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flow.py
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flow.py
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import numpy as np
import torch
import torch.nn.functional as F
from transformations import euler_matrix
def deg2rad(deg):
return deg / 180 * np.pi
def generate_pixel_grid(h=512, w=512):
"""
Generates a grid of pixel coordinates.
(W, H)
"""
xx, yy = torch.meshgrid(
torch.arange(w, dtype=torch.float32),
torch.arange(h, dtype=torch.float32)
)
zz = torch.ones(w, h)
return torch.stack([xx, yy, zz])
def to_camera_frame(pose_matrix):
"""
Transforms the pose from the standard right-handed
coordinate system (x forward )into the camera
coordinate system (z forward).
"""
batch = (pose_matrix.dim() == 3)
# Remember the old coordinate axes
if not batch:
i, j, k = pose_matrix[:3, :3].clone()
x, y, z = pose_matrix[:3, 3].clone()
# 0. Translate to origin
pose_matrix = pose_matrix.clone()
if batch:
t = pose_matrix[:, :4, 3].clone().unsqueeze(-1)
pose_matrix[:, :3, 3] = 0
else:
t = pose_matrix[:4, 3].clone()
pose_matrix[:3, 3] = 0
# 1. Yaw: apply RH -90 degrees
R_yaw = torch.Tensor(euler_matrix(0, 0, deg2rad(90)))
pose_matrix = R_yaw @ pose_matrix
t = R_yaw @ t
# 2. Roll: apply RH -90 degrees
R_roll = torch.Tensor(euler_matrix(deg2rad(90), 0, 0))
pose_matrix = R_roll @ pose_matrix
t = R_roll @ t
# 4. Translate back
if batch:
pose_matrix[:, :3, 3] = t[:, :3].squeeze(-1)
else:
pose_matrix[:3, 3] = t[:3]
# Check if everything is fine
if not batch:
i_, j_, k_ = pose_matrix[:3, :3]
x_, y_, z_ = pose_matrix[:3, 3]
assert torch.allclose(i, k_), (i, k_)
assert torch.allclose(j, -i_), (j, -i_)
assert torch.allclose(k, -j_), (k, -j_)
return pose_matrix
def unreal_to_right_pose(pose):
"""
Transform the pose from Unreal coordinate
system to the right-hand coordinate system.
pose: x, y, z, roll, pitch, yaw (6,) or (batch, 6)
"""
# batch = (pose.dim() == 2)
transform = torch.Tensor([
1, # x
-1, # y
1, # z
1, # roll
-1, # pitch
-1 # yaw -> Unreal uses left rotation for yaw
])
# if batch:
# transform = transform.unsqueeze(0)
return pose * transform
def pose_to_matrix(pose):
"""
Builds a homogeneous pose matrix out of
the pose vector.
(4, 4)
pose: x, y, z, roll, pitch, yaw (6,) or (B, 6)
"""
# Asserts
assert pose.dim() in {1, 2}
if pose.dim() == 1:
assert pose.size(0) == 6
elif pose.dim() == 2:
assert pose.size(1) == 6
# If it is a batch, do it recursively
if pose.dim() == 2:
poses = pose
return torch.stack(tuple(map(pose_to_matrix, poses)), dim=0) # (B, 4, 4)
pose = pose.clone()
roll, pitch, yaw = deg2rad(pose[3:])
R = euler_matrix(roll, pitch, yaw)
P = R.copy()
P[:3, 3] = pose[:3]
return torch.tensor(P, dtype=torch.float32) # (4, 4)
def camera_transform(pose0, pose1, camera_local, forward=True):
"""
Calculates the transform between two poses in the
camera frame: R and t.
forward: pose0 -> pose1
pose0: x, y, z, roll, pitch, yaw (6,) or (B, 6) in meters and degrees in Unreal frame
pose1: x, y, z, roll, pitch, yaw (6,) or (B, 6) in meters and degrees in Unreal frame
camera_local: x, y, z, roll, pitch, yaw (6,)
"""
batch = (pose0.dim() == 2)
