def screen_to_space(coords):
origin = screen_corners['upper left']
right_vector = fh.to_unit(screen_corners['upper right'] - origin)
down_vector = fh.to_unit(screen_corners['lower left'] - origin)
width = np.linalg.norm(screen_corners['upper right'] - origin)
height = np.linalg.norm(screen_corners['lower left'] - origin)
return (coords / np.array([1920, 1080]) *
np.array([width, height]) @ np.vstack(
(right_vector, down_vector))) + origin
def markers_to_ortho(*markers):
if len(markers) == 1:
marker1 = markers[0][..., 0:3]
marker2 = markers[0][..., 3:6]
marker3 = markers[0][..., 6:9]
elif len(markers) == 3:
marker1 = markers[0]
marker2 = markers[1]
marker3 = markers[2]
else:
raise Exception(
'Input must be either three marker arrays with 3 coordinates or one array with 9.'
)
side1 = freehead.to_unit(marker2 - marker1)
side2 = freehead.to_unit(marker3 - marker1)
normal1 = freehead.to_unit(np.cross(
side1, side2)) # should be unit length but let's be sure
normal2 = freehead.to_unit(np.cross(side1, normal1))
# these are all Nx3
v1 = side1
v2 = normal1
v3 = normal2
# single rotation matrix if there is only one rigidbody
if len(v1.shape) == 1:
V = np.empty((3, 3), np.float)
V[:, 0] = v1
V[:, 1] = v2
V[:, 2] = v3
return V
else:
length = v1.shape[0]
# add the orthonormal basis vectors to the array of rotation matrices as column vectors
V = np.empty((length, 3, 3), np.float)
# V[marker, row, column]
V[:, :, 0] = v1
V[:, :, 1] = v2
V[:, :, 2] = v3
return V
def normals_nonlinear_angular_transform(normals, *polynom_params):
if normals.ndim == 1:
normals = normals[None, :]
if len(polynom_params) == 1:
aa = polynom_params[0][0:2]
bb = polynom_params[0][2:4]
cc = polynom_params[0][4:6]
elif len(polynom_params) == 3:
aa = polynom_params[0]
bb = polynom_params[1]
cc = polynom_params[2]
else:
raise Exception('Polynomial parameters must either be three arrays (aa, bb, cc) or one array (aabbcc).')
# uses x right, y forward, z up assumption
elev_azim = np.arctan2(normals[:, [0, 2]], normals[:, 1, None])
elev_azim_transformed = aa * (elev_azim ** 2) + bb * elev_azim + cc
xz_transformed = np.tan(elev_azim_transformed)
xyz = np.ones(normals.shape, dtype=np.float64)
xyz[:, [0, 2]] = xz_transformed
xyz_normalized = fh.to_unit(xyz).squeeze()
return xyz_normalized
def is_eye_within_led_threshold(led, threshold):
eye_to_led = fh.to_unit(self.rig_leds[led, :] - T_eye_world)
gaze_normals_world = R_head_world @ fh.normals_nonlinear_angular_transform(
self.R_eye_head @ gaze_normals, self.nonlinear_parameters)
eye_to_led_azim_elev = np.rad2deg(
np.abs(
fh.to_azim_elev(gaze_normals_world) -
fh.to_azim_elev(eye_to_led)))
# threshold is only horizontal right now because of increased vertical angle noise and spikes
is_within_threshold = eye_to_led_azim_elev[0] <= threshold
return is_within_threshold
def precalculate_data(self):
fh.array_apply(
self.df,
OrderedDict([
('target_led', lambda r: r['fixation_led'] + r['amplitude']),
('shifted_target_led', lambda r: r['target_led'] + r['shift']),
# optotrak data interpolated onto pupil labs timestamps
('o_data_interp',
lambda r: fh.interpolate_a_onto_b_time(r['o_data'][:, 3:15],
r['o_data'][:, 30],
r['p_data'][:, 2],
kind='linear')),
# gaze data
('gaze_normals', lambda r: r['p_data'][:, 3:6]),
# rotation of head rigidbody
('R_head_world',
lambda r: r['helmet'].solve(r['o_data_interp'].reshape(
(-1, 4, 3)))[0]),
# yaw pitch roll head rigidbody
('ypr_head_world',
lambda r: fh.to_yawpitchroll(r['R_head_world'])),
# reference positions of head rigidbody
('Ts_head_world',
lambda r: r['helmet'].solve(r['o_data_interp'].reshape(
