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import pyopengv
import numpy as np
def normalized(x):
return x / np.linalg.norm(x)
def generateRandomPoint(maximumDepth, minimumDepth):
cleanPoint = np.random.uniform(-1.0, 1.0, 3)
direction = normalized(cleanPoint)
return (maximumDepth - minimumDepth) * cleanPoint + minimumDepth * direction
def generateRandomTranslation(maximumParallax):
return np.random.uniform(-maximumParallax, maximumParallax, 3)
def generateRandomRotation(maxAngle):
rpy = np.random.uniform(-maxAngle, maxAngle, 3)
R1 = np.array([[1.0, 0.0, 0.0],
[0.0, np.cos(rpy[0]), -np.sin(rpy[0])],
[0.0, np.sin(rpy[0]), np.cos(rpy[0])]])
R2 = np.array([[np.cos(rpy[1]), 0.0, np.sin(rpy[1])],
[0.0, 1.0, 0.0],
[-np.sin(rpy[1]), 0.0, np.cos(rpy[1])]])
R3 = np.array([[np.cos(rpy[2]), -np.sin(rpy[2]), 0.0],
[np.sin(rpy[2]), np.cos(rpy[2]), 0.0],
[0.0, 0.0, 1.0]])
return R3.dot(R2.dot(R1))
def addNoise(noiseLevel, cleanPoint):
noisyPoint = cleanPoint + np.random.uniform(-noiseLevel, noiseLevel, 3)
return normalized(noisyPoint)
def extractRelativePose(position1, position2, rotation1, rotation2):
relativeRotation = rotation1.T.dot(rotation2)
relativePosition = rotation1.T.dot(position2 - position1)
return relativePosition, relativeRotation
def essentialMatrix(position, rotation):
# E transforms vectors from vp 2 to 1: x_1^T * E * x_2 = 0
# and E = (t)_skew*R
t_skew = np.zeros((3, 3))
t_skew[0, 1] = -position[2]
t_skew[0, 2] = position[1]
t_skew[1, 0] = position[2]
t_skew[1, 2] = -position[0]
t_skew[2, 0] = -position[1]
t_skew[2, 1] = position[0]
E = t_skew.dot(rotation)
return normalized(E)
def getPerturbedPose(position, rotation, amplitude):
dp = generateRandomTranslation(amplitude)
dR = generateRandomRotation(amplitude)
return position + dp, rotation.dot(dR)
def proportional(x, y, tol=1e-2):
xn = normalized(x)
yn = normalized(y)
return (np.allclose(xn, yn, rtol=1e20, atol=tol) or
np.allclose(xn, -yn, rtol=1e20, atol=tol))
def matrix_in_list(a, l):
for b in l:
if proportional(a, b):
return True
return False
def same_transformation(position, rotation, transformation):
R = transformation[:, :3]
t = transformation[:, 3]
return proportional(position, t) and proportional(rotation, R)
class RelativePoseDataset:
def __init__(self, num_points, noise, outlier_fraction, rotation_only=False):
# generate a random pose for viewpoint 1
position1 = np.zeros(3)
rotation1 = np.eye(3)
# generate a random pose for viewpoint 2
if rotation_only:
position2 = np.zeros(3)
else:
position2 = generateRandomTranslation(2.0)
rotation2 = generateRandomRotation(0.5)
# derive correspondences based on random point-cloud
self.generateCorrespondences(
position1, rotation1, position2, rotation2,
num_points, noise, outlier_fraction)
# Extract the relative pose
self.position, self.rotation = extractRelativePose(
position1, position2, rotation1, rotation2)
if not rotation_only:
self.essential = essentialMatrix(self.position, self.rotation)
def generateCorrespondences(self,
position1, rotation1,
position2, rotation2,
num_points,
noise, outlier_fraction):
min_depth = 4
max_depth = 8
# initialize point-cloud
self.points = np.empty((num_points, 3))
for i in range(num_points):
self.points[i] = generateRandomPoint(max_depth, min_depth)
self.bearing_vectors1 = np.empty((num_points, 3))
self.bearing_vectors2 = np.empty((num_points, 3))
for i in range(num_points):
# get the point in viewpoint 1
body_point1 = rotation1.T.dot(self.points[i] - position1)
