def mpi_resample_cube(mpi, tgt, intrinsics, depth_planes, side_length,
cube_res):
"""Resample MPI onto cube centered at target point.
Args:
mpi: [B,H,W,D,C], input MPI
tgt: [B,3], [x,y,z] coordinates for cube center (in reference/mpi frame)
intrinsics: [B,3,3], MPI reference camera intrinsics
depth_planes: [D] depth values for MPI planes
side_length: metric side length of cube
cube_res: resolution of each cube dimension
Returns:
resampled: [B, cube_res, cube_res, cube_res, C]
"""
batch_size = tf.shape(mpi)[0]
num_depths = tf.shape(mpi)[3]
# compute MPI world coordinates
intrinsics_tile = tf.tile(intrinsics, [num_depths, 1, 1])
# create cube coordinates
b_vals = tf.to_float(tf.range(batch_size))
x_vals = tf.linspace(-side_length / 2.0, side_length / 2.0, cube_res)
y_vals = tf.linspace(-side_length / 2.0, side_length / 2.0, cube_res)
z_vals = tf.linspace(side_length / 2.0, -side_length / 2.0, cube_res)
b, y, x, z = tf.meshgrid(b_vals, y_vals, x_vals, z_vals, indexing='ij')
x = x + tgt[:, 0, tf.newaxis, tf.newaxis, tf.newaxis]
y = y + tgt[:, 1, tf.newaxis, tf.newaxis, tf.newaxis]
z = z + tgt[:, 2, tf.newaxis, tf.newaxis, tf.newaxis]
ones = tf.ones_like(x)
coords = tf.stack([x, y, z, ones], axis=1)
coords_r = tf.reshape(
tf.transpose(coords, [0, 4, 1, 2, 3]),
[batch_size * cube_res, 4, cube_res, cube_res])
# store elements with negative z vals for projection
bad_inds = tf.less(z, 0.0)
# project into reference camera to transform coordinates into MPI indices
filler = tf.constant([0.0, 0.0, 0.0, 1.0], shape=[1, 1, 4])
filler = tf.tile(filler, [batch_size * cube_res, 1, 1])
intrinsics_tile = tf.tile(intrinsics, [cube_res, 1, 1])
intrinsics_tile_4 = tf.concat(
[intrinsics_tile,
tf.zeros([batch_size * cube_res, 3, 1])], axis=2)
intrinsics_tile_4 = tf.concat([intrinsics_tile_4, filler], axis=1)
coords_proj = cam2pixel(coords_r, intrinsics_tile_4)
coords_depths = tf.transpose(coords_r[:, 2:3, :, :], [0, 2, 3, 1])
coords_depth_inds = (tf.to_float(num_depths) - 1) * (
(1.0 / coords_depths) -
(1.0 / depth_planes[0])) / ((1.0 / depth_planes[-1]) -
(1.0 / depth_planes[0]))
coords_proj = tf.concat([coords_proj, coords_depth_inds], axis=3)
coords_proj = tf.transpose(
tf.reshape(coords_proj, [batch_size, cube_res, cube_res, cube_res, 3]),
[0, 2, 3, 1, 4])
coords_proj = tf.concat([b[:, :, :, :, tf.newaxis], coords_proj], axis=4)
# trilinear interpolation gather from MPI
# interpolate pre-multiplied RGBAs, then un-pre-multiply
mpi_alpha = mpi[Ellipsis, -1:]
mpi_channels_p = mpi[Ellipsis, :-1] * mpi_alpha
mpi_p = tf.concat([mpi_channels_p, mpi_alpha], axis=-1)
resampled_p = sampling.trilerp_gather(mpi_p, coords_proj, bad_inds)
resampled_alpha = tf.clip_by_value(resampled_p[Ellipsis, -1:], 0.0, 1.0)
resampled_channels = resampled_p[Ellipsis, :-1] / (resampled_alpha + 1e-8)
resampled = tf.concat([resampled_channels, resampled_alpha], axis=-1)
return resampled, coords_proj
def spherical_cubevol_resample(vol, env2ref, cube_center, side_length, n_phi,
n_theta, n_r):
"""Resample cube volume onto spherical coordinates centered at target point.
