previous_key = int(1000 * (time - delta_time))
current_key = int(1000 * time)
# assign current key to the current timestamp
new_timestamps.insert((current_key, time))
# Add a guess for this pose to the new values
# Assume that the robot moves at 2 m/s. Position is time[s] *
# 2[m/s]
current_pose = Pose2(time * 2, 0, 0)
new_values.insert(current_key, current_pose)
# Add odometry factors from two different sources with different
# error stats
odometry_measurement_1 = Pose2(0.61, -0.08, 0.02)
odometry_noise_1 = gtsam.noiseModel.Diagonal.Sigmas(
np.array([0.1, 0.1, 0.05]))
new_factors.push_back(
gtsam.BetweenFactorPose2(previous_key, current_key,
odometry_measurement_1,
odometry_noise_1))
odometry_measurement_2 = Pose2(0.47, 0.03, 0.01)
odometry_noise_2 = gtsam.noiseModel.Diagonal.Sigmas(
np.array([0.05, 0.05, 0.05]))
new_factors.push_back(
gtsam.BetweenFactorPose2(previous_key, current_key,
odometry_measurement_2,
odometry_noise_2))
# Update the smoothers with the new factors. In this case,
# one iteration must pass for Levenberg-Marquardt to accurately
# estimate
if time >= 0.50:
smoother_batch.update(new_factors, new_values, new_timestamps)
estimate = smoother_batch.calculateEstimatePose2(current_key)
self.assertTrue(estimate.equals(ground_truth[i], 1e-4))
i += 1
new_timestamps.clear()
new_values.clear()
new_factors.resize(0)
time += delta_time
def test_ordering(self):
"""Test ordering"""
gfg = gtsam.GaussianFactorGraph()
x0 = X(0)
x1 = X(1)
x2 = X(2)
BETWEEN_NOISE = gtsam.noiseModel.Diagonal.Sigmas(np.ones(1))
PRIOR_NOISE = gtsam.noiseModel.Diagonal.Sigmas(np.ones(1))
gfg.add(x1, np.eye(1), x0, -np.eye(1), np.ones(1), BETWEEN_NOISE)
gfg.add(x2, np.eye(1), x1, -np.eye(1), 2 * np.ones(1), BETWEEN_NOISE)
gfg.add(x0, np.eye(1), np.zeros(1), PRIOR_NOISE)
keys = (x0, x1, x2)
ordering = gtsam.Ordering()
for key in keys[::-1]:
ordering.push_back(key)
bn = gfg.eliminateSequential(ordering)
self.assertEqual(bn.size(), 3)
keyVector = gtsam.KeyVector()
keyVector.append(keys[2])
ordering = gtsam.Ordering.ColamdConstrainedLastGaussianFactorGraph(
gfg, keyVector)
bn = gfg.eliminateSequential(ordering)
self.assertEqual(bn.size(), 3)
def test_find(self):
"""
Check that optimizing for Karcher mean (which minimizes Between distance)
gets correct result.
"""
R = Rot3.Expmap(np.array([0.1, 0, 0]))
rotations = gtsam.Rot3Vector([R, R.inverse()])
expected = Rot3()
actual = gtsam.FindKarcherMeanRot3(rotations)
self.gtsamAssertEquals(expected, actual)
def test_find_karcher_mean_identity(self):
"""Averaging 3 identity rotations should yield the identity."""
a1Rb1 = Rot3()
a2Rb2 = Rot3()
a3Rb3 = Rot3()
aRb_list = gtsam.Rot3Vector([a1Rb1, a2Rb2, a3Rb3])
aRb_expected = Rot3()
aRb = gtsam.FindKarcherMeanRot3(aRb_list)
self.gtsamAssertEquals(aRb, aRb_expected)
def test_factor(self):
"""Check that the InnerConstraint factor leaves the mean unchanged."""
