Spaces:
Sleeping
Sleeping
File size: 11,028 Bytes
e7bcdd2 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 | import torch
import numpy as np
import torch.nn.functional as F
from einops import rearrange
# ---------------------------------------------------------------------------
# General-purpose linear algebra utilities for camera matrices
# ---------------------------------------------------------------------------
def invert_SE3(transforms: torch.Tensor) -> torch.Tensor:
"""Invert a batch of 4×4 SE(3) matrices analytically."""
assert transforms.shape[-2:] == (4, 4)
Rinv = transforms[..., :3, :3].transpose(-1, -2)
out = torch.zeros_like(transforms)
out[..., :3, :3] = Rinv
out[..., :3, 3] = -torch.einsum("...ij,...j->...i", Rinv, transforms[..., :3, 3])
out[..., 3, 3] = 1.0
return out
# ---------------------------------------------------------------------------
# Ray generation related functions from camera parameters
# ---------------------------------------------------------------------------
def compute_plucmap(fxfycxcy, c2w, h, w):
"""Compute per-pixel Plucker ray maps from camera intrinsics and extrinsics.
Args:
fxfycxcy (torch.Tensor): Intrinsics [b, v, 4] as [fx, fy, cx, cy].
c2w (torch.Tensor): Camera-to-world matrices [b, v, 4, 4].
h (int): Image height in pixels.
w (int): Image width in pixels.
Returns:
ray_o (torch.Tensor): Ray origins with shape (b, v, 3, h, w).
ray_d (torch.Tensor): Normalized ray directions with shape (b, v, 3, h, w).
"""
b, v = fxfycxcy.size(0), fxfycxcy.size(1)
# Efficient meshgrid equivalent using broadcasting
idx_x = torch.arange(w, device=c2w.device)[None, :].expand(h, -1) # [h, w]
idx_y = torch.arange(h, device=c2w.device)[:, None].expand(-1, w) # [h, w]
idx_x = idx_x.flatten().expand(b * v, -1) # [b*v, h*w]
idx_y = idx_y.flatten().expand(b * v, -1) # [b*v, h*w]
fxfycxcy = fxfycxcy.reshape(b * v, 4) # [b*v, 4]
c2w = c2w.reshape(b * v, 4, 4) # [b*v, 4, 4]
x = (idx_x + 0.5 - fxfycxcy[:, 2:3]) / fxfycxcy[:, 0:1] # [b*v, h*w]
y = (idx_y + 0.5 - fxfycxcy[:, 3:4]) / fxfycxcy[:, 1:2] # [b*v, h*w]
z = torch.ones_like(x) # [b*v, h*w]
ray_d = torch.stack([x, y, z], dim=1) # [b*v, 3, h*w]
ray_d = torch.bmm(c2w[:, :3, :3], ray_d) # [b*v, 3, h*w]
ray_d = ray_d / torch.norm(ray_d, dim=1, keepdim=True) # [b*v, 3, h*w]
ray_o = c2w[:, :3, 3:4].expand(b * v, -1, h*w) # [b*v, 3, h*w]
ray_o = ray_o.reshape(b, v, 3, h, w) # [b, v, 3, h, w]
ray_d = ray_d.reshape(b, v, 3, h, w) # [b, v, 3, h, w]
return ray_o, ray_d
def compute_rays(fxfycxcy, c2w, h, w):
"""Compute per-pixel ray origins and directions, flattened across views and pixels.
Args:
fxfycxcy (torch.Tensor): Intrinsics [b, v, 4] as [fx, fy, cx, cy].
c2w (torch.Tensor): Camera-to-world matrices [b, v, 4, 4].
h (int): Image height in pixels.
w (int): Image width in pixels.
Returns:
ray_o (torch.Tensor): Ray origins with shape (b, v*h*w, 3).
ray_d (torch.Tensor): Normalized ray directions with shape (b, v*h*w, 3).
