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from abc import ABC, abstractmethod
from dataclasses import dataclass
from typing import Optional, Tuple, Union
import numpy as np
import torch
from shap_e.rendering.view_data import ProjectiveCamera
@dataclass
class DifferentiableCamera(ABC):
"""
An object describing how a camera corresponds to pixels in an image.
"""
@abstractmethod
def camera_rays(self, coords: torch.Tensor) -> torch.Tensor:
"""
For every (x, y) coordinate in a rendered image, compute the ray of the
corresponding pixel.
:param coords: an [N x ... x 2] integer array of 2D image coordinates.
:return: an [N x ... x 2 x 3] array of [2 x 3] (origin, direction) tuples.
The direction should always be unit length.
"""
@abstractmethod
def resize_image(self, width: int, height: int) -> "DifferentiableCamera":
"""
Creates a new camera with the same intrinsics and direction as this one,
but with resized image dimensions.
"""
@dataclass
class DifferentiableProjectiveCamera(DifferentiableCamera):
"""
Implements a batch, differentiable, standard pinhole camera
"""
origin: torch.Tensor # [batch_size x 3]
x: torch.Tensor # [batch_size x 3]
y: torch.Tensor # [batch_size x 3]
z: torch.Tensor # [batch_size x 3]
width: int
height: int
x_fov: float
y_fov: float
def __post_init__(self):
assert self.x.shape[0] == self.y.shape[0] == self.z.shape[0] == self.origin.shape[0]
assert self.x.shape[1] == self.y.shape[1] == self.z.shape[1] == self.origin.shape[1] == 3
assert (
len(self.x.shape)
== len(self.y.shape)
== len(self.z.shape)
== len(self.origin.shape)
== 2
)
def resolution(self):
return torch.from_numpy(np.array([self.width, self.height], dtype=np.float32))
def fov(self):
return torch.from_numpy(np.array([self.x_fov, self.y_fov], dtype=np.float32))
def image_coords(self) -> torch.Tensor:
"""
:return: coords of shape (width * height, 2)
"""
pixel_indices = torch.arange(self.height * self.width)
coords = torch.stack(
[
pixel_indices % self.width,
torch.div(pixel_indices, self.width, rounding_mode="trunc"),
],
axis=1,
)
return coords
def camera_rays(self, coords: torch.Tensor) -> torch.Tensor:
# import pdb; pdb.set_trace()
batch_size, *shape, n_coords = coords.shape
assert n_coords == 2
assert batch_size == self.origin.shape[0]
flat = coords.view(batch_size, -1, 2)
res = self.resolution().to(flat.device)
fov = self.fov().to(flat.device)
fracs = (flat.float() / (res - 1)) * 2 - 1
fracs = fracs * torch.tan(fov / 2)
fracs = fracs.view(batch_size, -1, 2)
directions = (
self.z.view(batch_size, 1, 3)
+ self.x.view(batch_size, 1, 3) * fracs[:, :, :1]
+ self.y.view(batch_size, 1, 3) * fracs[:, :, 1:]
)
directions = directions / directions.norm(dim=-1, keepdim=True)
rays = torch.stack(
[
torch.broadcast_to(
self.origin.view(batch_size, 1, 3), [batch_size, directions.shape[1], 3]
),
directions,
],
dim=2,
)
return rays.view(batch_size, *shape, 2, 3)
def resize_image(self, width: int, height: int) -> "DifferentiableProjectiveCamera":
"""
Creates a new camera for the resized view assuming the aspect ratio does not change.
"""
assert width * self.height == height * self.width, "The aspect ratio should not change."
return DifferentiableProjectiveCamera(
origin=self.origin,
x=self.x,
y=self.y,
z=self.z,
width=width,
height=height,
x_fov=self.x_fov,
y_fov=self.y_fov,
)
@dataclass
class DifferentiableCameraBatch(ABC):
"""
Annotate a differentiable camera with a multi-dimensional batch shape.
"""
shape: Tuple[int]
flat_camera: DifferentiableCamera
def normalize(vec: torch.Tensor) -> torch.Tensor:
return vec / vec.norm(dim=-1, keepdim=True)
def project_out(vec1: torch.Tensor, vec2: torch.Tensor) -> torch.Tensor:
"""
Removes the vec2 component from vec1
"""
vec2 = normalize(vec2)
proj = (vec1 * vec2).sum(dim=-1, keepdim=True)
return vec1 - proj * vec2
def camera_orientation(toward: torch.Tensor, up: Optional[torch.Tensor] = None) -> torch.Tensor:
"""
:param toward: [batch_size x 3] unit vector from camera position to the object
:param up: Optional [batch_size x 3] specifying the physical up direction in the world frame.
:return: [batch_size x 3 x 3]
"""
if up is None:
up = torch.zeros_like(toward)
up[:, 2] = 1
assert len(toward.shape) == 2
assert toward.shape[1] == 3
assert len(up.shape) == 2
assert up.shape[1] == 3
z = toward / toward.norm(dim=-1, keepdim=True)
y = -normalize(project_out(up, toward))
x = torch.cross(y, z, dim=1)
return torch.stack([x, y, z], dim=1)
def projective_camera_frame(
origin: torch.Tensor,
toward: torch.Tensor,
camera_params: Union[ProjectiveCamera, DifferentiableProjectiveCamera],
) -> DifferentiableProjectiveCamera:
"""
Given the origin and the direction of a view, return a differentiable
projective camera with the given parameters.
TODO: We need to support the rotation of the camera frame about the
`toward` vector to fully implement 6 degrees of freedom.
"""
rot = camera_orientation(toward)
camera = DifferentiableProjectiveCamera(
origin=origin,
x=rot[:, 0],
y=rot[:, 1],
z=rot[:, 2],
width=camera_params.width,
height=camera_params.height,
x_fov=camera_params.x_fov,
y_fov=camera_params.y_fov,
)
return camera
@torch.no_grad()
def get_image_coords(width, height) -> torch.Tensor:
pixel_indices = torch.arange(height * width)
# torch throws warnings for pixel_indices // width
pixel_indices_div = torch.div(pixel_indices, width, rounding_mode="trunc")
coords = torch.stack([pixel_indices % width, pixel_indices_div], dim=1)
return coords
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