# Make a graph with two variables, one between, and one InnerConstraint
# The optimal result should satisfy the between, while moving the other
# variable to make the mean the same as before.
# Mean of R and R' is identity. Let's make a BetweenFactor making R21 =
# R*R*R, i.e. geodesic length is 3 rather than 2.
R = Rot3.Expmap(np.array([0.1, 0, 0]))
MODEL = gtsam.noiseModel.Unit.Create(3)
graph = gtsam.NonlinearFactorGraph()
R12 = R.compose(R.compose(R))
graph.add(gtsam.BetweenFactorRot3(1, 2, R12, MODEL))
keys = gtsam.KeyVector()
keys.append(1)
keys.append(2)
graph.add(gtsam.KarcherMeanFactorRot3(keys))
initial = gtsam.Values()
initial.insert(1, R.inverse())
initial.insert(2, R)
expected = Rot3()
result = gtsam.GaussNewtonOptimizer(graph, initial).optimize()
actual = gtsam.FindKarcherMeanRot3(
gtsam.Rot3Vector([result.atRot3(1),
result.atRot3(2)]))
self.gtsamAssertEquals(expected, actual)
self.gtsamAssertEquals(R12, result.atRot3(1).between(result.atRot3(2)))
def test_align(self) -> None:
"""Ensure estimation of the Pose2 element to align two 2d point clouds succeeds.
Two point clouds represent horseshoe-shapes of the same size, just rotated and translated:
| X---X
| |
| X---X
------------------
|
|
O | O
| | |
O---O
"""
pts_a = [
Point2(1, -3),
Point2(1, -5),
Point2(-1, -5),
Point2(-1, -3),
]
pts_b = [
Point2(3, 1),
Point2(1, 1),
Point2(1, 3),
Point2(3, 3),
]
ab_pairs = Point2Pairs(list(zip(pts_a, pts_b)))
aTb = Pose2.Align(ab_pairs)
self.assertIsNotNone(aTb)
for pt_a, pt_b in zip(pts_a, pts_b):
pt_a_ = aTb.transformFrom(pt_b)
np.testing.assert_allclose(pt_a, pt_a_)
# Matrix version
A = np.array(pts_a).T
B = np.array(pts_b).T
aTb = Pose2.Align(A, B)
self.assertIsNotNone(aTb)
for pt_a, pt_b in zip(pts_a, pts_b):
pt_a_ = aTb.transformFrom(pt_b)
np.testing.assert_allclose(pt_a, pt_a_)
def test_align_squares(self):
"""Test if Align method can align 2 squares."""
square = np.array([[0, 0, 0], [0, 1, 0], [1, 1, 0], [1, 0, 0]],
float).T
sTt = Pose3(Rot3.Rodrigues(0, 0, -np.pi), gtsam.Point3(2, 4, 0))
transformed = sTt.transformTo(square)
st_pairs = gtsam.Point3Pairs()
for j in range(4):
st_pairs.append((square[:, j], transformed[:, j]))
# Recover the transformation sTt
estimated_sTt = Pose3.Align(st_pairs)
self.gtsamAssertEquals(estimated_sTt, sTt, 1e-10)
# Matrix version
estimated_sTt = Pose3.Align(square, transformed)
self.gtsamAssertEquals(estimated_sTt, sTt, 1e-10)
def test_constructorBetweenFactorPose2s(self) -> None:
"""Check if ShonanAveraging2 constructor works when not initialized from g2o file.
GT pose graph:
| cam 1 = (0,4)
--o
| .
. .
. .
| |
o-- ... o--
cam 0 cam 2 = (4,0)
(0,0)
"""
num_images = 3
wTi_list = [
Pose2(Rot2.fromDegrees(0), np.array([0, 0])),
Pose2(Rot2.fromDegrees(90), np.array([0, 4])),
Pose2(Rot2.fromDegrees(0), np.array([4, 0])),
]
edges = [(0, 1), (1, 2), (0, 2)]
i2Ri1_dict = {(i1, i2):
wTi_list[i2].inverse().compose(wTi_list[i1]).rotation()
for (i1, i2) in edges}
lm_params = LevenbergMarquardtParams.CeresDefaults()
shonan_params = ShonanAveragingParameters2(lm_params)
shonan_params.setUseHuber(False)
shonan_params.setCertifyOptimality(True)
noise_model = gtsam.noiseModel.Unit.Create(3)
between_factors = gtsam.BetweenFactorPose2s()
for (i1, i2), i2Ri1 in i2Ri1_dict.items():
i2Ti1 = Pose2(i2Ri1, np.zeros(2))
between_factors.append(
BetweenFactorPose2(i2, i1, i2Ti1, noise_model))
obj = ShonanAveraging2(between_factors, shonan_params)
initial = obj.initializeRandomly()
result_values, _ = obj.run(initial, min_p=2, max_p=100)
wRi_list = [result_values.atRot2(i) for i in range(num_images)]
thetas_deg = np.array([wRi.degrees() for wRi in wRi_list])
# map all angles to [-180,180)
thetas_deg = (thetas_deg - thetas_deg[0] + 180) % 360 - 180
expected_thetas_deg = np.array([0.0, 90.0, 0.0])
np.testing.assert_allclose(thetas_deg, expected_thetas_deg, atol=0.1)
def test_align_poses2_along_straight_line(self) -> None:
"""Test Align of list of Pose2Pair.
