def _rot_mat_to_zxz_euler(rot_mat):
# BS x 1
euler_angles_1 = _ivy.acos(rot_mat[..., 2, 2:3])
gimbal_validity = _ivy.abs(rot_mat[..., 0, 2:3]) > GIMBAL_TOL
r12 = rot_mat[..., 0, 1:2]
r11 = rot_mat[..., 0, 0:1]
gimbal_euler_angles_0 = _ivy.atan2(-r12, r11)
gimbal_euler_angles_2 = _ivy.zeros_like(gimbal_euler_angles_0)
# BS x 3
gimbal_euler_angles = _ivy.concatenate(
(gimbal_euler_angles_0, euler_angles_1, gimbal_euler_angles_2), -1)
# BS x 1
r31 = rot_mat[..., 2, 0:1]
r32 = rot_mat[..., 2, 1:2]
r13 = rot_mat[..., 0, 2:3]
r23 = rot_mat[..., 1, 2:3]
normal_euler_angles_0 = _ivy.atan2(r31, r32)
normal_euler_angles_2 = _ivy.atan2(r13, -r23)
# BS x 3
normal_euler_angles = _ivy.concatenate(
(normal_euler_angles_0, euler_angles_1, normal_euler_angles_2), -1)
return _ivy.where(gimbal_validity, normal_euler_angles,
gimbal_euler_angles)
def _rot_mat_to_yzy_euler(rot_mat):
# BS x 1
euler_angles_1 = _ivy.acos(rot_mat[..., 1, 1:2])
gimbal_validity = _ivy.abs(rot_mat[..., 1, 0:1]) > GIMBAL_TOL
r31 = rot_mat[..., 2, 0:1]
r33 = rot_mat[..., 2, 2:3]
gimbal_euler_angles_0 = _ivy.atan2(-r31, r33)
gimbal_euler_angles_2 = _ivy.zeros_like(gimbal_euler_angles_0)
# BS x 3
gimbal_euler_angles = _ivy.concatenate(
(gimbal_euler_angles_0, euler_angles_1, gimbal_euler_angles_2), -1)
# BS x 1
r23 = rot_mat[..., 1, 2:3]
r21 = rot_mat[..., 1, 0:1]
r32 = rot_mat[..., 2, 1:2]
r12 = rot_mat[..., 0, 1:2]
normal_euler_angles_0 = _ivy.atan2(r23, r21)
normal_euler_angles_2 = _ivy.atan2(r32, r12)
# BS x 3
normal_euler_angles = _ivy.concatenate(
(normal_euler_angles_0, euler_angles_1, normal_euler_angles_2), -1)
return _ivy.where(gimbal_validity, normal_euler_angles,
gimbal_euler_angles)
def _rot_mat_to_zyx_euler(rot_mat):
# BS x 1
euler_angles_1 = _ivy.asin(rot_mat[..., 0, 2:3])
gimbal_validity = _ivy.abs(rot_mat[..., 1, 1:2]) > GIMBAL_TOL
r21 = rot_mat[..., 1, 0:1]
r22 = rot_mat[..., 1, 1:2]
gimbal_euler_angles_0 = _ivy.atan2(r21, r22)
gimbal_euler_angles_2 = _ivy.zeros_like(gimbal_euler_angles_0)
# BS x 3
gimbal_euler_angles = _ivy.concatenate(
(gimbal_euler_angles_0, euler_angles_1, gimbal_euler_angles_2), -1)
# BS x 1
r12 = rot_mat[..., 0, 1:2]
r11 = rot_mat[..., 0, 0:1]
r23 = rot_mat[..., 1, 2:3]
r33 = rot_mat[..., 2, 2:3]
normal_euler_angles_0 = _ivy.atan2(-r12, r11)
normal_euler_angles_2 = _ivy.atan2(-r23, r33)
# BS x 3
normal_euler_angles = _ivy.concatenate(
(normal_euler_angles_0, euler_angles_1, normal_euler_angles_2), -1)
return _ivy.where(gimbal_validity, normal_euler_angles,
gimbal_euler_angles)
def smooth(self, fused_val, fused_variance, low_var_mask, smooth_mean,
smooth_kernel_size, variance_mode, fix_low_var_pixels,
batch_size):
variance_mode = True
var_for_smoothing = fused_variance
# image smoothing
if smooth_mean:
# pad borders
pad_size = int(smooth_kernel_size / 2)
fused_val_pad = ivy_vision.pad_omni_image(fused_val, pad_size,
self._sphere_img_dims)
fused_variance_pad = ivy_vision.pad_omni_image(
var_for_smoothing, pad_size, self._sphere_img_dims)
expanded_sphere_img_dims = [
item + 2 * pad_size for item in self._sphere_img_dims
]
# reshape for dilation and erosion
fused_val_pad_flat = ivy.reshape(
fused_val_pad[..., 2:],
[batch_size] + expanded_sphere_img_dims + [1 + self._feat_dim])
fused_var_pad_flat = ivy.reshape(
fused_variance_pad[..., 2:],
[batch_size] + expanded_sphere_img_dims + [1 + self._feat_dim])
if variance_mode:
smoothed_fused_val_flat, smoothed_fused_var_flat = \
ivy_vision.smooth_image_fom_var_image(fused_val_pad_flat, fused_var_pad_flat, smooth_kernel_size,
ivy.array([1.] * (1 + self._feat_dim), dev_str=self._dev_str))
else:
smoothed_fused_val_flat, smoothed_fused_var_flat = \
ivy_vision.weighted_image_smooth(fused_val_pad_flat, 1 - fused_var_pad_flat, smooth_kernel_size)
# reshape to image dims
smoothed_fused_val = ivy.reshape(
smoothed_fused_val_flat,
[batch_size] + self._sphere_img_dims + [1 + self._feat_dim])
smoothed_fused_val = ivy.concatenate(
(fused_val[..., 0:2], smoothed_fused_val), -1)
# replace temporary zeros with their prior values
# This ensures that the smoothing operation only changes the values for regions of high variance
if fix_low_var_pixels:
fused_val = ivy.where(low_var_mask, fused_val,
smoothed_fused_val)
else:
fused_val = smoothed_fused_val
return fused_val, fused_variance
def _kalman_filter_on_measurement_sequence(
self, prev_fused_val, prev_fused_variance, hole_prior,
hole_prior_var, meas, meas_vars, uniform_sphere_pixel_coords,
agent_rel_poses, agent_rel_pose_covs, agent_rel_mats, batch_size,
num_timesteps):
"""
Perform kalman filter on measurement sequence
:param prev_fused_val: Fused value from previous timestamp *[batch_size, oh, ow, (3+f)]*
:param prev_fused_variance: Fused variance from previous timestamp *[batch_size, oh, ow, (3+f)]*
:param hole_prior: Prior for holes in quantization *[batch_size, oh, ow, (1+f)]*
:param hole_prior_var: Prior variance for holes in quantization *[batch_size, oh, ow, (3+f)]*
:param meas: Measurements *[batch_size, num_timesteps, oh, ow, (3+f)]*
:param meas_vars: Measurement variances *[batch_size, num_timesteps, oh, ow, (3+f)]*
:param uniform_sphere_pixel_coords: Uniform sphere pixel co-ordinates *[batch_size, oh, ow, 3]*
:param agent_rel_poses: Relative poses of agents to the previous step *[batch_size, num_timesteps, 6]*
:param agent_rel_pose_covs: Agent relative pose covariances *[batch_size, num_timesteps, 6, 6]*
:param agent_rel_mats: Relative transformations matrix of agents to the previous step