Args:
vol: [B,H,W,D,C], input volume
env2ref: [B,4,4], relative pose transformation (transform env to ref)
cube_center: [B,3], [x,y,z] coordinates for center of cube volume
side_length: side length of cube
n_phi: number of samples along vertical spherical coordinate dim
n_theta: number of samples along horizontal spherical coordinate dim
n_r: number of samples along radius spherical coordinate dim
Returns:
resampled: [B, n_phi, n_theta, n_r, C]
"""
batch_size = tf.shape(vol)[0]
height = tf.shape(vol)[1]
cube_res = tf.to_float(height)
# create spherical coordinates
b_vals = tf.to_float(tf.range(batch_size))
phi_vals = tf.linspace(0.0, np.pi, n_phi)
theta_vals = tf.linspace(1.5 * np.pi, -0.5 * np.pi, n_theta)
# compute radii to use
x_vals = tf.linspace(-side_length / 2.0, side_length / 2.0,
tf.to_int32(cube_res))
y_vals = tf.linspace(-side_length / 2.0, side_length / 2.0,
tf.to_int32(cube_res))
z_vals = tf.linspace(side_length / 2.0, -side_length / 2.0,
tf.to_int32(cube_res))
y_c, x_c, z_c = tf.meshgrid(y_vals, x_vals, z_vals, indexing='ij')
x_c = x_c + cube_center[:, 0, tf.newaxis, tf.newaxis, tf.newaxis]
y_c = y_c + cube_center[:, 1, tf.newaxis, tf.newaxis, tf.newaxis]
z_c = z_c + cube_center[:, 2, tf.newaxis, tf.newaxis, tf.newaxis]
cube_coords = tf.stack([x_c, y_c, z_c], axis=4)
min_r = tf.reduce_min(
tf.norm(
cube_coords -
env2ref[:, :3, 3][:, tf.newaxis, tf.newaxis, tf.newaxis, :],
axis=4),
axis=[0, 1, 2, 3]) # side_length / cube_res
max_r = tf.reduce_max(
tf.norm(
cube_coords -
env2ref[:, :3, 3][:, tf.newaxis, tf.newaxis, tf.newaxis, :],
axis=4),
axis=[0, 1, 2, 3])
r_vals = tf.linspace(max_r, min_r, n_r)
b, phi, theta, r = tf.meshgrid(
b_vals, phi_vals, theta_vals, r_vals,
indexing='ij') # currently in env frame
# transform spherical coordinates into cartesian
# (currently in env frame, z points forwards)
x = r * tf.cos(theta) * tf.sin(phi)
z = r * tf.sin(theta) * tf.sin(phi)
y = r * tf.cos(phi)
# transform coordinates into ref frame
sphere_coords = tf.stack([x, y, z, tf.ones_like(x)], axis=-1)[Ellipsis, tf.newaxis]
sphere_coords_ref = tfmm(env2ref, sphere_coords)
x = sphere_coords_ref[Ellipsis, 0, 0]
y = sphere_coords_ref[Ellipsis, 1, 0]
z = sphere_coords_ref[Ellipsis, 2, 0]
# transform coordinates into vol indices
x_inds = (x - cube_center[:, 0, tf.newaxis, tf.newaxis, tf.newaxis] +
side_length / 2.0) * ((cube_res - 1) / side_length)
y_inds = -(y - cube_center[:, 1, tf.newaxis, tf.newaxis, tf.newaxis] -
side_length / 2.0) * ((cube_res - 1) / side_length)
z_inds = -(z - cube_center[:, 2, tf.newaxis, tf.newaxis, tf.newaxis] -
side_length / 2.0) * ((cube_res - 1) / side_length)
sphere_coords_inds = tf.stack([b, x_inds, y_inds, z_inds], axis=-1)
# trilinear interpolation gather from volume
# interpolate pre-multiplied RGBAs, then un-pre-multiply
vol_alpha = tf.clip_by_value(vol[Ellipsis, -1:], 0.0, 1.0)
vol_channels_p = vol[Ellipsis, :-1] * vol_alpha
vol_p = tf.concat([vol_channels_p, vol_alpha], axis=-1)
resampled_p = sampling.trilerp_gather(vol_p, sphere_coords_inds)
resampled_alpha = resampled_p[Ellipsis, -1:]
resampled_channels = resampled_p[Ellipsis, :-1] / (resampled_alpha + 1e-8)
resampled = tf.concat([resampled_channels, resampled_alpha], axis=-1)
return resampled, r_vals