Scenario:
3 object poses
same scale (no gauge ambiguity)
world frame has poses rotated about 180 degrees.
world and egovehicle frame translated by 15 meters w.r.t. each other
"""
R180 = Rot2.fromDegrees(180)
# Create source poses (three objects o1, o2, o3 living in the egovehicle "e" frame)
# Suppose they are 3d cuboids detected by an onboard sensor in the egovehicle frame
eTo0 = Pose2(Rot2(), np.array([5, 0]))
eTo1 = Pose2(Rot2(), np.array([10, 0]))
eTo2 = Pose2(Rot2(), np.array([15, 0]))
eToi_list = [eTo0, eTo1, eTo2]
# Create destination poses
# (same three objects, but instead living in the world "w" frame)
wTo0 = Pose2(R180, np.array([-10, 0]))
wTo1 = Pose2(R180, np.array([-5, 0]))
wTo2 = Pose2(R180, np.array([0, 0]))
wToi_list = [wTo0, wTo1, wTo2]
we_pairs = Pose2Pairs(list(zip(wToi_list, eToi_list)))
# Recover the transformation wSe (i.e. world_S_egovehicle)
wSe = Similarity2.Align(we_pairs)
for wToi, eToi in zip(wToi_list, eToi_list):
self.gtsamAssertEquals(wToi, wSe.transformFrom(eToi))
def test_align_poses2_along_straight_line_gauge(self):
"""Test if Align Pose2Pairs method can account for gauge ambiguity.
Scenario:
3 object poses
with gauge ambiguity (2x scale)
world frame has poses rotated by 90 degrees.
world and egovehicle frame translated by 11 meters w.r.t. each other
"""
R90 = Rot2.fromDegrees(90)
# Create source poses (three objects o1, o2, o3 living in the egovehicle "e" frame)
# Suppose they are 3d cuboids detected by an onboard sensor in the egovehicle frame
eTo0 = Pose2(Rot2(), np.array([1, 0]))
eTo1 = Pose2(Rot2(), np.array([2, 0]))
eTo2 = Pose2(Rot2(), np.array([4, 0]))
eToi_list = [eTo0, eTo1, eTo2]
# Create destination poses
# (same three objects, but instead living in the world/city "w" frame)
wTo0 = Pose2(R90, np.array([0, 12]))
wTo1 = Pose2(R90, np.array([0, 14]))
wTo2 = Pose2(R90, np.array([0, 18]))
wToi_list = [wTo0, wTo1, wTo2]
we_pairs = Pose2Pairs(list(zip(wToi_list, eToi_list)))
# Recover the transformation wSe (i.e. world_S_egovehicle)
wSe = Similarity2.Align(we_pairs)
for wToi, eToi in zip(wToi_list, eToi_list):
self.gtsamAssertEquals(wToi, wSe.transformFrom(eToi))
def test_align_poses2_scaled_squares(self):
"""Test if Align Pose2Pairs method can account for gauge ambiguity.
Make sure a big and small square can be aligned.
The u's represent a big square (10x10), and v's represents a small square (4x4).
Scenario:
4 object poses
with gauge ambiguity (2.5x scale)
"""
# 0, 90, 180, and 270 degrees yaw
R0 = Rot2.fromDegrees(0)
R90 = Rot2.fromDegrees(90)
R180 = Rot2.fromDegrees(180)
R270 = Rot2.fromDegrees(270)
aTi0 = Pose2(R0, np.array([2, 3]))
aTi1 = Pose2(R90, np.array([12, 3]))
aTi2 = Pose2(R180, np.array([12, 13]))
aTi3 = Pose2(R270, np.array([2, 13]))
aTi_list = [aTi0, aTi1, aTi2, aTi3]
bTi0 = Pose2(R0, np.array([4, 3]))
bTi1 = Pose2(R90, np.array([8, 3]))
bTi2 = Pose2(R180, np.array([8, 7]))
bTi3 = Pose2(R270, np.array([4, 7]))
bTi_list = [bTi0, bTi1, bTi2, bTi3]
ab_pairs = Pose2Pairs(list(zip(aTi_list, bTi_list)))
# Recover the transformation wSe (i.e. world_S_egovehicle)
aSb = Similarity2.Align(ab_pairs)
for aTi, bTi in zip(aTi_list, bTi_list):
self.gtsamAssertEquals(aTi, aSb.transformFrom(bTi))
def test_align_poses3_along_straight_line(self):
"""Test Align Pose3Pairs method.