*[batch_size, num_timesteps, 3, 4]*
:param batch_size: Size of batch
:param num_timesteps: Number of frames
:return: list of *[batch_size, oh, ow, (3+f)]*, list of *[batch_size, oh, ow, (3+f)]*
"""
fused_list = list()
fused_variances_list = list()
for i in range(num_timesteps):
# project prior from previous frame #
# ----------------------------------#
# B x OH x OW x (3+F)
prev_prior = prev_fused_val
prev_prior_variance = prev_fused_variance
# B x 3 x 4
agent_rel_mat = agent_rel_mats[:, i]
# B x 6
agent_rel_pose = agent_rel_poses[:, i]
# B x 6 x 6
agent_rel_pose_cov = agent_rel_pose_covs[:, i]
# B x OH x OW x (3+F) B x OH x OW x (3+F)
fused_projected, fused_projected_variance = self._omni_frame_to_omni_frame_projection(
agent_rel_pose, agent_rel_mat, uniform_sphere_pixel_coords,
prev_prior[..., 0:2], prev_prior[..., 2:3],
prev_prior[..., 3:], agent_rel_pose_cov, prev_prior_variance,
hole_prior, hole_prior_var, batch_size)
# reset prior
# B x OH x OW x (3+F)
prior = fused_projected
prior_var = fused_projected_variance
# per-pixel fusion with measurements #
# -----------------------------------#
# extract slice for frame
# B x OH x OW x (3+F)
measurement = meas[:, i]
measurement_variance = meas_vars[:, i]
# fuse prior and measurement
# B x 2 x OH x OW x (3+F)
prior_and_meas = ivy.concatenate(
(ivy.expand_dims(prior, 1), ivy.expand_dims(measurement, 1)),
1)
prior_and_meas_variance = ivy.concatenate((ivy.expand_dims(
prior_var, 1), ivy.expand_dims(measurement_variance, 1)), 1)
# B x OH x OW x (3+F)
low_var_mask = ivy.reduce_sum(
ivy.cast(
prior_and_meas_variance <
ivy.expand_dims(hole_prior_var, 1) *
self._threshold_var_factor, 'int32'), 1) > 0
# B x 1 x OH x OW x (3+F) B x 1 x OH x OW x (3+F)
# ToDo: handle this properly once re-implemented with a single scatter operation only
# currently depth values are fused even if these are clearly far apart
fused_val_unsmoothed, fused_variance_unsmoothed = \
self._fuse_measurements_with_uncertainty(prior_and_meas, prior_and_meas_variance, 1)
# B x OH x OW x (3+F)
# This prevents accumulating certainty from duplicate re-projections from prior measurements
fused_variance_unsmoothed = ivy.where(
low_var_mask, fused_variance_unsmoothed[:, 0], hole_prior_var)
# B x OH x OW x (3+F)
fused_val = fused_val_unsmoothed[:, 0]
fused_variance = fused_variance_unsmoothed
low_var_mask = fused_variance < hole_prior_var
# B x OH x OW x (3+F) B x OH x OW x (3+F)
fused_val, fused_variance = self.smooth(fused_val, fused_variance,
low_var_mask,
self._smooth_mean,
self._smooth_kernel_size,
True, True, batch_size)
# append to list for returning
# B x OH x OW x (3+F)
fused_list.append(fused_val)
# B x OH x OW x (3+F)
fused_variances_list.append(fused_variance)
# update for next time step
prev_fused_val = fused_val
prev_fused_variance = fused_variance
# list of *[batch_size, oh, ow, (3+f)]*, list of *[batch_size, oh, ow, (3+f)]*
return fused_list, fused_variances_list
def _convert_images_to_omni_observations(self, measurements,
uniform_sphere_pixel_coords,
holes_prior, batch_size,
num_timesteps, num_cams,
image_dims):
"""
Convert image to omni-directional measurements
:param measurements: perspective captured images and relative poses container
:param uniform_sphere_pixel_coords: Uniform sphere pixel coords *[batch_size, num_timesteps, oh, ow, 3]*
:param holes_prior: Prior for quantization holes *[batch_size, num_timesteps, oh, ow, 1+f]*
:param batch_size: Size of batch
:param num_timesteps: Number of frames
:param num_cams: Number of cameras
:param image_dims: Image dimensions
:return: *[batch_size, n, oh, ow, 3+f]* *[batch_size, n, oh, ow, 3+f]*
"""
# coords from all scene cameras wrt world
images_list = list()
images_var_list = list()
cam_rel_poses_list = list()
cam_rel_poses_cov_list = list()
cam_rel_mats_list = list()
validity_mask_list = list()
for key, item in measurements.to_iterator():
if key == 'img_mean':
# B x N x 1 x H x W x (3+f)
images_list.append(ivy.expand_dims(item, 2))
elif key == 'img_var':
# B x N x 1 x H x W x (3+f)
images_var_list.append(ivy.expand_dims(item, 2))
elif key == 'pose_mean':
# B x N x 1 x 6
cam_rel_poses_list.append(ivy.expand_dims(item, 2))
elif key == 'pose_cov':
# B x N x 1 x 6 x 6
cam_rel_poses_cov_list.append(ivy.expand_dims(item, 2))
elif key == 'cam_rel_mat':
# B x N x 1 x 3 x 4
cam_rel_mats_list.append(ivy.expand_dims(item, 2))
elif key == 'validity_mask':
validity_mask_list.append(ivy.expand_dims(item, 2))
else:
raise Exception('Invalid image key: {}'.format(key))
# B x N x C x H x W x (3+f)
images = ivy.concatenate(images_list, 2)
# B x N x C x H x W x (3+f)
var_to_project = ivy.concatenate(images_var_list, 2)
# B x N x C x 6
cam_to_cam_poses = ivy.concatenate(cam_rel_poses_list, 2)
# B x N x C x 3 x 4
cam_to_cam_mats = ivy.concatenate(cam_rel_mats_list, 2)
# B x N x C x 6 x 6
cam_to_cam_pose_covs = ivy.concatenate(cam_rel_poses_cov_list, 2)
# B x N x C x 1
validity_masks = ivy.concatenate(validity_mask_list, 2) > 0
# B x N x OH x OW x (3+f)
holes_prior_var = ivy.ones(
[batch_size, num_timesteps] + self._sphere_img_dims +
[3 + self._feat_dim],
dev_str=self._dev_str) * 1e12
# reset invalid regions to prior
# B x N x C x H x W x (3+f)
images = ivy.where(
validity_masks, images,
ivy.concatenate(
(images[..., 0:2],
ivy.zeros_like(images[..., 2:], dev_str=self._dev_str)), -1))
# B x N x C x H x W x (3+f)
var_to_project = ivy.where(
validity_masks, var_to_project,
ivy.ones_like(var_to_project, dev_str=self._dev_str) * 1e12)
