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import torch
import torch.nn.functional as F
pixel_coords = None
def set_id_grid(depth):
global pixel_coords
b, h, w = depth.size()
i_range = torch.arange(0, h).view(1, h, 1).expand(
1, h, w).type_as(depth) # [1, H, W]
j_range = torch.arange(0, w).view(1, 1, w).expand(
1, h, w).type_as(depth) # [1, H, W]
ones = torch.ones(1, h, w).type_as(depth)
pixel_coords = torch.stack((j_range, i_range, ones), dim=1) # [1, 3, H, W]
def check_sizes(input, input_name, expected):
condition = [input.ndimension() == len(expected)]
for i, size in enumerate(expected):
if size.isdigit():
condition.append(input.size(i) == int(size))
assert(all(condition)), "wrong size for {}, expected {}, got {}".format(
input_name, 'x'.join(expected), list(input.size()))
def pixel2cam(depth, intrinsics_inv):
global pixel_coords
"""Transform coordinates in the pixel frame to the camera frame.
Args:
depth: depth maps -- [B, H, W]
intrinsics_inv: intrinsics_inv matrix for each element of batch -- [B, 3, 3]
Returns:
array of (u,v,1) cam coordinates -- [B, 3, H, W]
"""
b, h, w = depth.size()
if (pixel_coords is None) or pixel_coords.size(2) < h:
set_id_grid(depth)
current_pixel_coords = pixel_coords[:, :, :h, :w].expand(
b, 3, h, w).reshape(b, 3, -1) # [B, 3, H*W]
cam_coords = (intrinsics_inv @ current_pixel_coords).reshape(b, 3, h, w)
out = depth.unsqueeze(1) * cam_coords
return out
def cam2pixel(cam_coords, proj_c2p_rot, proj_c2p_tr, padding_mode):
"""Transform coordinates in the camera frame to the pixel frame.
Args:
cam_coords: pixel coordinates defined in the first camera coordinates system -- [B, 4, H, W]
proj_c2p_rot: rotation matrix of cameras -- [B, 3, 4]
proj_c2p_tr: translation vectors of cameras -- [B, 3, 1]
Returns:
array of [-1,1] coordinates -- [B, 2, H, W]
"""
b, _, h, w = cam_coords.size()
cam_coords_flat = cam_coords.reshape(b, 3, -1) # [B, 3, H*W]
if proj_c2p_rot is not None:
pcoords = proj_c2p_rot @ cam_coords_flat
else:
pcoords = cam_coords_flat
if proj_c2p_tr is not None:
pcoords = pcoords + proj_c2p_tr # [B, 3, H*W]
X = pcoords[:, 0]
Y = pcoords[:, 1]
Z = pcoords[:, 2].clamp(min=1e-3)
# Normalized, -1 if on extreme left, 1 if on extreme right (x = w-1) [B, H*W]
X_norm = 2*(X / Z)/(w-1) - 1
Y_norm = 2*(Y / Z)/(h-1) - 1 # Idem [B, H*W]
pixel_coords = torch.stack([X_norm, Y_norm], dim=2) # [B, H*W, 2]
return pixel_coords.reshape(b, h, w, 2)
def euler2mat(angle):
"""Convert euler angles to rotation matrix.
Reference: https://github.com/pulkitag/pycaffe-utils/blob/master/rot_utils.py#L174
Args:
angle: rotation angle along 3 axis (in radians) -- size = [B, 3]
Returns:
Rotation matrix corresponding to the euler angles -- size = [B, 3, 3]
"""
B = angle.size(0)
x, y, z = angle[:, 0], angle[:, 1], angle[:, 2]
cosz = torch.cos(z)
sinz = torch.sin(z)
zeros = z.detach()*0
ones = zeros.detach()+1
zmat = torch.stack([cosz, -sinz, zeros,
sinz, cosz, zeros,
zeros, zeros, ones], dim=1).reshape(B, 3, 3)
cosy = torch.cos(y)
siny = torch.sin(y)
ymat = torch.stack([cosy, zeros, siny,
zeros, ones, zeros,
-siny, zeros, cosy], dim=1).reshape(B, 3, 3)
cosx = torch.cos(x)
sinx = torch.sin(x)
xmat = torch.stack([ones, zeros, zeros,
zeros, cosx, -sinx,
zeros, sinx, cosx], dim=1).reshape(B, 3, 3)
rotMat = xmat @ ymat @ zmat
return rotMat
def quat2mat(quat):
"""Convert quaternion coefficients to rotation matrix.