Scenario:
3 object poses
same scale (no gauge ambiguity)
world frame has poses rotated about x-axis (90 degree roll)
world and egovehicle frame translated by 15 meters w.r.t. each other
"""
Rx90 = Rot3.Rx(np.deg2rad(90))
# Create source poses (three objects o1, o2, o3 living in the egovehicle "e" frame)
# Suppose they are 3d cuboids detected by an onboard sensor in the egovehicle frame
eTo0 = Pose3(Rot3(), np.array([5, 0, 0]))
eTo1 = Pose3(Rot3(), np.array([10, 0, 0]))
eTo2 = Pose3(Rot3(), np.array([15, 0, 0]))
eToi_list = [eTo0, eTo1, eTo2]
# Create destination poses
# (same three objects, but instead living in the world/city "w" frame)
wTo0 = Pose3(Rx90, np.array([-10, 0, 0]))
wTo1 = Pose3(Rx90, np.array([-5, 0, 0]))
wTo2 = Pose3(Rx90, np.array([0, 0, 0]))
wToi_list = [wTo0, wTo1, wTo2]
we_pairs = gtsam.Pose3Pairs(list(zip(wToi_list, eToi_list)))
# Recover the transformation wSe (i.e. world_S_egovehicle)
wSe = Similarity3.Align(we_pairs)
for wToi, eToi in zip(wToi_list, eToi_list):
self.gtsamAssertEquals(wToi, wSe.transformFrom(eToi))
def test_align_poses3_along_straight_line_gauge(self):
"""Test if Align Pose3Pairs method can account for gauge ambiguity.
Scenario:
3 object poses
with gauge ambiguity (2x scale)
world frame has poses rotated about z-axis (90 degree yaw)
world and egovehicle frame translated by 11 meters w.r.t. each other
"""
Rz90 = Rot3.Rz(np.deg2rad(90))
# Create source poses (three objects o1, o2, o3 living in the egovehicle "e" frame)
# Suppose they are 3d cuboids detected by an onboard sensor in the egovehicle frame
eTo0 = Pose3(Rot3(), np.array([1, 0, 0]))
eTo1 = Pose3(Rot3(), np.array([2, 0, 0]))
eTo2 = Pose3(Rot3(), np.array([4, 0, 0]))
eToi_list = [eTo0, eTo1, eTo2]
# Create destination poses
# (same three objects, but instead living in the world/city "w" frame)
wTo0 = Pose3(Rz90, np.array([0, 12, 0]))
wTo1 = Pose3(Rz90, np.array([0, 14, 0]))
wTo2 = Pose3(Rz90, np.array([0, 18, 0]))
wToi_list = [wTo0, wTo1, wTo2]
we_pairs = gtsam.Pose3Pairs(list(zip(wToi_list, eToi_list)))
# Recover the transformation wSe (i.e. world_S_egovehicle)
wSe = Similarity3.Align(we_pairs)
for wToi, eToi in zip(wToi_list, eToi_list):
self.gtsamAssertEquals(wToi, wSe.transformFrom(eToi))
def test_align_poses3_scaled_squares(self):
"""Test if Align Pose3Pairs method can account for gauge ambiguity.
Make sure a big and small square can be aligned.
The u's represent a big square (10x10), and v's represents a small square (4x4).
