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#!/usr/bin/env python
""" """
__author__ = "Théo de la Hogue"
__credits__ = []
__copyright__ = "Copyright 2023, Ecole Nationale de l'Aviation Civile (ENAC)"
__license__ = "BSD"
from typing import TypeVar, Tuple
from dataclasses import dataclass, field
import json
import math
import itertools
import re
from argaze.ArUcoMarkers import ArUcoMarkersDictionary, ArUcoMarker, ArUcoOpticCalibrator
import numpy
import cv2 as cv
import cv2.aruco as aruco
T0 = numpy.array([0., 0., 0.])
"""Define no translation vector."""
R0 = numpy.array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]])
"""Define no rotation matrix."""
ArUcoMarkersGroupType = TypeVar('ArUcoMarkersGroup', bound="ArUcoMarkersGroup")
# Type definition for type annotation convenience
def make_rotation_matrix(x, y, z):
# Create rotation matrix around x axis
c = numpy.cos(numpy.deg2rad(x))
s = numpy.sin(numpy.deg2rad(x))
Rx = numpy.array([[1, 0, 0], [0, c, -s], [0, s, c]])
# Create rotation matrix around y axis
c = numpy.cos(numpy.deg2rad(y))
s = numpy.sin(numpy.deg2rad(y))
Ry = numpy.array([[c, 0, s], [0, 1, 0], [-s, 0, c]])
# Create rotation matrix around z axis
c = numpy.cos(numpy.deg2rad(z))
s = numpy.sin(numpy.deg2rad(z))
Rz = numpy.array([[c, -s, 0], [s, c, 0], [0, 0, 1]])
# Return intrinsic rotation matrix
return Rx.dot(Ry.dot(Rz))
def is_rotation_matrix(R):
Rt = numpy.transpose(R)
shouldBeIdentity = numpy.dot(Rt, R)
I = numpy.identity(3, dtype = R.dtype)
n = numpy.linalg.norm(I - shouldBeIdentity)
return n < 1e-3
def make_euler_rotation_vector(R):
assert(is_rotation_matrix(R))
sy = math.sqrt(R[0,0] * R[0,0] + R[1,0] * R[1,0])
singular = sy < 1e-6
if not singular :
x = math.atan2(R[2,1] , R[2,2])
y = math.atan2(-R[2,0], sy)
z = math.atan2(R[1,0], R[0,0])
else :
x = math.atan2(-R[1,2], R[1,1])
y = math.atan2(-R[2,0], sy)
z = 0
return numpy.array([numpy.rad2deg(x), numpy.rad2deg(y), numpy.rad2deg(z)])
@dataclass(frozen=True)
class Place():
"""Define a place as a pose and a marker.
Parameters:
translation: position in group referential.
rotation: rotation in group referential.
marker: ArUco marker linked to the place.
"""
translation: numpy.array
rotation: numpy.array
marker: dict
@dataclass
class ArUcoMarkersGroup():
"""Handle group of ArUco markers as one unique spatial entity and estimate its pose.
Parameters:
marker_size: expected size of all markers in the group.
dictionary: expected dictionary of all markers in the group.
places: expected markers place.
"""
marker_size: float = field(default=0.)
dictionary: ArUcoMarkersDictionary.ArUcoMarkersDictionary = field(default_factory=ArUcoMarkersDictionary.ArUcoMarkersDictionary)
places: dict = field(default_factory=dict)
def __post_init__(self):
"""Init group pose and places pose."""
