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# Copyright (c) 2023-2024, Zexin He
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import math
import torch
"""
R: (N, 3, 3)
T: (N, 3)
E: (N, 4, 4)
vector: (N, 3)
"""
def compose_extrinsic_R_T(R: torch.Tensor, T: torch.Tensor):
"""
Compose the standard form extrinsic matrix from R and T.
Batched I/O.
"""
RT = torch.cat((R, T.unsqueeze(-1)), dim=-1)
return compose_extrinsic_RT(RT)
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 decompose_extrinsic_R_T(E: torch.Tensor):
"""
Decompose the standard extrinsic matrix into R and T.
Batched I/O.
"""
RT = decompose_extrinsic_RT(E)
return RT[:, :, :3], RT[:, :, 3]
def decompose_extrinsic_RT(E: torch.Tensor):
"""
Decompose the standard extrinsic matrix into RT.
Batched I/O.
"""
return E[:, :3, :]
def camera_normalization_objaverse(normed_dist_to_center, poses: torch.Tensor, ret_transform: bool = False):
assert normed_dist_to_center is not None
pivotal_pose = compose_extrinsic_RT(poses[:1])
dist_to_center = pivotal_pose[:, :3, 3].norm(dim=-1, keepdim=True).item() \
if normed_dist_to_center == 'auto' else normed_dist_to_center
# compute camera norm (new version)
canonical_camera_extrinsics = torch.tensor([[
[1, 0, 0, 0],
[0, 0, -1, -dist_to_center],
[0, 1, 0, 0],
[0, 0, 0, 1],
]], dtype=torch.float32)
pivotal_pose_inv = torch.inverse(pivotal_pose)
camera_norm_matrix = torch.bmm(canonical_camera_extrinsics, pivotal_pose_inv)
# normalize all views
poses = compose_extrinsic_RT(poses)
poses = torch.bmm(camera_norm_matrix.repeat(poses.shape[0], 1, 1), poses)
poses = decompose_extrinsic_RT(poses)
if ret_transform:
return poses, camera_norm_matrix.squeeze(dim=0)
return poses
def get_normalized_camera_intrinsics(intrinsics: torch.Tensor):
"""
intrinsics: (N, 3, 2), [[fx, fy], [cx, cy], [width, height]]
Return batched fx, fy, cx, cy
"""
fx, fy = intrinsics[:, 0, 0], intrinsics[:, 0, 1]
cx, cy = intrinsics[:, 1, 0], intrinsics[:, 1, 1]
width, height = intrinsics[:, 2, 0], intrinsics[:, 2, 1]
fx, fy = fx / width, fy / height
cx, cy = cx / width, cy / height
return fx, fy, cx, cy
def build_camera_principle(RT: torch.Tensor, intrinsics: torch.Tensor):
"""
RT: (N, 3, 4)
intrinsics: (N, 3, 2), [[fx, fy], [cx, cy], [width, height]]
"""
fx, fy, cx, cy = get_normalized_camera_intrinsics(intrinsics)
return torch.cat([
RT.reshape(-1, 12),
fx.unsqueeze(-1), fy.unsqueeze(-1), cx.unsqueeze(-1), cy.unsqueeze(-1),
], dim=-1)
def build_camera_standard(RT: torch.Tensor, intrinsics: torch.Tensor):
"""
RT: (N, 3, 4)
intrinsics: (N, 3, 2), [[fx, fy], [cx, cy], [width, height]]
"""
E = compose_extrinsic_RT(RT)
fx, fy, cx, cy = get_normalized_camera_intrinsics(intrinsics)
I = torch.stack([
torch.stack([fx, torch.zeros_like(fx), cx], dim=-1),
torch.stack([torch.zeros_like(fy), fy, cy], dim=-1),
torch.tensor([[0, 0, 1]], dtype=torch.float32, device=RT.device).repeat(RT.shape[0], 1),
], dim=1)
return torch.cat([
E.reshape(-1, 16),
I.reshape(-1, 9),
], dim=-1)
def center_looking_at_camera_pose(
camera_position: torch.Tensor, look_at: torch.Tensor = None, up_world: torch.Tensor = None,
device: torch.device = torch.device('cpu'),
):
"""
camera_position: (M, 3)
look_at: (3)
up_world: (3)
return: (M, 3, 4)
"""
# by default, looking at the origin and world up is pos-z
if look_at is None:
look_at = torch.tensor([0, 0, 0], dtype=torch.float32, device=device)
if up_world is None:
up_world = torch.tensor([0, 0, 1], dtype=torch.float32, device=device)
look_at = look_at.unsqueeze(0).repeat(camera_position.shape[0], 1)
up_world = up_world.unsqueeze(0).repeat(camera_position.shape[0], 1)
z_axis = camera_position - look_at
z_axis = z_axis / z_axis.norm(dim=-1, keepdim=True)
x_axis = torch.cross(up_world, z_axis)
x_axis = x_axis / x_axis.norm(dim=-1, keepdim=True)
y_axis = torch.cross(z_axis, x_axis)
y_axis = y_axis / y_axis.norm(dim=-1, keepdim=True)
extrinsics = torch.stack([x_axis, y_axis, z_axis, camera_position], dim=-1)
return extrinsics
def surrounding_views_linspace(n_views: int, radius: float = 2.0, height: float = 0.8, device: torch.device = torch.device('cpu')):
"""
n_views: number of surrounding views
radius: camera dist to center
height: height of the camera
return: (M, 3, 4)
"""
assert n_views > 0
assert radius > 0
theta = torch.linspace(-torch.pi / 2, 3 * torch.pi / 2, n_views, device=device)
projected_radius = math.sqrt(radius ** 2 - height ** 2)
x = torch.cos(theta) * projected_radius
y = torch.sin(theta) * projected_radius
z = torch.full((n_views,), height, device=device)
camera_positions = torch.stack([x, y, z], dim=1)
extrinsics = center_looking_at_camera_pose(camera_positions, device=device)
return extrinsics
def create_intrinsics(
f: float,
c: float = None, cx: float = None, cy: float = None,
w: float = 1., h: float = 1.,
dtype: torch.dtype = torch.float32,
device: torch.device = torch.device('cpu'),
):
"""
return: (3, 2)
"""
fx = fy = f
if c is not None:
assert cx is None and cy is None, "c and cx/cy cannot be used together"
cx = cy = c
else:
assert cx is not None and cy is not None, "cx/cy must be provided when c is not provided"
fx, fy, cx, cy, w, h = fx/w, fy/h, cx/w, cy/h, 1., 1.
intrinsics = torch.tensor([
[fx, fy],
[cx, cy],
[w, h],
], dtype=dtype, device=device)
return intrinsics
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