File size: 5,884 Bytes
2568013 |
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 |
import cv2
import numpy as np
import torch
from jaxtyping import Float
from torch import Tensor
import torch.nn.functional as F
def decompose_extrinsic_RT(E: torch.Tensor):
"""
Decompose the standard extrinsic matrix into RT.
Batched I/O.
"""
return E[:, :3, :]
def compose_extrinsic_RT(RT: torch.Tensor):
"""
Compose the standard form extrinsic matrix from RT.
Batched I/O.
"""
return torch.cat([
RT,
torch.tensor([[[0, 0, 0, 1]]], dtype=RT.dtype, device=RT.device).repeat(RT.shape[0], 1, 1)
], dim=1)
def camera_normalization(pivotal_pose: torch.Tensor, poses: torch.Tensor):
# [1, 4, 4], [N, 4, 4]
canonical_camera_extrinsics = torch.tensor([[
[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1],
]], dtype=torch.float32, device=pivotal_pose.device)
pivotal_pose_inv = torch.inverse(pivotal_pose)
camera_norm_matrix = torch.bmm(canonical_camera_extrinsics, pivotal_pose_inv)
# normalize all views
poses = torch.bmm(camera_norm_matrix.repeat(poses.shape[0], 1, 1), poses)
return poses
####### Pose update from delta
def rt2mat(R, T):
mat = np.eye(4)
mat[0:3, 0:3] = R
mat[0:3, 3] = T
return mat
def skew_sym_mat(x):
device = x.device
dtype = x.dtype
ssm = torch.zeros(3, 3, device=device, dtype=dtype)
ssm[0, 1] = -x[2]
ssm[0, 2] = x[1]
ssm[1, 0] = x[2]
ssm[1, 2] = -x[0]
ssm[2, 0] = -x[1]
ssm[2, 1] = x[0]
return ssm
def SO3_exp(theta):
device = theta.device
dtype = theta.dtype
W = skew_sym_mat(theta)
W2 = W @ W
angle = torch.norm(theta)
I = torch.eye(3, device=device, dtype=dtype)
if angle < 1e-5:
return I + W + 0.5 * W2
else:
return (
I
+ (torch.sin(angle) / angle) * W
+ ((1 - torch.cos(angle)) / (angle**2)) * W2
)
def V(theta):
dtype = theta.dtype
device = theta.device
I = torch.eye(3, device=device, dtype=dtype)
W = skew_sym_mat(theta)
W2 = W @ W
angle = torch.norm(theta)
if angle < 1e-5:
V = I + 0.5 * W + (1.0 / 6.0) * W2
else:
V = (
I
+ W * ((1.0 - torch.cos(angle)) / (angle**2))
+ W2 * ((angle - torch.sin(angle)) / (angle**3))
)
return V
def SE3_exp(tau):
dtype = tau.dtype
device = tau.device
rho = tau[:3]
theta = tau[3:]
R = SO3_exp(theta)
t = V(theta) @ rho
T = torch.eye(4, device=device, dtype=dtype)
T[:3, :3] = R
T[:3, 3] = t
return T
def update_pose(cam_trans_delta: Float[Tensor, "batch 3"],
cam_rot_delta: Float[Tensor, "batch 3"],
extrinsics: Float[Tensor, "batch 4 4"],
# original_rot: Float[Tensor, "batch 3 3"],
# original_trans: Float[Tensor, "batch 3"],
# converged_threshold: float = 1e-4
):
# extrinsics is c2w, here we need w2c as input, so we need to invert it
bs = cam_trans_delta.shape[0]
tau = torch.cat([cam_trans_delta, cam_rot_delta], dim=-1)
T_w2c = extrinsics.inverse()
new_w2c_list = []
for i in range(bs):
new_w2c = SE3_exp(tau[i]) @ T_w2c[i]
new_w2c_list.append(new_w2c)
new_w2c = torch.stack(new_w2c_list, dim=0)
return new_w2c.inverse()
# converged = tau.norm() < converged_threshold
# camera.update_RT(new_R, new_T)
#
# camera.cam_rot_delta.data.fill_(0)
# camera.cam_trans_delta.data.fill_(0)
# return converged
####### Pose estimation
def inv(mat):
""" Invert a torch or numpy matrix
"""
if isinstance(mat, torch.Tensor):
return torch.linalg.inv(mat)
if isinstance(mat, np.ndarray):
return np.linalg.inv(mat)
raise ValueError(f'bad matrix type = {type(mat)}')
def get_pnp_pose(pts3d, opacity, K, H, W, opacity_threshold=0.3):
pixels = np.mgrid[:W, :H].T.astype(np.float32)
pts3d = pts3d.cpu().numpy()
opacity = opacity.cpu().numpy()
K = K.cpu().numpy()
K[0, :] = K[0, :] * W
K[1, :] = K[1, :] * H
mask = opacity > opacity_threshold
res = cv2.solvePnPRansac(pts3d[mask], pixels[mask], K, None,
iterationsCount=100, reprojectionError=5, flags=cv2.SOLVEPNP_SQPNP)
success, R, T, inliers = res
assert success
R = cv2.Rodrigues(R)[0] # world to cam
pose = inv(np.r_[np.c_[R, T], [(0, 0, 0, 1)]]) # cam to world
return torch.from_numpy(pose.astype(np.float32))
def pose_auc(errors, thresholds):
sort_idx = np.argsort(errors)
errors = np.array(errors.copy())[sort_idx]
recall = (np.arange(len(errors)) + 1) / len(errors)
errors = np.r_[0.0, errors]
recall = np.r_[0.0, recall]
aucs = []
for t in thresholds:
last_index = np.searchsorted(errors, t)
r = np.r_[recall[:last_index], recall[last_index - 1]]
e = np.r_[errors[:last_index], t]
aucs.append(np.trapz(r, x=e) / t)
return aucs
def rotation_6d_to_matrix(d6):
"""
Converts 6D rotation representation by Zhou et al. [1] to rotation matrix
using Gram--Schmidt orthogonalization per Section B of [1]. Adapted from pytorch3d.
Args:
d6: 6D rotation representation, of size (*, 6)
Returns:
batch of rotation matrices of size (*, 3, 3)
[1] Zhou, Y., Barnes, C., Lu, J., Yang, J., & Li, H.
On the Continuity of Rotation Representations in Neural Networks.
IEEE Conference on Computer Vision and Pattern Recognition, 2019.
Retrieved from http://arxiv.org/abs/1812.07035
"""
a1, a2 = d6[..., :3], d6[..., 3:]
b1 = F.normalize(a1, dim=-1)
b2 = a2 - (b1 * a2).sum(-1, keepdim=True) * b1
b2 = F.normalize(b2, dim=-1)
b3 = torch.cross(b1, b2, dim=-1)
return torch.stack((b1, b2, b3), dim=-2) |