"""
b, v = fxfycxcy.size(0), fxfycxcy.size(1)
# Efficient meshgrid equivalent using broadcasting
idx_x = torch.arange(w, device=c2w.device)[None, :].expand(h, -1) # [h, w]
idx_y = torch.arange(h, device=c2w.device)[:, None].expand(-1, w) # [h, w]
idx_x = idx_x.flatten().expand(b * v, -1) # [b*v, h*w]
idx_y = idx_y.flatten().expand(b * v, -1) # [b*v, h*w]
fxfycxcy = fxfycxcy.reshape(b * v, 4) # [b*v, 4]
c2w = c2w.reshape(b * v, 4, 4) # [b*v, 4, 4]
x = (idx_x + 0.5 - fxfycxcy[:, 2:3]) / fxfycxcy[:, 0:1] # [b*v, h*w]
y = (idx_y + 0.5 - fxfycxcy[:, 3:4]) / fxfycxcy[:, 1:2] # [b*v, h*w]
z = torch.ones_like(x) # [b*v, h*w]
ray_d = torch.stack([x, y, z], dim=1) # [b*v, 3, h*w]
ray_d = torch.bmm(c2w[:, :3, :3], ray_d) # [b*v, 3, h*w]
ray_d = ray_d / torch.norm(ray_d, dim=1, keepdim=True) # [b*v, 3, h*w]
ray_o = c2w[:, :3, 3:4].expand(b * v, -1, h*w) # [b*v, 3, h*w]
ray_o = ray_o.reshape(b, v, 3, h, w) # [b, v, 3, h, w]
ray_d = ray_d.reshape(b, v, 3, h, w) # [b, v, 3, h, w]
ray_o = rearrange(ray_o, 'b v c h w -> b (v h w) c')
ray_d = rearrange(ray_d, 'b v c h w -> b (v h w) c')
return ray_o, ray_d
# ---------------------------------------------------------------------------
# Camera matrix (intrinsics, extrinsics) conversions
# ---------------------------------------------------------------------------
def fxfycxcy_to_K(fxfycxcy: torch.Tensor) -> torch.Tensor:
"""Build a 3x3 intrinsic matrix from a [..., 4] vector [fx, fy, cx, cy]."""
K = torch.zeros(*fxfycxcy.shape[:-1], 3, 3, dtype=fxfycxcy.dtype, device=fxfycxcy.device)
K[..., 0, 0] = fxfycxcy[..., 0]
K[..., 1, 1] = fxfycxcy[..., 1]
K[..., 0, 2] = fxfycxcy[..., 2]
K[..., 1, 2] = fxfycxcy[..., 3]
K[..., 2, 2] = 1.0
return K
def lift_K(Ks: torch.Tensor) -> torch.Tensor:
"""Embed 3×3 intrinsics matrices into homogeneous 4×4 matrices."""
assert Ks.shape[-2:] == (3, 3)
out = torch.zeros(Ks.shape[:-2] + (4, 4), device=Ks.device)
out[..., :3, :3] = Ks
out[..., 3, 3] = 1.0
return out
def invert_K(Ks: torch.Tensor) -> torch.Tensor:
"""Invert 3×3 camera intrinsics matrices (assumes no skew)."""
assert Ks.shape[-2:] == (3, 3)
out = torch.zeros_like(Ks)
out[..., 0, 0] = 1.0 / Ks[..., 0, 0]
out[..., 1, 1] = 1.0 / Ks[..., 1, 1]
out[..., 0, 2] = -Ks[..., 0, 2] / Ks[..., 0, 0]
out[..., 1, 2] = -Ks[..., 1, 2] / Ks[..., 1, 1]
out[..., 2, 2] = 1.0
return out
def extrinsics_to_44(ext: torch.Tensor) -> torch.Tensor:
"""Pad a (B, V, 3, 4) extrinsics tensor to (B, V, 4, 4) with a [0,0,0,1] bottom row.
Args:
ext (torch.Tensor): Extrinsics with shape (B, V, 3, 4) or (B, V, 4, 4).
Returns:
torch.Tensor: Extrinsics with shape (B, V, 4, 4).
"""
if ext.shape[-2] == 3:
B, V = ext.shape[:2]
out = torch.eye(
4,
device=ext.device,
dtype=ext.dtype
).expand(B, V, 4, 4).clone() # (B, V, 4, 4)
out[:, :, :3, :4] = ext
return out
return ext
def quat_to_mat(quaternions: torch.Tensor) -> torch.Tensor:
"""Convert rotations given as quaternions to rotation matrices.
Quaternion order is XYZW (scalar-last / ijkr convention).
Args:
quaternions (torch.Tensor): Quaternions with real part last,
as tensor of shape (..., 4).
Returns:
torch.Tensor: Rotation matrices as tensor of shape (..., 3, 3).
