Spaces:
Sleeping
Sleeping
File size: 9,454 Bytes
947db12 |
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 |
from typing import List, Optional, Tuple
import numpy as np
import torch
from torch.nn import functional as F
def get_position_map_from_depth(depth, mask, intrinsics, extrinsics, image_wh=None):
"""Compute the position map from the depth map and the camera parameters for a batch of views.
Args:
depth (torch.Tensor): The depth maps with the shape (B, H, W, 1).
mask (torch.Tensor): The masks with the shape (B, H, W, 1).
intrinsics (torch.Tensor): The camera intrinsics matrices with the shape (B, 3, 3).
extrinsics (torch.Tensor): The camera extrinsics matrices with the shape (B, 4, 4).
image_wh (Tuple[int, int]): The image width and height.
Returns:
torch.Tensor: The position maps with the shape (B, H, W, 3).
"""
if image_wh is None:
image_wh = depth.shape[2], depth.shape[1]
B, H, W, _ = depth.shape
depth = depth.squeeze(-1)
u_coord, v_coord = torch.meshgrid(
torch.arange(image_wh[0]), torch.arange(image_wh[1]), indexing="xy"
)
u_coord = u_coord.type_as(depth).unsqueeze(0).expand(B, -1, -1)
v_coord = v_coord.type_as(depth).unsqueeze(0).expand(B, -1, -1)
# Compute the position map by back-projecting depth pixels to 3D space
x = (
(u_coord - intrinsics[:, 0, 2].unsqueeze(-1).unsqueeze(-1))
* depth
/ intrinsics[:, 0, 0].unsqueeze(-1).unsqueeze(-1)
)
y = (
(v_coord - intrinsics[:, 1, 2].unsqueeze(-1).unsqueeze(-1))
* depth
/ intrinsics[:, 1, 1].unsqueeze(-1).unsqueeze(-1)
)
z = depth
# Concatenate to form the 3D coordinates in the camera frame
camera_coords = torch.stack([x, y, z], dim=-1)
# Apply the extrinsic matrix to get coordinates in the world frame
coords_homogeneous = torch.nn.functional.pad(
camera_coords, (0, 1), "constant", 1.0
) # Add a homogeneous coordinate
world_coords = torch.matmul(
coords_homogeneous.view(B, -1, 4), extrinsics.transpose(1, 2)
).view(B, H, W, 4)
# Apply the mask to the position map
position_map = world_coords[..., :3] * mask
return position_map
def get_position_map_from_depth_ortho(
depth, mask, extrinsics, ortho_scale, image_wh=None
):
"""Compute the position map from the depth map and the camera parameters for a batch of views
using orthographic projection with a given ortho_scale.
Args:
depth (torch.Tensor): The depth maps with the shape (B, H, W, 1).
mask (torch.Tensor): The masks with the shape (B, H, W, 1).
extrinsics (torch.Tensor): The camera extrinsics matrices with the shape (B, 4, 4).
ortho_scale (torch.Tensor): The scaling factor for the orthographic projection with the shape (B, 1, 1, 1).
image_wh (Tuple[int, int]): Optional. The image width and height.
Returns:
torch.Tensor: The position maps with the shape (B, H, W, 3).
"""
if image_wh is None:
image_wh = depth.shape[2], depth.shape[1]
B, H, W, _ = depth.shape
depth = depth.squeeze(-1)
# Generating grid of coordinates in the image space
u_coord, v_coord = torch.meshgrid(
torch.arange(0, image_wh[0]), torch.arange(0, image_wh[1]), indexing="xy"
)
u_coord = u_coord.type_as(depth).unsqueeze(0).expand(B, -1, -1)
v_coord = v_coord.type_as(depth).unsqueeze(0).expand(B, -1, -1)
# Compute the position map using orthographic projection with ortho_scale
x = (u_coord - image_wh[0] / 2) / ortho_scale / image_wh[0]
y = (v_coord - image_wh[1] / 2) / ortho_scale / image_wh[1]
z = depth
# Concatenate to form the 3D coordinates in the camera frame
camera_coords = torch.stack([x, y, z], dim=-1)
# Apply the extrinsic matrix to get coordinates in the world frame
coords_homogeneous = torch.nn.functional.pad(
camera_coords, (0, 1), "constant", 1.0
) # Add a homogeneous coordinate
world_coords = torch.matmul(
coords_homogeneous.view(B, -1, 4), extrinsics.transpose(1, 2)
).view(B, H, W, 4)
# Apply the mask to the position map
position_map = world_coords[..., :3] * mask
return position_map
def get_opencv_from_blender(matrix_world, fov=None, image_size=None):
# convert matrix_world to opencv format extrinsics
opencv_world_to_cam = matrix_world.inverse()
opencv_world_to_cam[1, :] *= -1
opencv_world_to_cam[2, :] *= -1
R, T = opencv_world_to_cam[:3, :3], opencv_world_to_cam[:3, 3]
if fov is None: # orthographic camera
return R, T
R, T = R.unsqueeze(0), T.unsqueeze(0)
# convert fov to opencv format intrinsics
focal = 1 / np.tan(fov / 2)
intrinsics = np.diag(np.array([focal, focal, 1])).astype(np.float32)
opencv_cam_matrix = (
torch.from_numpy(intrinsics).unsqueeze(0).float().to(matrix_world.device)
)
opencv_cam_matrix[:, :2, -1] += torch.tensor([image_size / 2, image_size / 2]).to(
matrix_world.device
)
opencv_cam_matrix[:, [0, 1], [0, 1]] *= image_size / 2
return R, T, opencv_cam_matrix
def get_ray_directions(
H: int,
W: int,
focal: float,
principal: Optional[Tuple[float, float]] = None,
use_pixel_centers: bool = True,
) -> torch.Tensor:
"""
Get ray directions for all pixels in camera coordinate.
