179 lines
7.3 KiB
Python
179 lines
7.3 KiB
Python
"""
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GTSAM Copyright 2010-2019, Georgia Tech Research Corporation,
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Atlanta, Georgia 30332-0415
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All Rights Reserved
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See LICENSE for the license information
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Cal3Unified unit tests.
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Author: Frank Dellaert & Duy Nguyen Ta (Python)
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"""
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import unittest
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import numpy as np
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import gtsam
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from gtsam.utils.test_case import GtsamTestCase
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from gtsam.symbol_shorthand import K, L, P
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class TestCal3Unified(GtsamTestCase):
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@classmethod
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def setUpClass(cls):
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"""
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Stereographic fisheye projection
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An equidistant fisheye projection with focal length f is defined
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as the relation r/f = 2*tan(theta/2), with r being the radius in the
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image plane and theta the incident angle of the object point.
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"""
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x, y, z = 1.0, 0.0, 1.0
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r = np.linalg.norm([x, y, z])
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u, v = 2*x/(z+r), 0.0
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cls.obj_point = np.array([x, y, z])
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cls.img_point = np.array([u, v])
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fx, fy, s, u0, v0 = 2, 2, 0, 0, 0
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k1, k2, p1, p2 = 0, 0, 0, 0
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xi = 1
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cls.stereographic = gtsam.Cal3Unified(fx, fy, s, u0, v0, k1, k2, p1, p2, xi)
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p1 = [-1.0, 0.0, -1.0]
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p2 = [ 1.0, 0.0, -1.0]
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q1 = gtsam.Rot3(1.0, 0.0, 0.0, 0.0)
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q2 = gtsam.Rot3(1.0, 0.0, 0.0, 0.0)
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pose1 = gtsam.Pose3(q1, p1)
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pose2 = gtsam.Pose3(q2, p2)
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camera1 = gtsam.PinholeCameraCal3Unified(pose1, cls.stereographic)
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camera2 = gtsam.PinholeCameraCal3Unified(pose2, cls.stereographic)
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cls.origin = np.array([0.0, 0.0, 0.0])
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cls.poses = gtsam.Pose3Vector([pose1, pose2])
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cls.cameras = gtsam.CameraSetCal3Unified([camera1, camera2])
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cls.measurements = gtsam.Point2Vector([k.project(cls.origin) for k in cls.cameras])
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def test_Cal3Unified(self):
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K = gtsam.Cal3Unified()
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self.assertEqual(K.fx(), 1.)
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self.assertEqual(K.fx(), 1.)
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def test_distortion(self):
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"""Stereographic fisheye model of focal length f, defined as r/f = 2*tan(theta/2)"""
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x, y, z = self.obj_point
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r = np.linalg.norm([x, y, z])
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# Note: 2*tan(atan2(x, z)/2) = 2*x/(z+sqrt(x^2+z^2))
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self.assertAlmostEqual(2*np.tan(np.arctan2(x, z)/2), 2*x/(z+r))
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perspective_pt = self.obj_point[0:2]/self.obj_point[2]
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distorted_pt = self.stereographic.uncalibrate(perspective_pt)
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rectified_pt = self.stereographic.calibrate(distorted_pt)
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self.gtsamAssertEquals(distorted_pt, self.img_point)
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self.gtsamAssertEquals(rectified_pt, perspective_pt)
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def test_pinhole(self):
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"""Spatial stereographic camera projection"""
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x, y, z = self.obj_point
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u, v = self.img_point
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r = np.linalg.norm(self.obj_point)
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pose = gtsam.Pose3()
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camera = gtsam.PinholeCameraCal3Unified(pose, self.stereographic)
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pt1 = camera.Project(self.obj_point)
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self.gtsamAssertEquals(pt1, np.array([x/z, y/z]))
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pt2 = camera.project(self.obj_point)
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self.gtsamAssertEquals(pt2, self.img_point)
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obj1 = camera.backproject(self.img_point, z)
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self.gtsamAssertEquals(obj1, self.obj_point)
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r1 = camera.range(self.obj_point)
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self.assertEqual(r1, r)
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def test_generic_factor(self):
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"""Evaluate residual using pose and point as state variables"""
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graph = gtsam.NonlinearFactorGraph()
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state = gtsam.Values()
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measured = self.img_point
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noise_model = gtsam.noiseModel.Isotropic.Sigma(2, 1)
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pose_key, point_key = P(0), L(0)