Scenario:
4 object poses
with gauge ambiguity (2.5x scale)
"""
# 0, 90, 180, and 270 degrees yaw
R0 = Rot3.Rz(np.deg2rad(0))
R90 = Rot3.Rz(np.deg2rad(90))
R180 = Rot3.Rz(np.deg2rad(180))
R270 = Rot3.Rz(np.deg2rad(270))
aTi0 = Pose3(R0, np.array([2, 3, 0]))
aTi1 = Pose3(R90, np.array([12, 3, 0]))
aTi2 = Pose3(R180, np.array([12, 13, 0]))
aTi3 = Pose3(R270, np.array([2, 13, 0]))
aTi_list = [aTi0, aTi1, aTi2, aTi3]
bTi0 = Pose3(R0, np.array([4, 3, 0]))
bTi1 = Pose3(R90, np.array([8, 3, 0]))
bTi2 = Pose3(R180, np.array([8, 7, 0]))
bTi3 = Pose3(R270, np.array([4, 7, 0]))
bTi_list = [bTi0, bTi1, bTi2, bTi3]
ab_pairs = gtsam.Pose3Pairs(list(zip(aTi_list, bTi_list)))
# Recover the transformation wSe (i.e. world_S_egovehicle)
aSb = Similarity3.Align(ab_pairs)
for aTi, bTi in zip(aTi_list, bTi_list):
self.gtsamAssertEquals(aTi, aSb.transformFrom(bTi))
def generate_measurements(
self,
calibration: Union[Cal3Bundler, Cal3_S2],
camera_model: Union[PinholeCameraCal3Bundler, PinholeCameraCal3_S2],
cal_params: Iterable[Iterable[Union[int, float]]],
camera_set: Optional[Union[CameraSetCal3Bundler,
CameraSetCal3_S2]] = None,
) -> Tuple[List[Point2], Union[CameraSetCal3Bundler, CameraSetCal3_S2,
List[Cal3Bundler], List[Cal3_S2]]]:
"""
Generate vector of measurements for given calibration and camera model.
Args:
calibration: Camera calibration e.g. Cal3_S2
camera_model: Camera model e.g. PinholeCameraCal3_S2
cal_params: Iterable of camera parameters for `calibration` e.g. [K1, K2]
camera_set: Cameraset object (for individual calibrations)
Returns:
list of measurements and list/CameraSet object for cameras
"""
if camera_set is not None:
cameras = camera_set()
else:
cameras = []
measurements = gtsam.Point2Vector()
for k, pose in zip(cal_params, self.triangulation_poses):
K = calibration(*k)
camera = camera_model(pose, K)
cameras.append(camera)
z = camera.project(self.landmark)
measurements.append(z)
return measurements, cameras
def test_TriangulationExample(self) -> None:
"""Tests triangulation with shared Cal3_S2 calibration"""
# Some common constants
sharedCal = (1500, 1200, 0, 640, 480)
measurements, _ = self.generate_measurements(
calibration=Cal3_S2,
camera_model=PinholeCameraCal3_S2,
cal_params=(sharedCal, sharedCal))
triangulated_landmark = gtsam.triangulatePoint3(
self.triangulation_poses,
Cal3_S2(sharedCal),
measurements,
rank_tol=1e-9,
optimize=True)
self.gtsamAssertEquals(self.landmark, triangulated_landmark, 1e-9)
# Add some noise and try again: result should be ~ (4.995, 0.499167, 1.19814)
measurements_noisy = gtsam.Point2Vector()
measurements_noisy.append(measurements[0] - np.array([0.1, 0.5]))
measurements_noisy.append(measurements[1] - np.array([-0.2, 0.3]))
triangulated_landmark = gtsam.triangulatePoint3(
self.triangulation_poses,
Cal3_S2(sharedCal),
measurements_noisy,
rank_tol=1e-9,
optimize=True)
self.gtsamAssertEquals(self.landmark, triangulated_landmark, 1e-2)
def test_triangulation_robust_three_poses(self) -> None:
"""Ensure triangulation with a robust model works."""
sharedCal = Cal3_S2(1500, 1200, 0, 640, 480)
# landmark ~5 meters infront of camera
landmark = Point3(5, 0.5, 1.2)
pose1 = Pose3(UPRIGHT, Point3(0, 0, 1))
pose2 = pose1 * Pose3(Rot3(), Point3(1, 0, 0))
pose3 = pose1 * Pose3(Rot3.Ypr(0.1, 0.2, 0.1), Point3(0.1, -2, -0.1))
camera1 = PinholeCameraCal3_S2(pose1, sharedCal)
camera2 = PinholeCameraCal3_S2(pose2, sharedCal)
camera3 = PinholeCameraCal3_S2(pose3, sharedCal)
z1: Point2 = camera1.project(landmark)
z2: Point2 = camera2.project(landmark)
z3: Point2 = camera3.project(landmark)
poses = gtsam.Pose3Vector([pose1, pose2, pose3])
measurements = gtsam.Point2Vector([z1, z2, z3])
# noise free, so should give exactly the landmark
actual = gtsam.triangulatePoint3(poses,
sharedCal,
measurements,
rank_tol=1e-9,
optimize=False)
self.assertTrue(np.allclose(landmark, actual, atol=1e-2))
# Add outlier
measurements[0] += Point2(100, 120) # very large pixel noise!
