def setUpClass(cls):
"""
Equidistant fisheye projection
An equidistant fisheye projection with focal length f is defined
as the relation r/f = tan(theta), with r being the radius in the
image plane and theta the incident angle of the object point.
"""
x, y, z = 1.0, 0.0, 1.0
u, v = np.arctan2(x, z), 0.0
cls.obj_point = np.array([x, y, z])
cls.img_point = np.array([u, v])
p1 = [-1.0, 0.0, -1.0]
p2 = [1.0, 0.0, -1.0]
q1 = gtsam.Rot3(1.0, 0.0, 0.0, 0.0)
q2 = gtsam.Rot3(1.0, 0.0, 0.0, 0.0)
pose1 = gtsam.Pose3(q1, p1)
pose2 = gtsam.Pose3(q2, p2)
camera1 = gtsam.PinholeCameraCal3Fisheye(pose1)
camera2 = gtsam.PinholeCameraCal3Fisheye(pose2)
cls.origin = np.array([0.0, 0.0, 0.0])
cls.poses = gtsam.Pose3Vector([pose1, pose2])
cls.cameras = gtsam.CameraSetCal3Fisheye([camera1, camera2])
cls.measurements = gtsam.Point2Vector(
[k.project(cls.origin) for k in cls.cameras])
def setUpClass(cls):
"""
Stereographic fisheye projection
An equidistant fisheye projection with focal length f is defined
as the relation r/f = 2*tan(theta/2), with r being the radius in the
image plane and theta the incident angle of the object point.
"""
x, y, z = 1.0, 0.0, 1.0
r = np.linalg.norm([x, y, z])
u, v = 2*x/(z+r), 0.0
cls.obj_point = np.array([x, y, z])
cls.img_point = np.array([u, v])
fx, fy, s, u0, v0 = 2, 2, 0, 0, 0
k1, k2, p1, p2 = 0, 0, 0, 0
xi = 1
cls.stereographic = gtsam.Cal3Unified(fx, fy, s, u0, v0, k1, k2, p1, p2, xi)
p1 = [-1.0, 0.0, -1.0]
p2 = [ 1.0, 0.0, -1.0]
q1 = gtsam.Rot3(1.0, 0.0, 0.0, 0.0)
q2 = gtsam.Rot3(1.0, 0.0, 0.0, 0.0)
pose1 = gtsam.Pose3(q1, p1)
pose2 = gtsam.Pose3(q2, p2)
camera1 = gtsam.PinholeCameraCal3Unified(pose1, cls.stereographic)
camera2 = gtsam.PinholeCameraCal3Unified(pose2, cls.stereographic)
cls.origin = np.array([0.0, 0.0, 0.0])
cls.poses = gtsam.Pose3Vector([pose1, pose2])
cls.cameras = gtsam.CameraSetCal3Unified([camera1, camera2])
cls.measurements = gtsam.Point2Vector([k.project(cls.origin) for k in cls.cameras])
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 = 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))