# Init pose data
self._translation = numpy.zeros(3)
self._rotation = numpy.zeros(3)
# Normalize places data
new_places = {}
for identifier, data in self.places.items():
# Convert string identifier to int value
if type(identifier) == str:
identifier = int(identifier)
# Get translation vector
tvec = numpy.array(data.pop('translation')).astype(numpy.float32)
# Check rotation value shape
rvalue = numpy.array(data.pop('rotation')).astype(numpy.float32)
# Rotation matrix
if rvalue.shape == (3, 3):
rmat = rvalue
# Rotation vector (expected in degree)
elif rvalue.shape == (3,):
rmat = make_rotation_matrix(rvalue[0], rvalue[1], rvalue[2]).astype(numpy.float32)
else:
raise ValueError(f'Bad rotation value: {rvalue}')
assert(is_rotation_matrix(rmat))
new_marker = ArUcoMarker.ArUcoMarker(self.dictionary, identifier, self.marker_size)
new_places[identifier] = Place(tvec, rmat, new_marker)
# else places are configured using detected markers
elif isinstance(data, ArUcoMarker.ArUcoMarker):
new_places[identifier] = Place(data.translation, data.rotation, data)
# else places are already at expected format
elif (type(identifier) == int) and isinstance(data, Place):
new_places[identifier] = data
self.places = new_places
# Init place consistency
self.init_places_consistency()
@classmethod
def from_obj(self, obj_filepath: str) -> ArUcoMarkersGroupType:
"""Load ArUco markers group from .obj file.
!!! note
Expected object (o) name format: <DICTIONARY>#<IDENTIFIER>_Marker
!!! note
All markers have to belong to the same dictionary.
!!! note
Marker normal vectors (vn) expected.
"""
new_marker_size = 0
new_dictionary = None
new_places = {}
# Regex rules for .obj file parsing
OBJ_RX_DICT = {
'object': re.compile(r'o (.*)#([0-9]+)_(.*)\n'),
'vertice': re.compile(r'v ([+-]?[0-9]*[.]?[0-9]+) ([+-]?[0-9]*[.]?[0-9]+) ([+-]?[0-9]*[.]?[0-9]+)\n'),
'normal': re.compile(r'vn ([+-]?[0-9]*[.]?[0-9]+) ([+-]?[0-9]*[.]?[0-9]+) ([+-]?[0-9]*[.]?[0-9]+)\n'),
'face': re.compile(r'f ([0-9]+)//([0-9]+) ([0-9]+)//([0-9]+) ([0-9]+)//([0-9]+) ([0-9]+)//([0-9]+)\n'),
'comment': re.compile(r'#(.*)\n') # keep comment regex after object regex because the # is used in object string too
}
# Regex .obj line parser
def __parse_obj_line(line):
for key, rx in OBJ_RX_DICT.items():
match = rx.search(line)
if match:
return key, match
# If there are no matches
return None, None
# Start parsing
try:
identifier = None
vertices = []
normals = {}
faces = {}
# Open the file and read through it line by line
with open(obj_filepath, 'r') as file:
line = file.readline()
while line:
# At each line check for a match with a regex
key, match = __parse_obj_line(line)
# Extract comment
if key == 'comment':
pass
# Extract marker dictionary and identifier
elif key == 'object':
dictionary = str(match.group(1))
identifier = int(match.group(2))
last = str(match.group(3))
# Init new group dictionary with first dictionary name
if new_dictionary == None:
new_dictionary = ArUcoMarkersDictionary.ArUcoMarkersDictionary(dictionary)
# Check all others marker dictionary are equal to new group dictionary
elif dictionary != new_dictionary.name:
raise NameError(f'Marker {identifier} dictionary is not {new_dictionary.name}')
# Fill vertices array
elif key == 'vertice':
vertices.append(tuple([float(match.group(1)), float(match.group(2)), float(match.group(3))]))
# Extract normal to calculate rotation matrix
elif key == 'normal':
normals[identifier] = tuple([float(match.group(1)), float(match.group(2)), float(match.group(3))])
# Extract vertice ids
elif key == 'face':
faces[identifier] = [int(match.group(1)), int(match.group(3)), int(match.group(5)), int(match.group(7))]
# Go to next line
line = file.readline()
file.close()
# Retreive marker vertices thanks to face vertice ids
for identifier, face in faces.items():
# Gather place corners from counter clockwise ordered face vertices
corners = numpy.array([ vertices[i-1] for i in face ])
# Edit translation (Tp) allowing to move world axis (W) at place axis (P)
Tp = corners.mean(axis=0)
# Edit place axis from corners positions
place_x_axis = corners[1:3].mean(axis=0) - Tp
place_x_axis_norm = numpy.linalg.norm(place_x_axis)
place_x_axis = place_x_axis / place_x_axis_norm
place_y_axis = corners[2:4].mean(axis=0) - Tp
place_y_axis_norm = numpy.linalg.norm(place_y_axis)
place_y_axis = place_y_axis / place_y_axis_norm
place_z_axis = normals[identifier]
# Edit rotation (Rp) allowing to transform world axis (W) into place axis (P)
W = numpy.array([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]])
P = numpy.array([place_x_axis, place_y_axis, place_z_axis])
Rp = W.dot(P.T)
# Check axis size: they should be almost equal
if math.isclose(place_x_axis_norm, place_y_axis_norm, rel_tol=1e-3):
current_marker_size = place_x_axis_norm*2
# Check that all markers size are almost equal
if new_marker_size > 0:
if not math.isclose(current_marker_size, new_marker_size, rel_tol=1e-3):
raise ValueError('Markers size should be almost equal.')