"""
i, j, k, r = torch.unbind(quaternions, -1)
# pyre-fixme[58]: `/` is not supported for operand types `float` and `Tensor`.
two_s = 2.0 / (quaternions * quaternions).sum(-1)
o = torch.stack(
(
1 - two_s * (j * j + k * k),
two_s * (i * j - k * r),
two_s * (i * k + j * r),
two_s * (i * j + k * r),
1 - two_s * (i * i + k * k),
two_s * (j * k - i * r),
two_s * (i * k - j * r),
two_s * (j * k + i * r),
1 - two_s * (i * i + j * j),
),
-1,
)
return o.reshape(quaternions.shape[:-1] + (3, 3))
def mat_to_quat(matrix: torch.Tensor) -> torch.Tensor:
"""Convert rotations given as rotation matrices to quaternions.
Args:
matrix (torch.Tensor): Rotation matrices as tensor of shape (..., 3, 3).
Returns:
torch.Tensor: Quaternions with real part last, as tensor of shape (..., 4).
Quaternion order is XYZW (scalar-last / ijkr convention).
"""
if matrix.size(-1) != 3 or matrix.size(-2) != 3:
raise ValueError(f"Invalid rotation matrix shape {matrix.shape}.")
batch_dim = matrix.shape[:-2]
m00, m01, m02, m10, m11, m12, m20, m21, m22 = torch.unbind(matrix.reshape(batch_dim + (9,)), dim=-1)
q_abs = _sqrt_positive_part(
torch.stack(
[
1.0 + m00 + m11 + m22,
1.0 + m00 - m11 - m22,
1.0 - m00 + m11 - m22,
1.0 - m00 - m11 + m22,
],
dim=-1,
)
)
# we produce the desired quaternion multiplied by each of r, i, j, k
quat_by_rijk = torch.stack(
[
# pyre-fixme[58]: `**` is not supported for operand types `Tensor` and
# `int`.
torch.stack([q_abs[..., 0] ** 2, m21 - m12, m02 - m20, m10 - m01], dim=-1),
# pyre-fixme[58]: `**` is not supported for operand types `Tensor` and
# `int`.
torch.stack([m21 - m12, q_abs[..., 1] ** 2, m10 + m01, m02 + m20], dim=-1),
# pyre-fixme[58]: `**` is not supported for operand types `Tensor` and
# `int`.
torch.stack([m02 - m20, m10 + m01, q_abs[..., 2] ** 2, m12 + m21], dim=-1),
# pyre-fixme[58]: `**` is not supported for operand types `Tensor` and
# `int`.
torch.stack([m10 - m01, m20 + m02, m21 + m12, q_abs[..., 3] ** 2], dim=-1),
],
dim=-2,
)
# We floor here at 0.1 but the exact level is not important; if q_abs is small,
# the candidate won't be picked.
flr = torch.tensor(0.1).to(dtype=q_abs.dtype, device=q_abs.device)
quat_candidates = quat_by_rijk / (2.0 * q_abs[..., None].max(flr))
# if not for numerical problems, quat_candidates[i] should be same (up to a sign),
# forall i; we pick the best-conditioned one (with the largest denominator)
out = quat_candidates[F.one_hot(q_abs.argmax(dim=-1), num_classes=4) > 0.5, :].reshape(batch_dim + (4,))
# Convert from rijk to ijkr
out = out[..., [1, 2, 3, 0]]
out = standardize_quaternion(out)
return out
def _sqrt_positive_part(x: torch.Tensor) -> torch.Tensor:
"""Return sqrt(max(0, x)) with a zero subgradient where x is 0."""
ret = torch.zeros_like(x)
positive_mask = x > 0
if torch.is_grad_enabled():
ret[positive_mask] = torch.sqrt(x[positive_mask])
else:
ret = torch.where(positive_mask, torch.sqrt(x), ret)
return ret
def standardize_quaternion(quaternions: torch.Tensor) -> torch.Tensor:
"""Convert a unit quaternion to a standard form where the real part is non-negative.
Args:
quaternions (torch.Tensor): Quaternions with real part last,
as tensor of shape (..., 4).
Returns:
torch.Tensor: Standardized quaternions as tensor of shape (..., 4).
"""
return torch.where(quaternions[..., 3:4] < 0, -quaternions, quaternions)
|