Args:
H, W, focal, principal, use_pixel_centers: image height, width, focal length, principal point and whether use pixel centers
Outputs:
directions: (H, W, 3), the direction of the rays in camera coordinate
"""
pixel_center = 0.5 if use_pixel_centers else 0
cx, cy = W / 2, H / 2 if principal is None else principal
i, j = torch.meshgrid(
torch.arange(W, dtype=torch.float32) + pixel_center,
torch.arange(H, dtype=torch.float32) + pixel_center,
indexing="xy",
)
directions = torch.stack(
[(i - cx) / focal, -(j - cy) / focal, -torch.ones_like(i)], -1
)
return F.normalize(directions, dim=-1)
def get_rays(
directions: torch.Tensor, c2w: torch.Tensor
) -> Tuple[torch.Tensor, torch.Tensor]:
"""
Get ray origins and directions from camera coordinates to world coordinates
Args:
directions: (H, W, 3) ray directions in camera coordinates
c2w: (4, 4) camera-to-world transformation matrix
Outputs:
rays_o, rays_d: (H, W, 3) ray origins and directions in world coordinates
"""
# Rotate ray directions from camera coordinate to the world coordinate
rays_d = directions @ c2w[:3, :3].T
rays_o = c2w[:3, 3].expand(rays_d.shape)
return rays_o, rays_d
def compute_plucker_embed(
c2w: torch.Tensor, image_width: int, image_height: int, focal: float
) -> torch.Tensor:
"""
Computes Plucker coordinates for a camera.
Args:
c2w: (4, 4) camera-to-world transformation matrix
image_width: Image width
image_height: Image height
focal: Focal length of the camera
Returns:
plucker: (6, H, W) Plucker embedding
"""
directions = get_ray_directions(image_height, image_width, focal)
rays_o, rays_d = get_rays(directions, c2w)
# Cross product to get Plucker coordinates
cross = torch.cross(rays_o, rays_d, dim=-1)
plucker = torch.cat((rays_d, cross), dim=-1)
return plucker.permute(2, 0, 1)
def get_plucker_embeds_from_cameras(
c2w: List[torch.Tensor], fov: List[float], image_size: int
) -> torch.Tensor:
"""
Given lists of camera transformations and fov, returns the batched plucker embeddings.
Args:
c2w: list of camera-to-world transformation matrices
fov: list of field of view values
image_size: size of the image
Returns:
plucker_embeds: (B, 6, H, W) batched plucker embeddings
"""
plucker_embeds = []
for cam_matrix, cam_fov in zip(c2w, fov):
focal = 0.5 * image_size / np.tan(0.5 * cam_fov)
plucker = compute_plucker_embed(cam_matrix, image_size, image_size, focal)
plucker_embeds.append(plucker)
return torch.stack(plucker_embeds)
def get_plucker_embeds_from_cameras_ortho(
c2w: List[torch.Tensor], ortho_scale: List[float], image_size: int
):
"""
Given lists of camera transformations and fov, returns the batched plucker embeddings.
Parameters:
c2w: list of camera-to-world transformation matrices
fov: list of field of view values
image_size: size of the image
Returns:
plucker_embeds: plucker embeddings (B, 6, H, W)
"""
plucker_embeds = []
# compute pairwise mask and plucker embeddings
for cam_matrix, scale in zip(c2w, ortho_scale):
# blender to opencv to pytorch3d
R, T = get_opencv_from_blender(cam_matrix)
cam_pos = -R.T @ T
view_dir = R.T @ torch.tensor([0, 0, 1]).float().to(cam_matrix.device)
# normalize camera position
cam_pos = F.normalize(cam_pos, dim=0)
plucker = torch.concat([view_dir, cam_pos])
plucker = plucker.unsqueeze(-1).unsqueeze(-1).repeat(1, image_size, image_size)
plucker_embeds.append(plucker)
plucker_embeds = torch.stack(plucker_embeds)
return plucker_embeds
|