# B x N x OH x OW x (3+f) # B x N x OH x OW x (3+f)
return self._frame_to_omni_frame_projection(
cam_to_cam_poses, cam_to_cam_mats, uniform_sphere_pixel_coords,
images[..., 0:3], images[..., 3:], cam_to_cam_pose_covs,
var_to_project, holes_prior, holes_prior_var, batch_size,
num_timesteps, num_cams, image_dims)
def _kalman_filter_on_measurement_sequence(
self, prev_fused_val, prev_fused_variance, hole_prior,
hole_prior_var, meas, meas_vars, uniform_sphere_pixel_coords,
agent_rel_poses, agent_rel_pose_covs, agent_rel_mats, batch_size,
num_timesteps):
"""
Perform kalman filter on measurement sequence
:param prev_fused_val: Fused value from previous timestamp *[batch_size, oh, ow, (3+f)]*
:param prev_fused_variance: Fused variance from previous timestamp *[batch_size, oh, ow, (3+f)]*
:param hole_prior: Prior for holes in quantization *[batch_size, oh, ow, (1+f)]*
:param hole_prior_var: Prior variance for holes in quantization *[batch_size, oh, ow, (3+f)]*
:param meas: Measurements *[batch_size, num_timesteps, oh, ow, (3+f)]*
:param meas_vars: Measurement variances *[batch_size, num_timesteps, oh, ow, (3+f)]*
:param uniform_sphere_pixel_coords: Uniform sphere pixel co-ordinates *[batch_size, oh, ow, 3]*
:param agent_rel_poses: Relative poses of agents to the previous step *[batch_size, num_timesteps, 6]*
:param agent_rel_pose_covs: Agent relative pose covariances *[batch_size, num_timesteps, 6, 6]*
:param agent_rel_mats: Relative transformations matrix of agents to the previous step
*[batch_size, num_timesteps, 3, 4]*
:param batch_size: Size of batch
:param num_timesteps: Number of frames
:return: list of *[batch_size, oh, ow, (3+f)]*, list of *[batch_size, oh, ow, (3+f)]*
"""
fused_list = list()
fused_variances_list = list()
for i in range(num_timesteps):
# project prior from previous frame #
# ----------------------------------#
# B x OH x OW x (3+F)
prev_prior = prev_fused_val
prev_prior_variance = prev_fused_variance
# B x 3 x 4
agent_rel_mat = agent_rel_mats[:, i]
# B x 6
agent_rel_pose = agent_rel_poses[:, i]
# B x 6 x 6
agent_rel_pose_cov = agent_rel_pose_covs[:, i]
# B x OH x OW x (3+F) B x OH x OW x (3+F)
fused_projected, fused_projected_variance = self._omni_frame_to_omni_frame_projection(
agent_rel_pose, agent_rel_mat, uniform_sphere_pixel_coords,
prev_prior[..., 0:2], prev_prior[..., 2:3],
prev_prior[..., 3:], agent_rel_pose_cov, prev_prior_variance,
hole_prior, hole_prior_var, batch_size)
# reset prior
# B x OH x OW x (3+F)
prior = fused_projected
prior_var = fused_projected_variance
# per-pixel fusion with measurements #
# -----------------------------------#
# extract slice for frame
# B x OH x OW x (3+F)
measurement = meas[:, i]
measurement_variance = meas_vars[:, i]
# fuse prior and measurement
# B x 2 x OH x OW x (3+F)
prior_and_meas = ivy.concatenate(
(ivy.expand_dims(prior, 1), ivy.expand_dims(measurement, 1)),
1)
prior_and_meas_variance = ivy.concatenate((ivy.expand_dims(
prior_var, 1), ivy.expand_dims(measurement_variance, 1)), 1)
# B x OH x OW x (3+F)
low_var_mask = ivy.reduce_sum(
ivy.cast(
prior_and_meas_variance <
ivy.expand_dims(hole_prior_var, 1) *
self._threshold_var_factor, 'int32'), 1) > 0
# B x 1 x OH x OW x (3+F) B x 1 x OH x OW x (3+F)
if self._with_depth_buffer:
# ToDo: make this more efficient
prior_low_var_mask = ivy.reduce_max(ivy.cast(
prior_var >= hole_prior_var * self._threshold_var_factor,
'int32'),
-1,
keepdims=True) == 0
meas_low_var_mask = ivy.reduce_max(ivy.cast(
measurement_variance >=
hole_prior_var * self._threshold_var_factor, 'int32'),
-1,
keepdims=True) == 0
neiter_low_var_mask = ivy.logical_and(
ivy.logical_not(prior_low_var_mask),
ivy.logical_not(meas_low_var_mask))
prior_w_large = ivy.where(prior_low_var_mask, prior,
ivy.ones_like(prior) * 1e12)
meas_w_large = ivy.where(meas_low_var_mask, measurement,
ivy.ones_like(measurement) * 1e12)
prior_and_meas_w_large = ivy.concatenate((ivy.expand_dims(
prior_w_large, 1), ivy.expand_dims(meas_w_large, 1)), 1)
fused_val_unsmoothed = ivy.reduce_min(prior_and_meas_w_large,
1,
keepdims=True)
fused_val_unsmoothed = ivy.where(neiter_low_var_mask, prior,
fused_val_unsmoothed)
# ToDo: solve this variance correspondence properly, rather than assuming the most certain
fused_variance_unsmoothed = ivy.reduce_min(
prior_and_meas_variance, 1, keepdims=True)
else:
fused_val_unsmoothed, fused_variance_unsmoothed = \
self._fuse_measurements_with_uncertainty(prior_and_meas, prior_and_meas_variance, 1)
# B x OH x OW x (3+F)
# This prevents accumulating certainty from duplicate re-projections from prior measurements
fused_variance_unsmoothed = ivy.where(
low_var_mask, fused_variance_unsmoothed[:, 0], hole_prior_var)
# B x OH x OW x (3+F)
fused_val = fused_val_unsmoothed[:, 0]
fused_variance = fused_variance_unsmoothed
low_var_mask = fused_variance < hole_prior_var
# B x OH x OW x (3+F) B x OH x OW x (3+F)
fused_val, fused_variance = self.smooth(fused_val, fused_variance,
low_var_mask,
self._smooth_mean,
self._smooth_kernel_size,
True, True, batch_size)
# append to list for returning
# B x OH x OW x (3+F)
fused_list.append(fused_val)
# B x OH x OW x (3+F)
fused_variances_list.append(fused_variance)
# update for next time step
prev_fused_val = fused_val
prev_fused_variance = fused_variance
# list of *[batch_size, oh, ow, (3+f)]*, list of *[batch_size, oh, ow, (3+f)]*
return fused_list, fused_variances_list
def rot_mat_to_quaternion(rot_mat):
"""