# get the point in viewpoint 2
body_point2 = rotation2.T.dot(self.points[i] - position2)
self.bearing_vectors1[i] = normalized(body_point1)
self.bearing_vectors2[i] = normalized(body_point2)
# add noise
if noise > 0.0:
self.bearing_vectors1[i] = addNoise(noise, self.bearing_vectors1[i])
self.bearing_vectors2[i] = addNoise(noise, self.bearing_vectors2[i])
# add outliers
num_outliers = int(outlier_fraction * num_points)
for i in range(num_outliers):
# create random point
p = generateRandomPoint(max_depth, min_depth)
# project this point into viewpoint 2
body_point = rotation2.T.dot(p - position2)
# normalize the bearing vector
self.bearing_vectors2[i] = normalized(body_point)
def test_relative_pose():
print("Testing relative pose")
d = RelativePoseDataset(10, 0.0, 0.0)
# running experiments
twopt_translation = pyopengv.relative_pose_twopt(
d.bearing_vectors1, d.bearing_vectors2, d.rotation)
fivept_nister_essentials = pyopengv.relative_pose_fivept_nister(
d.bearing_vectors1, d.bearing_vectors2)
fivept_kneip_rotations = pyopengv.relative_pose_fivept_kneip(
d.bearing_vectors1, d.bearing_vectors2)
sevenpt_essentials = pyopengv.relative_pose_sevenpt(d.bearing_vectors1, d.bearing_vectors2)
eightpt_essential = pyopengv.relative_pose_eightpt(d.bearing_vectors1, d.bearing_vectors2)
t_perturbed, R_perturbed = getPerturbedPose(d.position, d.rotation, 0.01)
eigensolver_rotation = pyopengv.relative_pose_eigensolver(
d.bearing_vectors1, d.bearing_vectors2, R_perturbed)
t_perturbed, R_perturbed = getPerturbedPose(d.position, d.rotation, 0.1)
nonlinear_transformation = pyopengv.relative_pose_optimize_nonlinear(
d.bearing_vectors1, d.bearing_vectors2, t_perturbed, R_perturbed)
assert proportional(d.position, twopt_translation)
assert matrix_in_list(d.essential, fivept_nister_essentials)
assert matrix_in_list(d.rotation, fivept_kneip_rotations)
assert matrix_in_list(d.essential, sevenpt_essentials)
assert proportional(d.essential, eightpt_essential)
assert proportional(d.rotation, eigensolver_rotation)
assert same_transformation(d.position, d.rotation, nonlinear_transformation)
print("Done testing relative pose")
def test_relative_pose_ransac():
print("Testing relative pose ransac")
d = RelativePoseDataset(100, 0.0, 0.3)
ransac_transformation = pyopengv.relative_pose_ransac(
d.bearing_vectors1, d.bearing_vectors2, "NISTER", 0.01, 1000)
assert same_transformation(d.position, d.rotation, ransac_transformation)
print("Done testing relative pose ransac")
def test_relative_pose_ransac_rotation_only():
print("Testing relative pose ransac rotation only")
d = RelativePoseDataset(100, 0.0, 0.3, rotation_only=True)
ransac_rotation = pyopengv.relative_pose_ransac_rotation_only(
d.bearing_vectors1, d.bearing_vectors2, 0.01, 1000)
assert proportional(d.rotation, ransac_rotation)
print("Done testing relative pose ransac rotation only")
def test_triangulation():
print("Testing triangulation")
d = RelativePoseDataset(10, 0.0, 0.0)
points1 = pyopengv.triangulation_triangulate(
d.bearing_vectors1, d.bearing_vectors2, d.position, d.rotation)
assert np.allclose(d.points, points1)
points2 = pyopengv.triangulation_triangulate2(
d.bearing_vectors1, d.bearing_vectors2, d.position, d.rotation)
assert np.allclose(d.points, points2)
print("Done testing triangulation")
if __name__ == "__main__":
test_relative_pose()
test_relative_pose_ransac()
test_relative_pose_ransac_rotation_only()
test_triangulation()
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