new_marker_size = current_marker_size
# Create a new place related to a new marker
new_marker = ArUcoMarker.ArUcoMarker(new_dictionary, identifier, new_marker_size)
new_places[identifier] = Place(Tp, Rp, new_marker)
except IOError:
raise IOError(f'File not found: {obj_filepath}')
return ArUcoMarkersGroup(new_marker_size, new_dictionary, new_places)
@classmethod
def from_json(self, json_filepath: str) -> ArUcoMarkersGroupType:
"""Load ArUco markers group from .json file."""
new_marker_size = 0
new_dictionary = None
new_places = {}
with open(json_filepath) as configuration_file:
data = json.load(configuration_file)
new_marker_size = data.pop('marker_size')
new_dictionary = data.pop('dictionary')
new_places = data.pop('places')
return ArUcoMarkersGroup(new_marker_size, new_dictionary, new_places)
def __str__(self) -> str:
"""String display"""
output = f'\n\tDictionary: {self.dictionary}'
output += f'\n\tMarker size: {self.marker_size} cm'
output += '\n\n\tPlaces:'
for identifier, place in self.places.items():
output += f'\n\t\t- {identifier}:'
output += f'\n{place.translation}'
output += f'\n{place.rotation}'
output += '\n\n\tAngle cache:'
for A_identifier, A_angle_cache in self.__rotation_cache.items():
for B_identifier, angle in A_angle_cache.items():
output += f'\n\t\t- {A_identifier}/{B_identifier}: [{angle[0]:3f} {angle[1]:3f} {angle[2]:3f}]'
output += '\n\n\tDistance cache:'
for A_identifier, A_distance_cache in self.__translation_cache.items():
for B_identifier, distance in A_distance_cache.items():
output += f'\n\t\t- {A_identifier}/{B_identifier}: {distance:3f}'
return output
@property
def identifiers(self) -> list:
"""List place marker identifiers belonging to the group."""
return list(self.places.keys())
def filter_markers(self, detected_markers: dict) -> Tuple[dict, dict]:
"""Sort markers belonging to the group from given detected markers dict (cf ArUcoDetector.detect_markers()).
Returns:
dict of markers belonging to this group
dict of remaining markers not belonging to this group
"""
group_markers = {}
remaining_markers = {}
for (marker_id, marker) in detected_markers.items():
if marker_id in self.places.keys():
group_markers[marker_id] = marker
else:
remaining_markers[marker_id] = marker
return group_markers, remaining_markers
def init_places_consistency(self):
"""Initialize places consistency to speed up further markers consistency checking."""
# Process expected rotation between places combinations to speed up further calculations
self.__rotation_cache = {}
for (A_identifier, A_place), (B_identifier, B_place) in itertools.combinations(self.places.items(), 2):
A = self.places[A_identifier].rotation
B = self.places[B_identifier].rotation
if numpy.array_equal(A, B):
AB_rvec = [0., 0., 0.]