Args:
quat: first three coeff of quaternion of rotation. fourht is then computed to have a norm of 1 -- size = [B, 3]
Returns:
Rotation matrix corresponding to the quaternion -- size = [B, 3, 3]
"""
norm_quat = torch.cat([quat[:, :1].detach()*0 + 1, quat], dim=1)
norm_quat = norm_quat/norm_quat.norm(p=2, dim=1, keepdim=True)
w, x, y, z = norm_quat[:, 0], norm_quat[:,
1], norm_quat[:, 2], norm_quat[:, 3]
B = quat.size(0)
w2, x2, y2, z2 = w.pow(2), x.pow(2), y.pow(2), z.pow(2)
wx, wy, wz = w*x, w*y, w*z
xy, xz, yz = x*y, x*z, y*z
rotMat = torch.stack([w2 + x2 - y2 - z2, 2*xy - 2*wz, 2*wy + 2*xz,
2*wz + 2*xy, w2 - x2 + y2 - z2, 2*yz - 2*wx,
2*xz - 2*wy, 2*wx + 2*yz, w2 - x2 - y2 + z2], dim=1).reshape(B, 3, 3)
return rotMat
def pose_vec2mat(vec, rotation_mode='euler'):
"""
Convert 6DoF parameters to transformation matrix.
Args:s
vec: 6DoF parameters in the order of tx, ty, tz, rx, ry, rz -- [B, 6]
Returns:
A transformation matrix -- [B, 3, 4]
"""
translation = vec[:, :3].unsqueeze(-1) # [B, 3, 1]
rot = vec[:, 3:]
if rotation_mode == 'euler':
rot_mat = euler2mat(rot) # [B, 3, 3]
elif rotation_mode == 'quat':
rot_mat = quat2mat(rot) # [B, 3, 3]
transform_mat = torch.cat([rot_mat, translation], dim=2) # [B, 3, 4]
return transform_mat
def inverse_warp(img, depth, pose, intrinsics, rotation_mode='euler', padding_mode='zeros'):
"""
Inverse warp a source image to the target image plane.
Args:
img: the source image (where to sample pixels) -- [B, 3, H, W]
depth: depth map of the target image -- [B, H, W]
pose: 6DoF pose parameters from target to source -- [B, 6]
intrinsics: camera intrinsic matrix -- [B, 3, 3]
Returns:
projected_img: Source image warped to the target image plane
valid_points: Boolean array indicating point validity
"""
check_sizes(img, 'img', 'B3HW')
check_sizes(depth, 'depth', 'BHW')
check_sizes(pose, 'pose', 'B6')
check_sizes(intrinsics, 'intrinsics', 'B33')
batch_size, _, img_height, img_width = img.size()
cam_coords = pixel2cam(depth, intrinsics.inverse()) # [B,3,H,W]
pose_mat = pose_vec2mat(pose, rotation_mode) # [B,3,4]
# Get projection matrix for tgt camera frame to source pixel frame
proj_cam_to_src_pixel = intrinsics @ pose_mat # [B, 3, 4]
rot, tr = proj_cam_to_src_pixel[:, :, :3], proj_cam_to_src_pixel[:, :, -1:]
src_pixel_coords = cam2pixel(
cam_coords, rot, tr, padding_mode) # [B,H,W,2]
projected_img = F.grid_sample(
img, src_pixel_coords, padding_mode=padding_mode)
valid_points = src_pixel_coords.abs().max(dim=-1)[0] <= 1
return projected_img, valid_points
def cam2pixel2(cam_coords, proj_c2p_rot, proj_c2p_tr, padding_mode):
"""Transform coordinates in the camera frame to the pixel frame.
Args:
cam_coords: pixel coordinates defined in the first camera coordinates system -- [B, 4, H, W]
proj_c2p_rot: rotation matrix of cameras -- [B, 3, 4]
proj_c2p_tr: translation vectors of cameras -- [B, 3, 1]
Returns:
array of [-1,1] coordinates -- [B, 2, H, W]
"""
b, _, h, w = cam_coords.size()
cam_coords_flat = cam_coords.reshape(b, 3, -1) # [B, 3, H*W]
if proj_c2p_rot is not None:
pcoords = proj_c2p_rot @ cam_coords_flat
else:
pcoords = cam_coords_flat
if proj_c2p_tr is not None:
pcoords = pcoords + proj_c2p_tr # [B, 3, H*W]
X = pcoords[:, 0]
Y = pcoords[:, 1]
Z = pcoords[:, 2].clamp(min=1e-3)
# Normalized, -1 if on extreme left, 1 if on extreme right (x = w-1) [B, H*W]
X_norm = 2*(X / Z)/(w-1) - 1
Y_norm = 2*(Y / Z)/(h-1) - 1 # Idem [B, H*W]
if padding_mode == 'zeros':
X_mask = ((X_norm > 1)+(X_norm < -1)).detach()
# make sure that no point in warped image is a combinaison of im and gray
X_norm[X_mask] = 2
Y_mask = ((Y_norm > 1)+(Y_norm < -1)).detach()
Y_norm[Y_mask] = 2
pixel_coords = torch.stack([X_norm, Y_norm], dim=2) # [B, H*W, 2]
return pixel_coords.reshape(b, h, w, 2), Z.reshape(b, 1, h, w)
def inverse_warp2(img, depth, ref_depth, pose, intrinsics, padding_mode='zeros'):
"""
Inverse warp a source image to the target image plane.