Convert rotation matrix :math:`\mathbf{R}\in\mathbb{R}^{3×3}` to quaternion
:math:`\mathbf{q} = [q_i, q_j, q_k, q_r]`.\n
`[reference] <http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/>`_
:param rot_mat: Rotation matrix *[batch_shape,3,3]*
:type rot_mat: array
:return: Quaternion *[batch_shape,4]*
"""
# BS x 1 x 1
tr = rot_mat[..., 0:1, 0:1] + rot_mat[..., 1:2, 1:2] + rot_mat[..., 2:3,
2:3]
# if tf > 0
# BS x 1 x 1
s_1 = ((tr + 1)**0.5) * 2
qw_1 = 0.25 * s_1
qx_1 = (rot_mat[..., 2:3, 1:2] -
rot_mat[..., 1:2, 2:3]) / (s_1 + MIN_DENOMINATOR)
qy_1 = (rot_mat[..., 0:1, 2:3] -
rot_mat[..., 2:3, 0:1]) / (s_1 + MIN_DENOMINATOR)
qz_1 = (rot_mat[..., 1:2, 0:1] -
rot_mat[..., 0:1, 1:2]) / (s_1 + MIN_DENOMINATOR)
# BS x 4 x 1
quat_1 = _ivy.concatenate((qx_1, qy_1, qz_1, qw_1), -2)
# elif (m[:,0,0] > m[:,1,1]) and (m[:,0,0] > m[:,2,2])
# BS x 1 x 1
s_2 = ((1 + rot_mat[..., 0:1, 0:1] - rot_mat[..., 1:2, 1:2] -
rot_mat[..., 2:3, 2:3])**0.5) * 2
qw_2 = (rot_mat[..., 2:3, 1:2] -
rot_mat[..., 1:2, 2:3]) / (s_2 + MIN_DENOMINATOR)
qx_2 = 0.25 * s_2
qy_2 = (rot_mat[..., 0:1, 1:2] +
rot_mat[..., 1:2, 0:1]) / (s_2 + MIN_DENOMINATOR)
qz_2 = (rot_mat[..., 0:1, 2:3] +
rot_mat[..., 2:3, 0:1]) / (s_2 + MIN_DENOMINATOR)
# BS x 4 x 1
quat_2 = _ivy.concatenate((qx_2, qy_2, qz_2, qw_2), -2)
# elif m[:,1,1] > m[:,2,2]
# BS x 1 x 1
s_3 = ((1 + rot_mat[..., 1:2, 1:2] - rot_mat[..., 0:1, 0:1] -
rot_mat[..., 2:3, 2:3])**0.5) * 2
qw_3 = (rot_mat[..., 0:1, 2:3] -
rot_mat[..., 2:3, 0:1]) / (s_3 + MIN_DENOMINATOR)
qx_3 = (rot_mat[..., 0:1, 1:2] +
rot_mat[..., 1:2, 0:1]) / (s_3 + MIN_DENOMINATOR)
qy_3 = 0.25 * s_3
qz_3 = (rot_mat[..., 1:2, 2:3] +
rot_mat[..., 2:3, 1:2]) / (s_3 + MIN_DENOMINATOR)
# BS x 4 x 1
quat_3 = _ivy.concatenate((qx_3, qy_3, qz_3, qw_3), -2)
# else
# BS x 1 x 1
s_4 = ((1 + rot_mat[..., 2:3, 2:3] - rot_mat[..., 0:1, 0:1] -
rot_mat[..., 1:2, 1:2])**0.5) * 2
qw_4 = (rot_mat[..., 1:2, 0:1] -
rot_mat[..., 0:1, 1:2]) / (s_4 + MIN_DENOMINATOR)
qx_4 = (rot_mat[..., 0:1, 2:3] +
rot_mat[..., 2:3, 0:1]) / (s_4 + MIN_DENOMINATOR)
qy_4 = (rot_mat[..., 1:2, 2:3] +
rot_mat[..., 2:3, 1:2]) / (s_4 + MIN_DENOMINATOR)
qz_4 = 0.25 * s_4
# BS x 4 x 1
quat_4 = _ivy.concatenate((qx_4, qy_4, qz_4, qw_4), -2)
quat_3_or_other = _ivy.where(
rot_mat[..., 1:2, 1:2] > rot_mat[..., 2:3, 2:3], quat_3, quat_4)
quat_2_or_other = \
_ivy.where(_ivy.logical_and((rot_mat[..., 0:1, 0:1] > rot_mat[..., 1:2, 1:2]),
(rot_mat[..., 0:1, 0:1] > rot_mat[..., 2:3, 2:3])), quat_2, quat_3_or_other)
# BS x 4
return _ivy.where(tr > 0, quat_1, quat_2_or_other)[..., 0]
def velocity_from_cam_coords_id_image_and_object_trans(cam_coords_t,
id_image,
obj_ids,
obj_trans,
delta_t,
batch_shape=None,
image_dims=None,
dev_str=None):
"""
Compute velocity image from co-ordinate image, id image, and object transformations.
:param cam_coords_t: Camera-centric homogeneous co-ordinates image in frame t *[batch_shape,h,w,4]*
:type cam_coords_t: array
:param id_image: Image containing per-pixel object ids *[batch_shape,h,w,1]*
:type id_image: array
:param obj_ids: Object ids *[batch_shape,num_obj,1]*
:type obj_ids: array
:param obj_trans: Object transformations for this frame over time *[batch_shape,num_obj,3,4]*
:type obj_trans: array
:param delta_t: Time difference between frame at timestep t-1 and t *[batch_shape,1]*
:type delta_t: array
:param batch_shape: Shape of batch. Inferred from inputs if None.
:type batch_shape: sequence of ints, optional
:param image_dims: Image dimensions. Inferred from inputs in None.
:type image_dims: sequence of ints, optional
:param dev_str: device on which to create the array 'cuda:0', 'cuda:1', 'cpu' etc. Same as x if None.
:type dev_str: str, optional
:return: Relative velocity image *[batch_shape,h,w,3]*
"""
if batch_shape is None:
batch_shape = cam_coords_t.shape[:-3]
if image_dims is None:
image_dims = cam_coords_t.shape[-3:-1]
if dev_str is None:
dev_str = _ivy.dev_str(cam_coords_t)
# shapes as list
batch_shape = list(batch_shape)
image_dims = list(image_dims)
# get co-ordinate re-projections
# BS x H x W x 4
cam_coords_t_all_trans, motion_mask =\
project_cam_coords_with_object_transformations(cam_coords_t, id_image, obj_ids, obj_trans,
_ivy.identity(4, batch_shape=batch_shape)[..., 0:3, :],
batch_shape, image_dims)
# BS x H x W x 4
cam_coords_t_all_trans = \
_ivy.where(motion_mask, cam_coords_t_all_trans, _ivy.zeros_like(cam_coords_t_all_trans, dev_str=dev_str))
# compute velocities
# BS x H x W x 3
vel = (cam_coords_t[..., 0:3] - cam_coords_t_all_trans[..., 0:3]) / delta_t
# prune velocities
# BS x H x W x 3
return _ivy.where(motion_mask, vel, _ivy.zeros_like(vel, dev_str=dev_str))
def project_cam_coords_with_object_transformations(cam_coords_1,
id_image,
obj_ids,
obj_trans,
cam_1_to_2_ext_mat,
batch_shape=None,
image_dims=None):
"""
Compute velocity image from co-ordinate image, id image, and object transformations.
:param cam_coords_1: Camera-centric homogeneous co-ordinates image in frame t *[batch_shape,h,w,4]*
:type cam_coords_1: array
:param id_image: Image containing per-pixel object ids *[batch_shape,h,w,1]*
:type id_image: array
:param obj_ids: Object ids *[batch_shape,num_obj,1]*
:type obj_ids: array
:param obj_trans: Object transformations for this frame over time *[batch_shape,num_obj,3,4]*
:type obj_trans: array
:param cam_1_to_2_ext_mat: Camera 1 to camera 2 extrinsic projection matrix *[batch_shape,3,4]*
:type cam_1_to_2_ext_mat: array
:param batch_shape: Shape of batch. Inferred from inputs if None.