BA_rvec = [0., 0., 0.]
else:
# Calculate euler angle representation of AB and BA rotation matrix
AB_rvec = make_euler_rotation_vector(B.dot(A.T))
BA_rvec = make_euler_rotation_vector(A.dot(B.T))
try:
self.__rotation_cache[A_identifier][B_identifier] = AB_rvec
except:
self.__rotation_cache[A_identifier] = {B_identifier: AB_rvec}
try:
self.__rotation_cache[B_identifier][A_identifier] = BA_rvec
except:
self.__rotation_cache[B_identifier] = {A_identifier: BA_rvec}
# Process translation between each places combinations to speed up further calculations
self.__translation_cache = {}
for (A_identifier, A_place), (B_identifier, B_place) in itertools.combinations(self.places.items(), 2):
A = self.places[A_identifier].translation
B = self.places[B_identifier].translation
# Calculate translation between A and B position
AB_tvec = numpy.linalg.norm(B - A)
try:
self.__translation_cache[A_identifier][B_identifier] = AB_tvec
except:
self.__translation_cache[A_identifier] = {B_identifier: AB_tvec}
try:
self.__translation_cache[B_identifier][A_identifier] = AB_tvec
except:
self.__translation_cache[B_identifier] = {A_identifier: AB_tvec}
def check_markers_consistency(self, group_markers: dict, angle_tolerance: float, distance_tolerance: float) -> Tuple[dict, dict, dict]:
"""Evaluate if given markers configuration match related places configuration.
Returns:
dict of consistent markers
dict of unconsistent markers
dict of identified distance or angle unconsistencies and out-of-bounds values
"""
consistent_markers = {}
unconsistencies = {'rotation': {}, 'translation': {}}
for (A_identifier, A_marker), (B_identifier, B_marker) in itertools.combinations(group_markers.items(), 2):
try:
# Rotation matrix from A marker to B marker
AB = B_marker.rotation.dot(A_marker.rotation.T)
# Calculate euler angle representation of AB rotation matrix
AB_rvec = make_euler_rotation_vector(AB)
expected_rvec= self.__rotation_cache[A_identifier][B_identifier]
# Calculate distance between A marker center and B marker center
AB_tvec = numpy.linalg.norm(A_marker.translation - B_marker.translation)
expected_tvec = self.__translation_cache[A_identifier][B_identifier]
# Check angle and distance according given tolerance then normalise marker pose
consistent_rotation = numpy.allclose(AB_rvec, expected_rvec, atol=angle_tolerance)
consistent_translation = math.isclose(AB_tvec, expected_tvec, abs_tol=distance_tolerance)
if consistent_rotation and consistent_translation:
if A_identifier not in consistent_markers.keys():
# Remember this marker is already validated
consistent_markers[A_identifier] = A_marker
if B_identifier not in consistent_markers.keys():
# Remember this marker is already validated
consistent_markers[B_identifier] = B_marker
else:
if not consistent_rotation:
unconsistencies['rotation'][f'{A_identifier}/{B_identifier}'] = {'current': AB_rvec, 'expected': expected_rvec}
if not consistent_translation:
unconsistencies['translation'][f'{A_identifier}/{B_identifier}'] = {'current': AB_tvec, 'expected': expected_tvec}
except KeyError:
raise ValueError(f'Marker {A_identifier} or {B_identifier} don\'t belong to the group.')
# Gather unconsistent markers
unconsistent_markers = {}
for identifier, marker in group_markers.items():
if identifier not in consistent_markers.keys():
unconsistent_markers[identifier] = marker
return consistent_markers, unconsistent_markers, unconsistencies
def estimate_pose_from_single_marker(self, marker: ArUcoMarker.ArUcoMarker) -> Tuple[numpy.array, numpy.array]:
"""Calculate rotation and translation that move a marker to its place."""
# Get the place related to the given marker
try:
place = self.places[marker.identifier]
# Rotation matrix that transform marker to related place
self._rotation = marker.rotation.dot(place.rotation.T)
# Translation vector that transform marker to related place
self._translation = marker.translation - place.translation.dot(place.rotation).dot(marker.rotation.T)
return self._translation, self._rotation
except KeyError:
raise ValueError(f'Marker {marker.identifier} doesn\'t belong to the group.')
def estimate_pose_from_markers(self, markers: dict) -> Tuple[numpy.array, numpy.array]:
"""Calculate average rotation and translation that move markers to their related places."""
rotations = []
translations = []
for identifier, marker in markers.items():
try:
place = self.places[identifier]
# Rotation matrix that transform marker to related place
R = marker.rotation.dot(place.rotation.T)
# Translation vector that transform marker to related place
T = marker.translation - place.translation.dot(place.rotation).dot(marker.rotation.T)
rotations.append(R)
translations.append(T)
except KeyError:
raise ValueError(f'Marker {marker.identifier} doesn\'t belong to the group.')