(-1, 4, 3)))[1]),
# position of target led
('target_pos', lambda r: self.rig_leds[r['target_led'], :]),
# vector from eye to target position
('eye_to_target', lambda r: fh.to_unit(r['target_pos'] - r[
'Ts_head_world'][:, 5, :])),
# gaze vector in head without distortion correction
('gaze_head_distorted', lambda r:
(r['R_eye_head'] @ r['gaze_normals'].T).T),
# gaze vector in head with distortion correction
('gaze_head', lambda r: fh.normals_nonlinear_angular_transform(
r['gaze_head_distorted'], r['nonlinear_parameters'])),
# gaze vector in world
('gaze_world', lambda r: np.einsum('tij,tj->ti', r[
'R_head_world'], r['gaze_head'])),
# gaze angles in world
('gaze_ang_world',
lambda r: np.rad2deg(fh.to_azim_elev(r['gaze_world']))),
# angles from eye to target in world
('eye_ang_target',
lambda r: np.rad2deg(fh.to_azim_elev(r['eye_to_target']))),
# difference of eye to target angles and gaze in world
('d_ang_gaze_eye_target',
lambda r: r['gaze_ang_world'] - r['eye_ang_target']),
# time steps
]),
add_inplace=True)
def err_func(T_eye_head):
T_eye_world = np.einsum('tij,j->ti', R_head_world,
T_eye_head) + T_head_world
eye_to_target = fh.to_unit(T_target_world - T_eye_world)
gaze_normals_world = np.einsum(
'tij,tj->ti', R_head_world,
np.einsum('ij,tj->ti', R_eye_head, gaze_normals))
angles = np.rad2deg(
np.arccos(np.einsum('ti,ti->t', gaze_normals_world,
eye_to_target)))
return np.sum(angles)
def err_func_nonlinear_direct(ypr_aa_bb_cc):
ypr = ypr_aa_bb_cc[0:3]
aa = ypr_aa_bb_cc[None, 3:5]
bb = ypr_aa_bb_cc[None, 5:7]
cc = ypr_aa_bb_cc[None, 7:9]
R = fh.from_yawpitchroll(ypr)
gaze_rotated = (R @ gaze_normals.T).T
gaze_transformed = gaze_rotated.copy()
gaze_transformed[:,
[0, 2]] = aa * (gaze_transformed[:, [0, 2]]**
2) + bb * gaze_transformed[:, [0, 2]] + cc
gaze_transformed = fh.to_unit(gaze_transformed)
azim_elev_nonlinear = np.rad2deg(
np.arctan2(gaze_transformed[:, [0, 2]], gaze_transformed[:, 1, None]))
return ((angles_from_eye - azim_elev_nonlinear)**2).sum()
def err_func(parameters):
R_eye_head = fh.from_yawpitchroll(parameters[0:3])
T_eye_head = parameters[3:6]
T_eye_world = np.einsum('tij,j->ti', R_head_world,
T_eye_head) + T_head_world
eye_to_target = fh.to_unit(T_target_world - T_eye_world)
gaze_normals_world = np.einsum(
'tij,tj->ti', R_head_world,
np.einsum('ij,tj->ti', R_eye_head, gaze_normals))
angles = np.rad2deg(
np.arccos(np.einsum('ti,ti->t', gaze_normals_world,
eye_to_target)))
return np.mean(angles)
def err_func(params):
T_eye_head = ini_T_eye_head
R_eye_head = fh.from_yawpitchroll(params[0:3])
aa = params[3:5]
bb = params[5:7]
cc = params[7:9]
T_eye_world = np.einsum('tij,j->ti', R_head_world,
T_eye_head) + T_head_world
eye_to_target = fh.to_unit(T_target_world - T_eye_world)
gaze_normals_head = np.einsum('ij,tj->ti', R_eye_head,
gaze_normals)
gaze_normals_head_transformed = fh.normals_nonlinear_angular_transform(
gaze_normals_head, aa, bb, cc)
gaze_normals_world = np.einsum('tij,tj->ti', R_head_world,
gaze_normals_head_transformed)
angles = np.rad2deg(
np.arccos(
np.einsum('ti,ti->t', gaze_normals_world, eye_to_target)))
return angles.mean()
def normals_nonlinear_transform(normals, *polynom_params):
if normals.ndim == 1:
normals = normals[None, :]
if len(polynom_params) == 1:
aa = polynom_params[0][0:2]
bb = polynom_params[0][2:4]
cc = polynom_params[0][4:6]
elif len(polynom_params) == 3:
aa = polynom_params[0]
bb = polynom_params[1]
cc = polynom_params[2]
else:
raise Exception('Polynomial parameters must either be three arrays (aa, bb, cc) or one array (aabbcc).')