:type batch_shape: sequence of ints, optional
:param image_dims: Image dimensions. Inferred from inputs in None.
:type image_dims: sequence of ints, optional
:return: Relative velocity image *[batch_shape,h,w,3]*
"""
if batch_shape is None:
batch_shape = cam_coords_1.shape[:-3]
if image_dims is None:
image_dims = cam_coords_1.shape[-3:-1]
# shapes as list
batch_shape = list(batch_shape)
image_dims = list(image_dims)
num_batch_dims = len(batch_shape)
# Transform the co-ordinate image by each transformation
# BS x (num_obj x 3) x 4
obj_trans = _ivy.reshape(obj_trans, batch_shape + [-1, 4])
# BS x 4 x H x W
cam_coords_1_ = _ivy.transpose(
cam_coords_1,
list(range(num_batch_dims)) + [i + num_batch_dims for i in [2, 0, 1]])
# BS x 4 x (HxW)
cam_coords_1_ = _ivy.reshape(cam_coords_1_, batch_shape + [4, -1])
# BS x (num_obj x 3) x (HxW)
cam_coords_2_all_obj_trans = _ivy.matmul(obj_trans, cam_coords_1_)
# BS x (HxW) x (num_obj x 3)
cam_coords_2_all_obj_trans = \
_ivy.transpose(cam_coords_2_all_obj_trans, list(range(num_batch_dims)) + [i + num_batch_dims for i in [1, 0]])
# BS x H x W x num_obj x 3
cam_coords_2_all_obj_trans = _ivy.reshape(
cam_coords_2_all_obj_trans, batch_shape + image_dims + [-1, 3])
# Multiplier
# BS x 1 x 1 x num_obj
obj_ids = _ivy.reshape(obj_ids, batch_shape + [1, 1] + [-1])
# BS x H x W x num_obj x 1
multiplier = _ivy.cast(_ivy.expand_dims(obj_ids == id_image, -1),
'float32')
# compute validity mask, for pixels which are on moving objects
# BS x H x W x 1
motion_mask = _ivy.reduce_sum(multiplier, -2) > 0
# make invalid transformations equal to zero
# BS x H x W x num_obj x 3
cam_coords_2_all_obj_trans_w_zeros = cam_coords_2_all_obj_trans * multiplier
# reduce to get only valid transformations
# BS x H x W x 3
cam_coords_2_all_obj_trans = _ivy.reduce_sum(
cam_coords_2_all_obj_trans_w_zeros, -2)
# find cam coords to for zero motion pixels
# BS x H x W x 3
cam_coords_2_wo_motion = _ivy_tvg.cam_to_cam_coords(
cam_coords_1, cam_1_to_2_ext_mat, batch_shape, image_dims)
# BS x H x W x 4
cam_coords_2_all_trans_homo =\
_ivy_mech.make_coordinates_homogeneous(cam_coords_2_all_obj_trans, batch_shape + image_dims)
cam_coords_2 = _ivy.where(motion_mask, cam_coords_2_all_trans_homo,
cam_coords_2_wo_motion)
# return
# BS x H x W x 3, BS x H x W x 1
return cam_coords_2, motion_mask
def velocity_from_flow_cam_coords_and_cam_mats(flow_t_to_tm1,
cam_coords_t,
cam_coords_tm1,
cam_tm1_to_t_ext_mat,
delta_t,
uniform_pixel_coords=None,
batch_shape=None,
image_dims=None,
dev_str=None):
"""
Compute relative cartesian velocity from optical flow, camera co-ordinates, and camera extrinsics.
:param flow_t_to_tm1: Optical flow from frame t to t-1 *[batch_shape,h,w,2]*
:type flow_t_to_tm1: array
:param cam_coords_t: Camera-centric homogeneous co-ordinates image in frame t *[batch_shape,h,w,4]*
:type cam_coords_t: array
:param cam_coords_tm1: Camera-centric homogeneous co-ordinates image in frame t-1 *[batch_shape,h,w,4]*
:type cam_coords_tm1: array
:param cam_tm1_to_t_ext_mat: Camera t-1 to camera t extrinsic projection matrix *[batch_shape,3,4]*
:type cam_tm1_to_t_ext_mat: array
:param delta_t: Time difference between frame at timestep t-1 and t *[batch_shape,1]*
:type delta_t: array
:param uniform_pixel_coords: Homogeneous uniform (integer) pixel co-ordinate images, inferred from image_dims if None *[batch_shape,h,w,3]*
:type uniform_pixel_coords: array, optional
:param batch_shape: Shape of batch. Inferred from inputs if None.
:type batch_shape: sequence of ints, optional
:param image_dims: Image dimensions. Inferred from inputs in None.
:type image_dims: sequence of ints, optional
:param dev_str: device on which to create the array 'cuda:0', 'cuda:1', 'cpu' etc. Same as x if None.
:type dev_str: str, optional
:return: Cartesian velocity measurements relative to the camera *[batch_shape,h,w,3]*
"""
if batch_shape is None:
batch_shape = flow_t_to_tm1.shape[:-3]
if image_dims is None:
image_dims = flow_t_to_tm1.shape[-3:-1]
# shapes as list
batch_shape = list(batch_shape)
image_dims = list(image_dims)
if dev_str is None:
dev_str = _ivy.dev_str(flow_t_to_tm1)
if uniform_pixel_coords is None:
uniform_pixel_coords = _ivy_svg.create_uniform_pixel_coords_image(
image_dims, batch_shape, dev_str)
# Interpolate cam coords from frame t-1
# BS x H x W x 2
warp = uniform_pixel_coords[..., 0:2] + flow_t_to_tm1
# BS x H x W x 4
cam_coords_tm1_interp = _ivy.image.bilinear_resample(cam_coords_tm1, warp)
# Project to frame t
# BS x H x W x 4
cam_coords_t_proj = _ivy_tvg.cam_to_cam_coords(cam_coords_tm1_interp,
cam_tm1_to_t_ext_mat,
batch_shape, image_dims)
# delta co-ordinates
# BS x H x W x 3
delta_cam_coords_t = (cam_coords_t - cam_coords_t_proj)[..., 0:3]
# velocity
# BS x H x W x 3
vel = delta_cam_coords_t / _ivy.reshape(delta_t, batch_shape + [1] * 3)
# Validity mask
# BS x H x W x 1
validity_mask = \
_ivy.reduce_sum(_ivy.cast(warp < _ivy.array([image_dims[1], image_dims[0]], 'float32', dev_str=dev_str),
'int32'), -1, keepdims=True) == 2
# pruned
# BS x H x W x 3, BS x H x W x 1
return _ivy.where(validity_mask, vel,
_ivy.zeros_like(vel, dev_str=dev_str)), validity_mask
def quantize_to_image(pixel_coords,
final_image_dims,
feat=None,
feat_prior=None,
with_db=False,
pixel_coords_var=1e-3,
feat_var=1e-3,
pixel_coords_prior_var=1e12,
feat_prior_var=1e12,
var_threshold=(1e-3, 1e12),
uniform_pixel_coords=None,
batch_shape=None,
dev_str=None):
"""
Quantize pixel co-ordinates with d feature channels (for depth, rgb, normals etc.), from
images :math:`\mathbf{X}\in\mathbb{R}^{input\_images\_shape×(2+d)}`, which may have been reprojected from a host of
different cameras (leading to non-integer pixel values), to a new quantized pixel co-ordinate image with the same
feature channels :math:`\mathbf{X}\in\mathbb{R}^{h×w×(2+d)}`, and with integer pixel co-ordinates.