# now estimate does not match landmark
actual2 = gtsam.triangulatePoint3(poses,
sharedCal,
measurements,
rank_tol=1e-9,
optimize=False)
# DLT is surprisingly robust, but still off (actual error is around 0.26m)
self.assertTrue(np.linalg.norm(landmark - actual2) >= 0.2)
self.assertTrue(np.linalg.norm(landmark - actual2) <= 0.5)
# Again with nonlinear optimization
actual3 = gtsam.triangulatePoint3(poses,
sharedCal,
measurements,
rank_tol=1e-9,
optimize=True)
# result from nonlinear (but non-robust optimization) is close to DLT and still off
self.assertTrue(np.allclose(actual2, actual3, atol=0.1))
# Again with nonlinear optimization, this time with robust loss
model = gtsam.noiseModel.Robust.Create(
gtsam.noiseModel.mEstimator.Huber.Create(1.345),
gtsam.noiseModel.Unit.Create(2))
actual4 = gtsam.triangulatePoint3(poses,
sharedCal,
measurements,
rank_tol=1e-9,
optimize=True,
model=model)
# using the Huber loss we now have a quite small error!! nice!
self.assertTrue(np.allclose(landmark, actual4, atol=0.05))
def test_outliers_and_far_landmarks(self) -> None:
"""Check safe triangulation function."""
pose1, pose2 = self.poses
K1 = Cal3_S2(1500, 1200, 0, 640, 480)
# create first camera. Looking along X-axis, 1 meter above ground plane (x-y)
camera1 = PinholeCameraCal3_S2(pose1, K1)
# create second camera 1 meter to the right of first camera
K2 = Cal3_S2(1600, 1300, 0, 650, 440)
camera2 = PinholeCameraCal3_S2(pose2, K2)
# 1. Project two landmarks into two cameras and triangulate
z1 = camera1.project(self.landmark)
z2 = camera2.project(self.landmark)
cameras = CameraSetCal3_S2()
cameras.append(camera1)
cameras.append(camera2)
measurements = gtsam.Point2Vector()
measurements.append(z1)
measurements.append(z2)
landmarkDistanceThreshold = 10 # landmark is closer than that
# all default except landmarkDistanceThreshold:
params = TriangulationParameters(1.0, False, landmarkDistanceThreshold)
actual: TriangulationResult = gtsam.triangulateSafe(
cameras, measurements, params)
self.gtsamAssertEquals(actual.get(), self.landmark, 1e-2)
self.assertTrue(actual.valid())
landmarkDistanceThreshold = 4 # landmark is farther than that
params2 = TriangulationParameters(1.0, False,
landmarkDistanceThreshold)
actual = gtsam.triangulateSafe(cameras, measurements, params2)
self.assertTrue(actual.farPoint())
# 3. Add a slightly rotated third camera above with a wrong measurement
# (OUTLIER)
pose3 = pose1 * Pose3(Rot3.Ypr(0.1, 0.2, 0.1), Point3(0.1, -2, -.1))
K3 = Cal3_S2(700, 500, 0, 640, 480)
camera3 = PinholeCameraCal3_S2(pose3, K3)
z3 = camera3.project(self.landmark)
cameras.append(camera3)
measurements.append(z3 + Point2(10, -10))
landmarkDistanceThreshold = 10 # landmark is closer than that
outlierThreshold = 100 # loose, the outlier is going to pass
params3 = TriangulationParameters(1.0, False,
landmarkDistanceThreshold,
outlierThreshold)
actual = gtsam.triangulateSafe(cameras, measurements, params3)
self.assertTrue(actual.valid())
# now set stricter threshold for outlier rejection
outlierThreshold = 5 # tighter, the outlier is not going to pass
params4 = TriangulationParameters(1.0, False,
landmarkDistanceThreshold,
outlierThreshold)
actual = gtsam.triangulateSafe(cameras, measurements, params4)
self.assertTrue(actual.outlier())
if __name__ == "__main__":
unittest.main()