xyz = normals.copy()
xyz[:, [0, 2]] = aa * (xyz[:, [0, 2]] ** 2) + bb * xyz[:, [0, 2]] + cc
xyz_normalized = fh.to_unit(xyz).squeeze()
return xyz_normalized
def create_helmet(self):
head_measurement_points = [
'head straight', 'nasion', 'inion', 'right eye'
]
for i, measurement_point in enumerate(head_measurement_points):
print('Press space to measure: ' + measurement_point)
# light up an led to signal which measurement is going on
signal_led = 255
signal_length = 1
while True:
self.athread.write_uint8(
signal_led, 255, 255,
255) # bright light to start and see something
fh.wait_for_keypress(pygame.K_SPACE)
current_sample = self.othread.current_sample.copy()
helmet_leds = current_sample[HELMET].reshape((4, 3))
if np.any(np.isnan(helmet_leds)):
print('Helmet LEDs not all visible. Try again.')
self.athread.write_uint8(signal_led, 255, 0,
0) # red light for failure
time.sleep(signal_length)
continue
if i == I_BARY:
helmet = fh.Rigidbody(helmet_leds)
self.athread.write_uint8(signal_led, 0, 255,
0) # green light for success
time.sleep(signal_length)
break
else:
_, probe_tip = fh.FourMarkerProbe().solve(
current_sample[PROBE].reshape((4, 3)))
if np.any(np.isnan(probe_tip)):
print('Probe not visible. Try again.')
self.athread.write_uint8(signal_led, 255, 0,
0) # red light for failure
time.sleep(signal_length)
continue
helmet.add_reference_points(helmet_leds, probe_tip)
# replace eye measurement
if i == I_EYE:
nasion_to_inion = fh.to_unit(
helmet.ref_points[I_INION, :] -
helmet.ref_points[I_NASION, :])
# estimate eye at 15 mm inwards from probe in nasion inion direction
estimated_eye_position = helmet.ref_points[
I_EYE, :] + 15 * nasion_to_inion
# replace measured value with estimation
helmet.ref_points[I_EYE, :] = estimated_eye_position
self.athread.write_uint8(signal_led, 0, 255,
0) # green light for success
time.sleep(signal_length)
break
self.helmet = helmet
print('Helmet creation done.')