Duplicates during the quantization are either probabilistically fused based on variance, or the minimum depth is
chosen when using depth buffer mode.
:param pixel_coords: Pixel co-ordinates *[batch_shape,input_size,2]*
:type pixel_coords: array
:param final_image_dims: Image dimensions of the final image.
:type final_image_dims: sequence of ints
:param feat: Features (i.e. depth, rgb, encoded), default is None. *[batch_shape,input_size,d]*
:type feat: array, optional
:param feat_prior: Prior feature image mean, default is None. *[batch_shape,input_size,d]*
:type feat_prior: array or float to fill with
:param with_db: Whether or not to use depth buffer in rendering, default is false
:type with_db: bool, optional
:param pixel_coords_var: Pixel coords variance *[batch_shape,input_size,2]*
:type pixel_coords_var: array or float to fill with
:param feat_var: Feature variance *[batch_shape,input_size,d]*
:type feat_var: array or float to fill with
:param pixel_coords_prior_var: Pixel coords prior variance *[batch_shape,h,w,2]*
:type pixel_coords_prior_var: array or float to fill with
:param feat_prior_var: Features prior variance *[batch_shape,h,w,3]*
:type feat_prior_var: array or float to fill with
:param var_threshold: Variance threshold, for projecting valid coords and clipping *[batch_shape,2+d,2]*
:type var_threshold: array or sequence of floats to fill with
:param uniform_pixel_coords: Homogeneous uniform (integer) pixel co-ordinate images, inferred from final_image_dims
if None *[batch_shape,h,w,3]*
:type uniform_pixel_coords: array, optional
:param batch_shape: Shape of batch. Assumed no batches if None.
:type batch_shape: sequence of ints, optional
:param dev_str: device on which to create the array 'cuda:0', 'cuda:1', 'cpu' etc. Same as x if None.
:type dev_str: str, optional
:return: Quantized pixel co-ordinates image with d feature channels (for depth, rgb, normals etc.) *[batch_shape,h,w,2+d]*,
maybe the quantized variance, *[batch_shape,h,w,2+d]*, and scatter counter image *[batch_shape,h,w,1]*
"""
# ToDo: make variance fully optional. If not specified,
# then do not compute and scatter during function call for better efficiency.
# config
if batch_shape is None:
batch_shape = pixel_coords.shape[:-2]
if dev_str is None:
dev_str = _ivy.dev_str(pixel_coords)
if feat is None:
d = 0
else:
d = feat.shape[-1]
min_depth_diff = _ivy.array([MIN_DEPTH_DIFF], dev_str=dev_str)
red = 'min' if with_db else 'sum'
# shapes as list
batch_shape = list(batch_shape)
final_image_dims = list(final_image_dims)
num_batch_dims = len(batch_shape)
# variance threshold
if isinstance(var_threshold, tuple) or isinstance(var_threshold, list):
ones = _ivy.ones(batch_shape + [1, 2 + d, 1])
var_threshold = _ivy.concatenate(
(ones * var_threshold[0], ones * var_threshold[1]), -1)
else:
var_threshold = _ivy.reshape(var_threshold,
batch_shape + [1, 2 + d, 2])
# uniform pixel coords
if uniform_pixel_coords is None:
uniform_pixel_coords =\
_ivy_svg.create_uniform_pixel_coords_image(final_image_dims, batch_shape, dev_str=dev_str)
uniform_pixel_coords = uniform_pixel_coords[..., 0:2]
# Extract Values #
feat_prior = _ivy.ones_like(feat) * feat_prior if isinstance(
feat_prior, float) else feat_prior
pixel_coords_var = _ivy.ones_like(pixel_coords) * pixel_coords_var\
if isinstance(pixel_coords_var, float) else pixel_coords_var
feat_var = _ivy.ones_like(feat) * feat_var if isinstance(
feat_var, float) else feat_var
pixel_coords_prior_var = _ivy.ones(batch_shape + final_image_dims + [2]) * pixel_coords_prior_var\
if isinstance(pixel_coords_prior_var, float) else pixel_coords_prior_var
feat_prior_var = _ivy.ones(batch_shape + final_image_dims + [d]) * feat_prior_var\
if isinstance(feat_prior_var, float) else feat_prior_var
# Quantize #
# BS x N x 2
quantized_pixel_coords = _ivy.reshape(
_ivy.cast(_ivy.round(pixel_coords), 'int32'), batch_shape + [-1, 2])
# Combine #
# BS x N x (2+D)
pc_n_feat = _ivy.reshape(_ivy.concatenate((pixel_coords, feat), -1),
batch_shape + [-1, 2 + d])
pc_n_feat_var = _ivy.reshape(
_ivy.concatenate((pixel_coords_var, feat_var), -1),
batch_shape + [-1, 2 + d])
# BS x H x W x (2+D)
prior = _ivy.concatenate((uniform_pixel_coords, feat_prior), -1)
prior_var = _ivy.concatenate((pixel_coords_prior_var, feat_prior_var), -1)
# Validity Mask #
# BS x N x 1
var_validity_mask = \
_ivy.reduce_sum(_ivy.cast(pc_n_feat_var < var_threshold[..., 1], 'int32'), -1, keepdims=True) == 2+d
bounds_validity_mask = _ivy.logical_and(
_ivy.logical_and(quantized_pixel_coords[..., 0:1] >= 0,
quantized_pixel_coords[..., 1:2] >= 0),
_ivy.logical_and(
quantized_pixel_coords[..., 0:1] <= final_image_dims[1] - 1,
quantized_pixel_coords[..., 1:2] <= final_image_dims[0] - 1))
validity_mask = _ivy.logical_and(var_validity_mask, bounds_validity_mask)
# num_valid_indices x len(BS)+2
validity_indices = _ivy.reshape(
_ivy.cast(_ivy.indices_where(validity_mask), 'int32'),
[-1, num_batch_dims + 2])
num_valid_indices = validity_indices.shape[-2]
if num_valid_indices == 0:
return _ivy.concatenate((uniform_pixel_coords[..., 0:2], feat_prior), -1), \
_ivy.concatenate((pixel_coords_prior_var, feat_prior_var), -1),\
_ivy.zeros_like(feat[..., 0:1], dev_str=dev_str)
# Depth Based Scaling #
mean_depth_min = None
mean_depth_range = None
pc_n_feat_wo_depth_range = None
pc_n_feat_wo_depth_min = None
var_vals_range = None
var_vals_min = None
if with_db:
# BS x N x 1
mean_depth = pc_n_feat[..., 2:3]