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k = self.stereographic
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state.insert_pose3(pose_key, gtsam.Pose3())
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state.insert_point3(point_key, self.obj_point)
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factor = gtsam.GenericProjectionFactorCal3Unified(measured, noise_model, pose_key, point_key, k)
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graph.add(factor)
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score = graph.error(state)
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self.assertAlmostEqual(score, 0)
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def test_sfm_factor2(self):
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"""Evaluate residual with camera, pose and point as state variables"""
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r = np.linalg.norm(self.obj_point)
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graph = gtsam.NonlinearFactorGraph()
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state = gtsam.Values()
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measured = self.img_point
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noise_model = gtsam.noiseModel.Isotropic.Sigma(2, 1)
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camera_key, pose_key, landmark_key = K(0), P(0), L(0)
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k = self.stereographic
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state.insert_cal3unified(camera_key, k)
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state.insert_pose3(pose_key, gtsam.Pose3())
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state.insert_point3(landmark_key, self.obj_point)
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factor = gtsam.GeneralSFMFactor2Cal3Unified(measured, noise_model, pose_key, landmark_key, camera_key)
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graph.add(factor)
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score = graph.error(state)
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self.assertAlmostEqual(score, 0)
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def test_jacobian(self):
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"""Evaluate jacobian at optical axis"""
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obj_point_on_axis = np.array([0, 0, 1])
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img_point = np.array([0.0, 0.0])
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pose = gtsam.Pose3()
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camera = gtsam.Cal3Unified()
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state = gtsam.Values()
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camera_key, pose_key, landmark_key = K(0), P(0), L(0)
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state.insert_cal3unified(camera_key, camera)
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state.insert_point3(landmark_key, obj_point_on_axis)
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state.insert_pose3(pose_key, pose)
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g = gtsam.NonlinearFactorGraph()
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noise_model = gtsam.noiseModel.Unit.Create(2)
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factor = gtsam.GeneralSFMFactor2Cal3Unified(img_point, noise_model, pose_key, landmark_key, camera_key)
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g.add(factor)
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f = g.error(state)
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gaussian_factor_graph = g.linearize(state)
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H, z = gaussian_factor_graph.jacobian()
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self.assertAlmostEqual(f, 0)
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self.gtsamAssertEquals(z, np.zeros(2))
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self.gtsamAssertEquals(H @ H.T, 4*np.eye(2))
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Dcal = np.zeros((2, 10), order='F')
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Dp = np.zeros((2, 2), order='F')
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camera.calibrate(img_point, Dcal, Dp)
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self.gtsamAssertEquals(Dcal, np.array(
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[[ 0., 0., 0., -1., 0., 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., -1., 0., 0., 0., 0., 0.]]))
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self.gtsamAssertEquals(Dp, np.array(
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[[ 1., -0.],
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[-0., 1.]]))
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@unittest.skip("triangulatePoint3 currently seems to require perspective projections.")
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def test_triangulation(self):
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"""Estimate spatial point from image measurements"""
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triangulated = gtsam.triangulatePoint3(self.cameras, self.measurements, rank_tol=1e-9, optimize=True)
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self.gtsamAssertEquals(triangulated, self.origin)
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def test_triangulation_rectify(self):
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"""Estimate spatial point from image measurements using rectification"""
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rectified = gtsam.Point2Vector([k.calibration().calibrate(pt) for k, pt in zip(self.cameras, self.measurements)])
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shared_cal = gtsam.Cal3_S2()
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triangulated = gtsam.triangulatePoint3(self.poses, shared_cal, rectified, rank_tol=1e-9, optimize=False)
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self.gtsamAssertEquals(triangulated, self.origin)
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def test_retract(self):
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expected = gtsam.Cal3Unified(100 + 2, 105 + 3, 0.0 + 4, 320 + 5, 240 + 6,
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1e-3 + 7, 2.0*1e-3 + 8, 3.0*1e-3 + 9, 4.0*1e-3 + 10, 0.1 + 1)
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K = gtsam.Cal3Unified(100, 105, 0.0, 320, 240,
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1e-3, 2.0*1e-3, 3.0*1e-3, 4.0*1e-3, 0.1)
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d = np.array([2, 3, 4, 5, 6, 7, 8, 9, 10, 1], order='F')
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actual = K.retract(d)
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self.gtsamAssertEquals(actual, expected)
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np.testing.assert_allclose(d, K.localCoordinates(actual))
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if __name__ == "__main__":
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unittest.main()
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