self.athread.write_uint8(255, 0, 0, 0) # turn off leds
print('NaN values in pupil data, repeat')
continue
break
R_head_world[i, :, :] = rotation
T_head_world[i, :] = ref_points[0, :]
gaze_normals[i, :] = gaze_normal
athread.write_uint8(255, 0, 0, 0)
#%%
calibration_result = fh.calibrate_pupil(
T_head_world,
R_head_world,
gaze_normals,
T_target_world,
ini_T_eye_head=(helmet.ref_points[5, :] - helmet.ref_points[0, :]) +
15 * fh.to_unit(helmet.ref_points[2, :] - helmet.ref_points[1, :]
), # add 15 mm of nasion to inion to measured eye position
bounds_mm=50)
R_eye_head = fh.from_yawpitchroll(calibration_result.x[0:3])
T_eye_head = calibration_result.x[3:6]
#%%
helmet.ref_points[5, :] = T_eye_head + helmet.ref_points[0, :]
# %%
settings = {
'trials_per_shift': 2,
'shift_magnitudes': np.arange(-5, 6) * 4,
'default_fixation_led_index': 50,
'default_target_led_index': 200,
break
start_time = time.monotonic()
duration = 60
last_i = None
while time.monotonic() - start_time < duration:
current_i = othread.i_current_sample
if current_i == last_i:
time.sleep(0)
continue
last_i = current_i
current_sample = othread.current_sample.copy()
rotation, ref_points = helmet.solve(extract_helmet(current_sample))
if np.any(np.isnan(rotation)):
continue
inion_to_nasion = fh.to_unit(ref_points[1, :] - ref_points[2, :]).squeeze()
nasion_to_leds = fh.to_unit(rig_led_positions - ref_points[1, :])
angles = np.rad2deg(
np.arccos(np.einsum('li,i->l', nasion_to_leds, inion_to_nasion)))
closest_led = int(np.argmin(angles))
if angles.min() > 5:
closest_led = 255
arduino.write(struct.pack('>B', closest_led))
othread.should_stop.set()
othread.join()
pygame.quit()
arduino.write(struct.pack('>B', 255))
arduino.close()
def apply_analysis_pipeline_for_all_trials(df: pd.DataFrame):
warnings.filterwarnings('ignore', category=np.RankWarning)
df.rename(columns={'shift_percent_approx': 'shift_percent'}, inplace=True)
fh.array_apply(
df,
OrderedDict([
# chosen so that to target direction is positive (right to left is positive angle in mathematics)
('direction_sign', lambda r: -1 if r['left_to_right'] else +1),
('fixation_led', lambda r: r['fixation_led'] if r['left_to_right'] else 254 - r['fixation_led']),
(('df', 'target_led'), lambda df: df['fixation_led'] - df['direction_sign'] * df['amplitude']),
(('df', 'starget_led'), lambda df: df['target_led'] - df['direction_sign'] * df['shift']),
('is_outward_response', lambda r: r['response'] == ('right' if r['left_to_right'] else 'left')),
('response_ward', lambda r: 'outward' if r['is_outward_response'] else 'inward'),
('correct_response', lambda r: None if r['shift'] == 0 else 'right' if (r['shift'] > 0) == r['left_to_right'] else 'left'),
('is_correct', lambda r: None if r['correct_response'] is None else r['correct_response'] == r['response']),
('shift_percent_uni', lambda r: r['shift_percent'] if r['left_to_right'] else -r['shift_percent']),
# new time index for upsampling
('t_sacc', lambda r: np.arange(-400, 801, 5)),
# pupil data in around saccade interval upsampled
('p_data_upsampled', lambda r: fh.interpolate_a_onto_b_time(r['p_data'][:, 2:5],
1000 * (r['p_data'][:, 0] - r['t_saccade_started']),
r['t_sacc'], kind='linear')),
# optotrak data upsampled
('o_data_upsampled', lambda r: fh.interpolate_a_onto_b_time(r['o_data'][:, 3:15],
1000 * (r['o_data'][:, 30] - r['t_saccade_started']),
r['t_sacc'], kind='linear')),
# latency of pupil signal
('pupil_latency', lambda r: fh.interpolate_a_onto_b_time(r['p_data'][:, 1] - r['p_data'][:, 0], 1000 * (
r['p_data'][:, 0] - r['t_saccade_started']), r['t_sacc'], kind='linear')),
# rotation of head rigidbody
('R_head_world', lambda r: r['helmet'].solve(r['o_data_upsampled'].reshape((-1, 4, 3)))[0]),
# yaw pitch roll head rigidbody
('ypr_head_world', lambda r: fh.to_yawpitchroll(r['R_head_world'])),