# BS x 1 x 1
mean_depth_min = _ivy.reduce_min(mean_depth, -2, keepdims=True)
mean_depth_max = _ivy.reduce_max(mean_depth, -2, keepdims=True)
mean_depth_range = mean_depth_max - mean_depth_min
# BS x N x 1
scaled_depth = (mean_depth - mean_depth_min) / (
mean_depth_range * min_depth_diff + MIN_DENOMINATOR)
if d == 1:
# BS x 1 x 1+D
pc_n_feat_wo_depth_min = _ivy.zeros(batch_shape + [1, 0],
dev_str=dev_str)
pc_n_feat_wo_depth_range = _ivy.ones(batch_shape + [1, 0],
dev_str=dev_str)
else:
# feat without depth
# BS x N x 1+D
pc_n_feat_wo_depth = _ivy.concatenate(
(pc_n_feat[..., 0:2], pc_n_feat[..., 3:]), -1)
# find the min and max of each value
# BS x 1 x 1+D
pc_n_feat_wo_depth_max = _ivy.reduce_max(
pc_n_feat_wo_depth, -2, keepdims=True) + 1
pc_n_feat_wo_depth_min = _ivy.reduce_min(
pc_n_feat_wo_depth, -2, keepdims=True) - 1
pc_n_feat_wo_depth_range = pc_n_feat_wo_depth_max - pc_n_feat_wo_depth_min
# BS x N x 1+D
normed_pc_n_feat_wo_depth = (pc_n_feat_wo_depth - pc_n_feat_wo_depth_min) / \
(pc_n_feat_wo_depth_range + MIN_DENOMINATOR)
# combine with scaled depth
# BS x N x 1+D
pc_n_feat_wo_depth_scaled = normed_pc_n_feat_wo_depth + scaled_depth
# BS x N x (2+D)
pc_n_feat = _ivy.concatenate(
(pc_n_feat_wo_depth_scaled[..., 0:2], mean_depth,
pc_n_feat_wo_depth_scaled[..., 2:]), -1)
# scale variance
# BS x 1 x (2+D)
var_vals_max = _ivy.reduce_max(pc_n_feat_var, -2, keepdims=True) + 1
var_vals_min = _ivy.reduce_min(pc_n_feat_var, -2, keepdims=True) - 1
var_vals_range = var_vals_max - var_vals_min
# BS x N x (2+D)
normed_var_vals = (pc_n_feat_var - var_vals_min) / (var_vals_range +
MIN_DENOMINATOR)
pc_n_feat_var = normed_var_vals + scaled_depth
# ready for later reversal with full image dimensions
# BS x 1 x 1 x D
var_vals_min = _ivy.expand_dims(var_vals_min, -2)
var_vals_range = _ivy.expand_dims(var_vals_range, -2)
# Validity Pruning #
# num_valid_indices x (2+D)
pc_n_feat = _ivy.gather_nd(pc_n_feat,
validity_indices[..., 0:num_batch_dims + 1])
pc_n_feat_var = _ivy.gather_nd(pc_n_feat_var,
validity_indices[..., 0:num_batch_dims + 1])
# num_valid_indices x 2
quantized_pixel_coords = _ivy.gather_nd(
quantized_pixel_coords, validity_indices[..., 0:num_batch_dims + 1])
if with_db:
means_to_scatter = pc_n_feat
vars_to_scatter = pc_n_feat_var
else:
# num_valid_indices x (2+D)
vars_to_scatter = 1 / (pc_n_feat_var + MIN_DENOMINATOR)
means_to_scatter = pc_n_feat * vars_to_scatter
# Scatter #
# num_valid_indices x 1
counter = _ivy.ones_like(pc_n_feat[..., 0:1], dev_str=dev_str)
if with_db:
counter *= -1
# num_valid_indices x 2(2+D)+1
values_to_scatter = _ivy.concatenate(
(means_to_scatter, vars_to_scatter, counter), -1)
# num_valid_indices x (num_batch_dims + 2)
all_indices = _ivy.flip(quantized_pixel_coords, -1)
if num_batch_dims > 0:
all_indices = _ivy.concatenate(
(validity_indices[..., :-2], all_indices), -1)
# BS x H x W x (2(2+D) + 1)
quantized_img = _ivy.scatter_nd(
_ivy.reshape(all_indices, [-1, num_batch_dims + 2]),
_ivy.reshape(values_to_scatter, [-1, 2 * (2 + d) + 1]),
batch_shape + final_image_dims + [2 * (2 + d) + 1],
reduction='replace' if _ivy.backend == 'mxnd' else red)
# BS x H x W x 1
quantized_counter = quantized_img[..., -1:]
if with_db:
invalidity_mask = quantized_counter != -1
else:
invalidity_mask = quantized_counter == 0
if with_db:
# BS x H x W x (2+D)
quantized_mean_scaled = quantized_img[..., 0:2 + d]
quantized_var_scaled = quantized_img[..., 2 + d:2 * (2 + d)]
# BS x H x W x 1
quantized_depth_mean = quantized_mean_scaled[..., 2:3]
# BS x 1 x 1 x 1
mean_depth_min = _ivy.expand_dims(mean_depth_min, -2)
mean_depth_range = _ivy.expand_dims(mean_depth_range, -2)
# BS x 1 x 1 x (1+D)
pc_n_feat_wo_depth_min = _ivy.expand_dims(pc_n_feat_wo_depth_min, -2)
pc_n_feat_wo_depth_range = _ivy.expand_dims(pc_n_feat_wo_depth_range,
-2)
# BS x 1 x 1 x (2+D) x 2
var_threshold = _ivy.expand_dims(var_threshold, -3)
# BS x H x W x (1+D)
quantized_mean_wo_depth_scaled = _ivy.concatenate(
(quantized_mean_scaled[..., 0:2], quantized_mean_scaled[..., 3:]),
-1)
quantized_mean_wo_depth_normed = quantized_mean_wo_depth_scaled - (quantized_depth_mean - mean_depth_min) / \
(mean_depth_range * min_depth_diff + MIN_DENOMINATOR)
quantized_mean_wo_depth = quantized_mean_wo_depth_normed * pc_n_feat_wo_depth_range + pc_n_feat_wo_depth_min
prior_wo_depth = _ivy.concatenate((prior[..., 0:2], prior[..., 3:]),
-1)
quantized_mean_wo_depth = _ivy.where(invalidity_mask, prior_wo_depth,
quantized_mean_wo_depth)
# BS x H x W x (2+D)
quantized_mean = _ivy.concatenate(
(quantized_mean_wo_depth[..., 0:2], quantized_depth_mean,
quantized_mean_wo_depth[..., 2:]), -1)
# BS x H x W x (2+D)
quantized_var_normed = quantized_var_scaled - (quantized_depth_mean - mean_depth_min) / \
(mean_depth_range * min_depth_diff + MIN_DENOMINATOR)
quantized_var = _ivy.maximum(
quantized_var_normed * var_vals_range + var_vals_min,
var_threshold[..., 0])
quantized_var = _ivy.where(invalidity_mask, prior_var, quantized_var)
else:
# BS x H x W x (2+D)
quantized_sum_mean_x_recip_var = quantized_img[..., 0:2 + d]
quantized_var_wo_increase = _ivy.where(
invalidity_mask, prior_var,
(1 / (quantized_img[..., 2 + d:2 * (2 + d)] + MIN_DENOMINATOR)))
quantized_var = _ivy.maximum(
quantized_var_wo_increase * quantized_counter,
_ivy.expand_dims(var_threshold[..., 0], -2))
quantized_var = _ivy.where(invalidity_mask, prior_var, quantized_var)
quantized_mean = _ivy.where(
invalidity_mask, prior,
quantized_var_wo_increase * quantized_sum_mean_x_recip_var)