# Consider ArUcoMarkersGroup rotation as the mean of all marker rotations
# !!! WARNING !!! This is a bad hack : processing rotations average is a very complex problem that needs to well define the distance calculation method before.
self._rotation = numpy.mean(numpy.array(rotations), axis=0)
# Consider ArUcoMarkersGroup translation as the mean of all marker translations
self._translation = numpy.mean(numpy.array(translations), axis=0)
return self._translation, self._rotation
def estimate_pose_from_axis_markers(self, origin_marker: ArUcoMarker.ArUcoMarker, horizontal_axis_marker: ArUcoMarker.ArUcoMarker, vertical_axis_marker: ArUcoMarker.ArUcoMarker) -> Tuple[numpy.array, numpy.array]:
"""Calculate rotation and translation from 3 markers defining an orthogonal axis."""
O_marker = origin_marker
A_marker = horizontal_axis_marker
B_marker = vertical_axis_marker
O_place = self.places[O_marker.identifier]
A_place = self.places[A_marker.identifier]
B_place = self.places[B_marker.identifier]
# Place axis
OA = A_place.translation - O_place.translation
OA = OA / numpy.linalg.norm(OA)
OB = B_place.translation - O_place.translation
OB = OB / numpy.linalg.norm(OB)
# Detect and correct bad place axis orientation
X_sign = numpy.sign(OA)[0]
Y_sign = numpy.sign(OB)[1]
P = numpy.array([OA*X_sign, OB*Y_sign, numpy.cross(OA*X_sign, OB*Y_sign)])
# Marker axis
OA = A_marker.translation - O_marker.translation
OA = OA / numpy.linalg.norm(OA)
OB = B_marker.translation - O_marker.translation
OB = OB / numpy.linalg.norm(OB)
# Detect and correct bad place axis orientation
X_sign = numpy.sign(OA)[0]
Y_sign = -numpy.sign(OB)[1]
M = numpy.array([OA*X_sign, OB*Y_sign, numpy.cross(OA*X_sign, OB*Y_sign)])
# Then estimate ArUcoMarkersGroup rotation
self._rotation = P.dot(M.T)
# Consider ArUcoMarkersGroup translation as the translation of the marker at axis origin
self._translation = O_marker.translation - O_place.translation.dot(O_place.rotation).dot(M.T)
return self._translation, self._rotation
@property
def translation(self) -> numpy.array:
"""Access to group translation vector."""
return self._translation
@translation.setter
def translation(self, tvec):
self._translation = tvec
@property
def rotation(self) -> numpy.array:
"""Access to group rotation matrix."""
return self._translation
@rotation.setter
def rotation(self, rmat):
self._rotation = rmat
def draw_axes(self, image: numpy.array, K, D, thickness: int = 0, length: float = 0):
"""Draw group axes."""
try:
axisPoints = numpy.float32([[length, 0, 0], [0, length, 0], [0, 0, length], [0, 0, 0]]).reshape(-1, 3)
axisPoints, _ = cv.projectPoints(axisPoints, self._rotation, self._translation, numpy.array(K), numpy.array(D))
axisPoints = axisPoints.astype(int)
cv.line(image, tuple(axisPoints[3].ravel()), tuple(axisPoints[0].ravel()), (0, 0, 255), thickness) # X (red)
cv.line(image, tuple(axisPoints[3].ravel()), tuple(axisPoints[1].ravel()), (0, 255, 0), thickness) # Y (green)
cv.line(image, tuple(axisPoints[3].ravel()), tuple(axisPoints[2].ravel()), (255, 0, 0), thickness) # Z (blue)
# Ignore errors due to out of field axis: their coordinate are larger than int32 limitations.
except cv.error:
pass
def draw_places(self, image: numpy.array, K, D, color: tuple = None, border_size: int = 0):
"""Draw group places."""