# reference positions of head rigidbody
('Ts_head_world', lambda r: r['helmet'].solve(r['o_data_upsampled'].reshape((-1, 4, 3)))[1]),
# position of fixation led
('fixation_pos', lambda r: r['rig'][r['fixation_led'], :]),
# position of target led
('target_pos', lambda r: r['rig'][r['target_led'], :]),
# position of shifted target led
('starget_pos', lambda r: r['rig'][r['starget_led'], :]),
# vector from eye to target position
('eye_to_fixation', lambda r: fh.to_unit(r['fixation_pos'] - r['Ts_head_world'][:, 3, :])),
# vector from eye to target position
('eye_to_target', lambda r: fh.to_unit(r['target_pos'] - r['Ts_head_world'][:, 3, :])),
# vector from eye to shifted target position
('eye_to_starget', lambda r: fh.to_unit(r['starget_pos'] - r['Ts_head_world'][:, 3, :])),
# gaze vector in head without distortion correction
('gaze_in_head_distorted', lambda r: (r['R_eye_head'] @ r['p_data_upsampled'].T).T),
# gaze vector in head with distortion correction
('gaze_in_head',
lambda r: fh.normals_nonlinear_angular_transform(r['gaze_in_head_distorted'], r['nonlinear_parameters'])),
# gaze angles in head
('gaze_in_head_ang', lambda r: np.rad2deg(fh.to_azim_elev(r['gaze_in_head']))),
# gaze vector in world
('gaze_in_world', lambda r: np.einsum('tij,tj->ti', r['R_head_world'], r['gaze_in_head'])),
# gaze angles in world
('gaze_in_world_ang', lambda r: np.rad2deg(fh.to_azim_elev(r['gaze_in_world']))),
# angles from eye to target in world
('eye_to_target_ang', lambda r: np.rad2deg(fh.to_azim_elev(r['eye_to_target']))),
# difference of eye to target angles and gaze in world
('gaze_angle_vs_target', lambda r: r['gaze_in_world_ang'] - r['eye_to_target_ang']),
# angles from eye to shifted target in world
('eye_to_starget_ang', lambda r: np.rad2deg(fh.to_azim_elev(r['eye_to_starget']))),
# difference of eye to shifted target angles and gaze in world
('gaze_angle_vs_starget', lambda r: r['gaze_in_world_ang'] - r['eye_to_starget_ang']),
# angles from eye to fixation in world
('eye_to_fixation_ang', lambda r: np.rad2deg(fh.to_azim_elev(r['eye_to_fixation']))),
# difference of eye to fixation angles and gaze in world
('gaze_angle_vs_fixation', lambda r: r['gaze_in_world_ang'] - r['eye_to_fixation_ang']),
# time steps
('dt', lambda r: fh.padded_diff(r['t_sacc'])),
# velocity of difference of eye to target angles and gaze in world
('gaze_angvel_vs_target', lambda r: fh.padded_diff(r['gaze_angle_vs_target']) / r['dt'][:, None]),
('gaze_angvel_vs_target_savgol',
lambda r: prepend_nan(
savgol_filter(r['gaze_angvel_vs_target'][1:, ...], 3, 1, axis=0),
axis=0)),
# saccade detection engbert & mergenthaler
('eng_merg', lambda r: fh.sacc_dec_engb_merg_horizontal(r['gaze_angle_vs_target'][:, 0],
r['gaze_angvel_vs_target_savgol'][:, 0], 6, 5)),
]),
add_inplace=True,
print_log=True
)
df.drop(
columns=[
'p_data',
'o_data',
# 'helmet',
'o_data_upsampled',
'p_data_upsampled',
'gaze_in_head_distorted',
],
inplace=True
)
dt_fixation = 0
continue
R_head_world, ref_points = helmet.solve(
extract_helmet(othread.current_sample.copy()))
if np.any(np.isnan(R_head_world)):
if phase != fix_phase:
athread.write_uint8(led_fixation, *should_fix_color)
phase = fix_phase
was_fixating_eye = False
t_started_fixating = False
dt_fixation = 0
continue
T_eye_world = ref_points[5, :]
if phase == fix_phase:
eye_to_fixpoint = fh.to_unit(rig_led_positions[led_fixation, :] -
T_eye_world)
gaze_normals_world = R_head_world @ R_eye_head @ gaze_normals
eye_to_fixpoint_angle = np.rad2deg(
np.arccos(eye_to_fixpoint @ gaze_normals_world))
is_fixating_eye = eye_to_fixpoint_angle <= fix_threshold_eye
if not is_fixating_eye and was_fixating_eye:
athread.write_uint8(led_fixation, *should_fix_color)
was_fixating_eye = False
if is_fixating_eye and not was_fixating_eye:
athread.write_uint8(led_fixation, *is_fix_color)
was_fixating_eye = True
t_started_fixating = time.monotonic()
if is_fixating_eye and was_fixating_eye:
if dt_fixation < fixation_duration:
def apply_analysis_pipeline_for_valid_trials(df: pd.DataFrame):
df.drop(
df[df.apply(lambda r: r['eng_merg'] is None, axis=1)].index,
inplace=True
)
def i_shift_done_rel(r):
difference = r['t_led_shift_done'] - r['t_saccade_started']
in_ms = 1000 * difference
distances_to_available_timestamps = in_ms - r['t_sacc']
i_closest_timestamp = np.argmin(np.abs(distances_to_available_timestamps))
return i_closest_timestamp
fh.array_apply(
df,
OrderedDict([
# index of fastest saccade
('i_max_amp_sacc', lambda r: np.argmax(np.abs(r['eng_merg'][3]))),
('max_sacc_amp', lambda r: r['eng_merg'][3][r['i_max_amp_sacc']]),
(('df', 'max_sacc_amp_uni'), lambda df: df['direction_sign'] * df['max_sacc_amp']),
('i_start_max_amp_sacc', lambda r: r['eng_merg'][0][r['i_max_amp_sacc']][0]),
('i_end_max_amp_sacc', lambda r: r['eng_merg'][0][r['i_max_amp_sacc']][1]),
('start_max_amp_sacc', lambda r: r['t_sacc'][r['i_start_max_amp_sacc']]),
('end_max_amp_sacc', lambda r: r['t_sacc'][r['i_end_max_amp_sacc']]),
# real amplitude dependent on eye position
('real_amplitude',
lambda r: r['eye_to_target_ang'][r['i_start_max_amp_sacc'] - 5, 0] # 5 samples before saccade onset
- r['eye_to_fixation_ang'][r['i_start_max_amp_sacc'] - 5, 0]),
(('df', 'real_amplitude_uni'), lambda df: df['real_amplitude'] * df['direction_sign']),
# detected saccade related timestamps
(('df', 't_det_sacc'), lambda df: df['t_sacc'] - df['start_max_amp_sacc']),
# relative led shift
('i_shift_done_rel', i_shift_done_rel),
# amplitude of saccade with highest peak velocity
('vpeak_max_amp_sacc', lambda r: r['eng_merg'][1][r['i_max_amp_sacc']]),
# duration of fastest saccade
(('df','dur_max_amp_sacc'), lambda df: df['end_max_amp_sacc'] - df['start_max_amp_sacc']),
# landing points of main saccades
('land_pos_sacc_hor', lambda r: r['gaze_angle_vs_target'][r['i_end_max_amp_sacc'], 0]),
('land_pos_sacc_ver', lambda r: r['gaze_angle_vs_target'][r['i_end_max_amp_sacc'], 1]),
# ratio max amplitude real amplitude
(('df', 'ratio_max_real_amp'), lambda df: df['max_sacc_amp'] / df['real_amplitude']),
# landing error
(('df', 'landing_error'), lambda df: df['ratio_max_real_amp'] - 1),
# abs landing error
(('df', 'landing_err_abs'), lambda df: df['landing_error'].abs()),
# head contribution
('head_contrib_sacc',
lambda r: r['ypr_head_world'][r['i_end_max_amp_sacc'], 0] - r['ypr_head_world'][r['i_start_max_amp_sacc'], 0]),
# head contribution unidirectional
(('df', 'head_contrib_sacc_uni'), lambda df: df['head_contrib_sacc'] * df['direction_sign']),
# relative head contribution
(('df', 'rel_head_contrib_sacc'), lambda df: df['head_contrib_sacc'] / df['max_sacc_amp']),
# head contribution
('head_contrib_shift_done',
lambda r: r['ypr_head_world'][r['i_shift_done_rel'], 0] - r['ypr_head_world'][r['i_start_max_amp_sacc'], 0]),
# relative head contribution
('rel_head_contrib_shift_done', lambda r: r['head_contrib_shift_done'] / r['max_sacc_amp']),
# max head velocity
('max_head_velocity',
lambda r: np.nanmax(np.abs(np.diff(r['ypr_head_world'][:, 0]) / np.diff(r['t_det_sacc'])))),
# was the max amp saccade detected after the recorded trigger? then it should be dismissed
('saccade_after_threshold', lambda r: r['start_max_amp_sacc'] > 0),
# did the led change happen before the saccade was over? if not, it should be dismissed
('led_change_before_saccade_end',
lambda r: r['end_max_amp_sacc'] >= (
(r['t_target_turned_off'] if r['blanking_duration'] > 0 else r['t_led_shift_done'])
- r['t_saccade_started'])),
# max amp saccade ratio criterion
('max_amp_saccade_length_valid', lambda r: 1.25 > r['ratio_max_real_amp'] > 0.75),