# Forward or backward transform?
if not forward:
return camera_transform(pose1, pose0, camera_local)
# Convert weird Unreal coordinate system to the right coordinate system
pose0 = unreal_to_right_pose(pose0)
pose1 = unreal_to_right_pose(pose1)
camera_local = unreal_to_right_pose(camera_local)
# Build pose matrices
P0 = pose_to_matrix(pose0)
P1 = pose_to_matrix(pose1)
C = pose_to_matrix(camera_local)
C0 = P0 @ C # Global pose of the previous camera # (4 x 4) * (4 x 4)
C1 = P1 @ C # Global pose of the current camera
C0_local = torch.eye(4) # Previous camera pose in the previous camera's frame (identity)
C1_local = C0.inverse() @ C1 # Current camera pose in the previous camera's frame
# Move cameras into camera coordinate system
C0_local = to_camera_frame(C0_local)
C1_local = to_camera_frame(C1_local)
# Get the transform from C0 to C1
M = C1_local @ C0_local.inverse()
if batch:
t = M[:, :4, 3].clone()
R = M.clone()
R[:, :3, 3] = 0
return R[:, :-1, :-1], t[:, :-1]
else:
t = M[:4, 3].clone()
R = M.clone()
R[:3, 3] = 0
return R[:-1, :-1], t[:-1]
def calculate_egomotion_flow(R, t, z, K, K_inv=None):
"""
Calculates the optical flow induced by ego-motion.
Arguments (all torch.Tensors):
R: rotation matrix (3, 3) or (B, 3, 3)
t: translation (3,) or (B, 3)
z: current depth (1, H, W) in meters or (B, 1, H, W)
K: camera intrinsic matrix (3, 3)
K_inv (optional): inverse of camera instrinsic matrix (3, 3) or (B, 3, 3)
"""
batch = (R.dim() == 3)
R = R.to(z.device)
t = t.to(z.device)
# Get height and width
if z.dim() == 4:
_, _, H, W = z.size()
elif z.dim() == 3:
_, H, W = z.size()
# Calculate the inverse if not provided
if K_inv is None:
K_inv = K.inverse()
# Generate a grid of pixels coordinates
X = generate_pixel_grid(H, W).to(z.device) # [3, W, H]
# Pixel rotation
pre_C = K @ R @ K_inv
# Pixel translation
if batch:
B = R.size(0)
T = torch.ones(B, 3, W, H).to(z.device) * t.view(-1, 3, 1, 1)
else:
T = torch.ones(3, W, H).to(z.device) * t.view(3, 1, 1)
z = torch.clamp(z, min=1e-12) # Avoid division by 0
l = T / (z.transpose(1, 2) if not batch else z.transpose(2, 3)) # [1, W, H]
# Transform the pixels
X_ = torch.tensordot(pre_C, X, dims=1)
if batch:
if K.dim() == 3: # Intrinsics also provided in a batch [B, 3, 3]
B, _, W, H = l.size()
l = l.view(B, 3, -1) # [B, 3, W * H]
Kl = K @ l # [B, 3, W * H]
X_ = X_ + Kl.view(B, 3, W, H)
else:
X_ = X_ + torch.tensordot(K, l, dims=([1], [1])).transpose(0, 1)
else:
X_ = X_ + torch.tensordot(K, l, dims=1)
# Pixels: homogenous -> Cartesian
if batch:
denominator = X_[:, 2, None, :, :]
else:
denominator = X_[2, :, :]
denominator[denominator == 0.] = denominator[denominator == 0.] + 1e-8
X_ = X_ / denominator
# Calculate the optical flow
egoflow = X_ - X
# Optical flow: remove the homogenous channel
if batch:
egoflow = egoflow[:, :2, :, :]
return egoflow, X_[:, :2, :, :] # [2, W, H]
else:
egoflow = egoflow[:2, :, :]
return egoflow, X_[:2, :, :] # [2, W, H]
def warp_image(image, pixels, mode="bilinear", padding="zeros", eps=0.2):
"""
Warps the given image using the specified pixel coordinates.
image: (3, H, W) or (?, 3, H, W)
pixels: (2, W, H) or (?, 2, W, H)
"""
squeeze_later = False
if image.dim() == 3:
squeeze_later = True
image = image.unsqueeze(0)
if pixels.dim() == 3:
pixels = pixels.unsqueeze(0)
# [0, SIZE] -> [-1, 1]
_, _, H, W = image.size()
normalization = torch.FloatTensor([2 / (W - 1), 2 / (H - 1)]).unsqueeze(1).unsqueeze(2).to(pixels.device)
pixels = pixels * normalization - 1
pixels = torch.clamp(pixels, min=-1. - eps, max=1 + eps)
# [1, 2, W, H] -> [1, H, W, 2]
pixels = pixels.permute(0, 3, 2, 1)
warped = F.grid_sample(image, pixels.to(image.device), mode=mode, padding_mode=padding)
mask = pixels.ge(-1) & pixels.le(1)
mask = (mask[:, :, :, 0] & mask[:, :, :, 1]).float().unsqueeze(1)
if squeeze_later:
warped = warped.squeeze(0)
mask = mask.squeeze(0) if mask is not None else None
return warped, mask