l = self.marker_size / 2
for identifier, place in self.places.items():
try:
T = self.places[identifier].translation
R = self.places[identifier].rotation
placePoints = (T + numpy.float32([R.dot([-l, -l, 0]), R.dot([l, -l, 0]), R.dot([l, l, 0]), R.dot([-l, l, 0])])).reshape(-1, 3)
placePoints, _ = cv.projectPoints(placePoints, self._rotation, self._translation, numpy.array(K), numpy.array(D))
placePoints = placePoints.astype(int)
cv.line(image, tuple(placePoints[0].ravel()), tuple(placePoints[1].ravel()), color, border_size)
cv.line(image, tuple(placePoints[1].ravel()), tuple(placePoints[2].ravel()), color, border_size)
cv.line(image, tuple(placePoints[2].ravel()), tuple(placePoints[3].ravel()), color, border_size)
cv.line(image, tuple(placePoints[3].ravel()), tuple(placePoints[0].ravel()), color, border_size)
# Ignore errors due to out of field places: their coordinate are larger than int32 limitations.
except cv.error:
pass
def draw_places_axes(self, image: numpy.array, K, D, thickness: int = 0, length: float = 0):
"""Draw group place axes."""
for identifier, place in self.places.items():
try:
T = self.places[identifier].translation
R = self.places[identifier].rotation
axisPoints = (T + numpy.float32([R.dot([length, 0, 0]), R.dot([0, length, 0]), R.dot([0, 0, length]), R.dot([0, 0, 0])])).reshape(-1, 3)
axisPoints, _ = cv.projectPoints(axisPoints, self._rotation, self._translation, numpy.array(K), numpy.array(D))
axisPoints = axisPoints.astype(int)
cv.line(image, tuple(axisPoints[3].ravel()), tuple(axisPoints[0].ravel()), (0, 0, 255), thickness) # X (red)
cv.line(image, tuple(axisPoints[3].ravel()), tuple(axisPoints[1].ravel()), (0, 255, 0), thickness) # Y (green)
cv.line(image, tuple(axisPoints[3].ravel()), tuple(axisPoints[2].ravel()), (255, 0, 0), thickness) # Z (blue)
# Ignore errors due to out of field places: their coordinate are larger than int32 limitations.
except cv.error:
pass
def draw(self, image: numpy.array, K, D, draw_axes: dict = None, draw_places: dict = None, draw_places_axes: dict = None):
"""Draw group axes and places.
Parameters:
draw_axes: draw_axes parameters (if None, no axes drawn)
draw_places: draw_places parameters (if None, no places drawn)
draw_places_axes: draw_places_axes parameters (if None, no places axes drawn)
"""
# Draw axes if required
if draw_axes is not None:
self.draw_axes(image, K, D, **draw_axes)
# Draw places if required
if draw_places is not None:
self.draw_places(image, K, D, **draw_places)
# Draw places axes if required
if draw_places_axes is not None:
self.draw_places_axes(image, K, D, **draw_places_axes)
def to_obj(self, obj_filepath):
"""Save group to .obj file."""
with open(obj_filepath, 'w', encoding='utf-8') as file:
file.write('# ArGaze OBJ File\n')
file.write('# http://achil.recherche.enac.fr/features/eye/argaze/\n')
v_count = 0
for identifier, place in self.places.items():
file.write(f'o {self.dictionary.name}#{identifier}_Marker\n')
vertices = ''
T = place.translation
R = place.rotation
points = (T + numpy.float32([R.dot(place.marker.points[0]), R.dot(place.marker.points[1]), R.dot(place.marker.points[2]), R.dot(place.marker.points[3])])).reshape(-1, 3)
print(points)
# Write vertices in reverse order
for i in [3, 2, 1, 0]:
file.write(f'v {" ".join(map(str, points[i]))}\n')
v_count += 1
vertices += f' {v_count}'
file.write('s off\n')
file.write(f'f{vertices}\n')
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