# do all criteria apply?
('valid_trials', lambda r: (not r['saccade_after_threshold']) and r['led_change_before_saccade_end'] and r[
'max_amp_saccade_length_valid']),
# direction vectors from inion to nasion in world
('inion_nasion_world', lambda r: fh.to_unit(r['Ts_head_world'][:, 1, :] - r['Ts_head_world'][:, 2, :])),
# angles for inion to nasion
('inion_nasion_ang', lambda r: np.rad2deg(fh.to_azim_elev(r['inion_nasion_world']))),
# difference of inion->nasion and eye->target vector angles
('d_ininas_eye_target_ang', lambda r: r['inion_nasion_ang'] - r['eye_to_target_ang']),
# difference of inion->nasion and eye->fixation vector angles
('d_ininas_eye_fix_ang', lambda r: r['inion_nasion_ang'] - r['eye_to_fixation_ang']),
# difference of inion->nasion and gaze vector angles
('d_gaze_ininas_ang', lambda r: r['inion_nasion_ang'] - r['gaze_in_world_ang']),
# inion nasion angle relative to head for centering the in head angles
('ininas_ref_ang',
lambda r: np.rad2deg(fh.to_azim_elev(r['helmet'].ref_points[1, :] - r['helmet'].ref_points[2, :]))),
# centered gaze ang head
('gaze_ang_head_centered', lambda r: r['gaze_in_head_ang'] - r['ininas_ref_ang'])
]),
add_inplace=True,
print_log=True
)
return ((angles_from_eye - azim_elev_nonlinear)**2).sum()
optim_result_nonlinear_2 = minimize(err_func_nonlinear_direct, np.zeros(9))
R_eye_nonlinear_2 = fh.from_yawpitchroll(optim_result_nonlinear_2.x)
aa_2 = optim_result_nonlinear_2.x[3:5]
bb_2 = optim_result_nonlinear_2.x[5:7]
cc_2 = optim_result_nonlinear_2.x[7:9]
gaze_corrected_nonlinear_2 = (R_eye_nonlinear_2 @ gaze_normals.T).T
gaze_transformed_2 = gaze_corrected_nonlinear_2.copy()
gaze_transformed_2[:, [0, 2]] = aa_2 * (
gaze_transformed_2[:, [0, 2]]**
2) + bb_2 * gaze_transformed_2[:, [0, 2]] + cc_2
gaze_transformed_2 = fh.to_unit(gaze_transformed_2)
azim_elev_nonlinear_2 = np.rad2deg(
np.arctan2(gaze_transformed_2[:, [0, 2]], gaze_transformed_2[:, 1, None]))
#%%
plt.figure()
plt.scatter(angles_from_eye[:, 0],
angles_from_eye[:, 1],
c=np.arange(angles_from_eye.shape[0]),
cmap='winter',
label='real')
plt.scatter(azim_elev[:, 0],
azim_elev[:, 1],
marker='x',
c=np.arange(azim_elev.shape[0]),