# BS x H x W x (2+D) BS x H x W x (2+D) BS x H x W x 1
return quantized_mean, quantized_var, quantized_counter
def main(interactive=True, f=None):
global INTERACTIVE
INTERACTIVE = interactive
# Framework Setup #
# ----------------#
# choose random framework
f = choose_random_framework() if f is None else f
set_framework(f)
# Camera Geometry #
# ----------------#
# intrinsics
# common intrinsic params
img_dims = [512, 512]
pp_offsets = ivy.array([dim / 2 - 0.5 for dim in img_dims], 'float32')
cam_persp_angles = ivy.array([60 * np.pi / 180] * 2, 'float32')
# ivy cam intrinsics container
intrinsics = ivy_vision.persp_angles_and_pp_offsets_to_intrinsics_object(
cam_persp_angles, pp_offsets, img_dims)
# extrinsics
# 3 x 4
cam1_inv_ext_mat = ivy.array(np.load(data_dir + '/cam1_inv_ext_mat.npy'),
'float32')
cam2_inv_ext_mat = ivy.array(np.load(data_dir + '/cam2_inv_ext_mat.npy'),
'float32')
# full geometry
# ivy cam geometry container
cam1_geom = ivy_vision.inv_ext_mat_and_intrinsics_to_cam_geometry_object(
cam1_inv_ext_mat, intrinsics)
cam2_geom = ivy_vision.inv_ext_mat_and_intrinsics_to_cam_geometry_object(
cam2_inv_ext_mat, intrinsics)
cam_geoms = [cam1_geom, cam2_geom]
# Camera Geometry Check #
# ----------------------#
# assert camera geometry shapes
for cam_geom in cam_geoms:
assert cam_geom.intrinsics.focal_lengths.shape == (2, )
assert cam_geom.intrinsics.persp_angles.shape == (2, )
assert cam_geom.intrinsics.pp_offsets.shape == (2, )
assert cam_geom.intrinsics.calib_mats.shape == (3, 3)
assert cam_geom.intrinsics.inv_calib_mats.shape == (3, 3)
assert cam_geom.extrinsics.cam_centers.shape == (3, 1)
assert cam_geom.extrinsics.Rs.shape == (3, 3)
assert cam_geom.extrinsics.inv_Rs.shape == (3, 3)
assert cam_geom.extrinsics.ext_mats_homo.shape == (4, 4)
assert cam_geom.extrinsics.inv_ext_mats_homo.shape == (4, 4)
assert cam_geom.full_mats_homo.shape == (4, 4)
assert cam_geom.inv_full_mats_homo.shape == (4, 4)
# Image Data #
# -----------#
# load images
# h x w x 3
color1 = ivy.array(
cv2.imread(data_dir + '/rgb1.png').astype(np.float32) / 255)
color2 = ivy.array(
cv2.imread(data_dir + '/rgb2.png').astype(np.float32) / 255)
# h x w x 1
depth1 = ivy.array(
np.reshape(
np.frombuffer(
cv2.imread(data_dir + '/depth1.png', -1).tobytes(),
np.float32), img_dims + [1]))
depth2 = ivy.array(
np.reshape(
np.frombuffer(
cv2.imread(data_dir + '/depth2.png', -1).tobytes(),
np.float32), img_dims + [1]))
# depth scaled pixel coords
# h x w x 3
u_pix_coords = ivy_vision.create_uniform_pixel_coords_image(img_dims)
ds_pixel_coords1 = u_pix_coords * depth1
ds_pixel_coords2 = u_pix_coords * depth2
# depth limits
depth_min = ivy.reduce_min(ivy.concatenate((depth1, depth2), 0))
depth_max = ivy.reduce_max(ivy.concatenate((depth1, depth2), 0))
depth_limits = [depth_min, depth_max]
# show images
show_rgb_and_depth_images(color1, color2, depth1, depth2, depth_limits)
# Flow and Depth Triangulation #
# -----------------------------#
# required mat formats
cam1to2_full_mat_homo = ivy.matmul(cam2_geom.full_mats_homo,
cam1_geom.inv_full_mats_homo)
cam1to2_full_mat = cam1to2_full_mat_homo[..., 0:3, :]
full_mats_homo = ivy.concatenate(
(ivy.expand_dims(cam1_geom.full_mats_homo,
0), ivy.expand_dims(cam2_geom.full_mats_homo, 0)), 0)
full_mats = full_mats_homo[..., 0:3, :]
# flow
flow1to2 = ivy_vision.flow_from_depth_and_cam_mats(ds_pixel_coords1,
cam1to2_full_mat)
# depth again
depth1_from_flow = ivy_vision.depth_from_flow_and_cam_mats(
flow1to2, full_mats)
# show images
show_flow_and_depth_images(depth1, flow1to2, depth1_from_flow,
depth_limits)
# Inverse Warping #
# ----------------#
# inverse warp rendering
warp = u_pix_coords[..., 0:2] + flow1to2
color2_warp_to_f1 = ivy.reshape(ivy.bilinear_resample(color2, warp),
color1.shape)
# projected depth scaled pixel coords 2
ds_pixel_coords1_wrt_f2 = ivy_vision.ds_pixel_to_ds_pixel_coords(
ds_pixel_coords1, cam1to2_full_mat)
# projected depth 2
depth1_wrt_f2 = ds_pixel_coords1_wrt_f2[..., -1:]
# inverse warp depth
depth2_warp_to_f1 = ivy.reshape(ivy.bilinear_resample(depth2, warp),
depth1.shape)
# depth validity
depth_validity = ivy.abs(depth1_wrt_f2 - depth2_warp_to_f1) < 0.01
# inverse warp rendering with mask
color2_warp_to_f1_masked = ivy.where(depth_validity, color2_warp_to_f1,
ivy.zeros_like(color2_warp_to_f1))
# show images
show_inverse_warped_images(depth1_wrt_f2, depth2_warp_to_f1,
depth_validity, color1, color2_warp_to_f1,
color2_warp_to_f1_masked, depth_limits)
# Forward Warping #
# ----------------#
# forward warp rendering
ds_pixel_coords1_proj = ivy_vision.ds_pixel_to_ds_pixel_coords(
ds_pixel_coords2,
ivy.inv(cam1to2_full_mat_homo)[..., 0:3, :])
depth1_proj = ds_pixel_coords1_proj[..., -1:]
ds_pixel_coords1_proj = ds_pixel_coords1_proj[..., 0:2] / depth1_proj
features_to_render = ivy.concatenate((depth1_proj, color2), -1)
# without depth buffer
f1_forward_warp_no_db, _, _ = ivy_vision.quantize_to_image(
ivy.reshape(ds_pixel_coords1_proj, (-1, 2)),
img_dims,
ivy.reshape(features_to_render, (-1, 4)),
ivy.zeros_like(features_to_render),
with_db=False)
# with depth buffer
f1_forward_warp_w_db, _, _ = ivy_vision.quantize_to_image(
ivy.reshape(ds_pixel_coords1_proj, (-1, 2)),
img_dims,
ivy.reshape(features_to_render, (-1, 4)),
ivy.zeros_like(features_to_render),
with_db=False if ivy.get_framework() == 'mxnd' else True)
# show images
show_forward_warped_images(depth1, color1, f1_forward_warp_no_db,
f1_forward_warp_w_db, depth_limits)
# message
print('End of Run Through Demo!')