Args:
img: the source image (where to sample pixels) -- [B, 3, H, W]
depth: depth map of the target image -- [B, 1, H, W]
ref_depth: the source depth map (where to sample depth) -- [B, 1, H, W]
pose: 6DoF pose parameters from target to source -- [B, 6]
intrinsics: camera intrinsic matrix -- [B, 3, 3]
Returns:
projected_img: Source image warped to the target image plane
valid_mask: Float array indicating point validity
projected_depth: sampled depth from source image
computed_depth: computed depth of source image using the target depth
"""
check_sizes(img, 'img', 'B3HW')
check_sizes(depth, 'depth', 'B1HW')
check_sizes(ref_depth, 'ref_depth', 'B1HW')
check_sizes(pose, 'pose', 'B6')
check_sizes(intrinsics, 'intrinsics', 'B33')
batch_size, _, img_height, img_width = img.size()
cam_coords = pixel2cam(depth.squeeze(1), intrinsics.inverse()) # [B,3,H,W]
pose_mat = pose_vec2mat(pose) # [B,3,4]
# Get projection matrix for tgt camera frame to source pixel frame
proj_cam_to_src_pixel = intrinsics @ pose_mat # [B, 3, 4]
rot, tr = proj_cam_to_src_pixel[:, :, :3], proj_cam_to_src_pixel[:, :, -1:]
src_pixel_coords, computed_depth = cam2pixel2(cam_coords, rot, tr, padding_mode) # [B,H,W,2]
projected_img = F.grid_sample(img, src_pixel_coords, padding_mode=padding_mode, align_corners=False)
projected_depth = F.grid_sample(ref_depth, src_pixel_coords, padding_mode=padding_mode, align_corners=False)
return projected_img, projected_depth, computed_depth
def inverse_rotation_warp(img, rot, intrinsics, padding_mode='zeros'):
b, _, h, w = img.size()
cam_coords = pixel2cam(torch.ones(b, h, w).type_as(img), intrinsics.inverse()) # [B,3,H,W]
rot_mat = euler2mat(rot) # [B, 3, 3]
# Get projection matrix for tgt camera frame to source pixel frame
proj_cam_to_src_pixel = intrinsics @ rot_mat # [B, 3, 3]
src_pixel_coords, computed_depth = cam2pixel2(cam_coords, proj_cam_to_src_pixel, None, padding_mode) # [B,H,W,2]
projected_img = F.grid_sample(img, src_pixel_coords, padding_mode=padding_mode, align_corners=True)
return projected_img
def grid_to_flow(grid):
b, h, w, _ = grid.size()
i_range = torch.arange(0, h).view(1, h, 1).expand(1, h, w).type_as(grid) # [1, H, W]
j_range = torch.arange(0, w).view(1, 1, w).expand(1, h, w).type_as(grid) # [1, H, W]
image_coords = torch.stack((j_range, i_range), dim=1) # [1, 2, H, W]
flow = torch.zeros_like(grid).type_as(grid)
flow[:, :, :, 0] = (grid[:, :, :, 0]+1) / 2 * (w-1)
flow[:, :, :, 1] = (grid[:, :, :, 1]+1) / 2 * (h-1)
flow = flow.permute([0, 3, 1, 2])
flow -= image_coords
return flow
def compute_translation_flow(depth, pose, intrinsics):
cam_coords = pixel2cam(depth.squeeze(1), intrinsics.inverse()) # [B,3,H,W]
pose_mat = pose_vec2mat(pose) # [B,3,4]
# Get projection matrix for tgt camera frame to source pixel frame
proj_cam_to_src_pixel = intrinsics @ pose_mat # [B, 3, 4]
rot, tr = proj_cam_to_src_pixel[:, :, :3], proj_cam_to_src_pixel[:, :, -1:]
grid_all, _ = cam2pixel2(cam_coords, rot, tr, padding_mode='zeros') # [B,H,W,2]
grid_rot, _ = cam2pixel2(cam_coords, rot, None, padding_mode='zeros') # [B,H,W,2]
flow_all = grid_to_flow(grid_all)
flow_rot = grid_to_flow(grid_rot)
flow_tr = (flow_all - flow_rot)
return flow_tr
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