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"""Implementation of the pinhole, simple radial, and simple divisional camera models."""
from typing import Tuple
import torch
from siclib.geometry.base_camera import BaseCamera
from siclib.utils.tensor import autocast
# flake8: noqa: E741
# mypy: ignore-errors
class Pinhole(BaseCamera):
"""Implementation of the pinhole camera model."""
def distort(self, p2d: torch.Tensor, return_scale: bool = False) -> Tuple[torch.Tensor]:
"""Distort normalized 2D coordinates."""
if return_scale:
return p2d.new_ones(p2d.shape[:-1] + (1,))
return p2d, p2d.new_ones((p2d.shape[0], 1)).bool()
def J_distort(self, p2d: torch.Tensor, wrt: str = "pts") -> torch.Tensor:
"""Jacobian of the distortion function."""
if wrt == "pts":
return torch.eye(2, device=p2d.device, dtype=p2d.dtype).expand(p2d.shape[:-1] + (2, 2))
else:
raise ValueError(f"Unknown wrt: {wrt}")
def undistort(self, pts: torch.Tensor) -> Tuple[torch.Tensor]:
"""Undistort normalized 2D coordinates."""
return pts, pts.new_ones((pts.shape[0], 1)).bool()
def J_undistort(self, p2d: torch.Tensor, wrt: str = "pts") -> torch.Tensor:
"""Jacobian of the undistortion function."""
if wrt == "pts":
return torch.eye(2, device=p2d.device, dtype=p2d.dtype).expand(p2d.shape[:-1] + (2, 2))
else:
raise ValueError(f"Unknown wrt: {wrt}")
class SimpleRadial(BaseCamera):
"""Implementation of the simple radial camera model."""
@property
def dist(self) -> torch.Tensor:
"""Distortion parameters, with shape (..., 1)."""
return self._data[..., 6:]
@property
def k1(self) -> torch.Tensor:
"""Distortion parameters, with shape (...)."""
return self._data[..., 6]
@property
def k1_hat(self) -> torch.Tensor:
"""Distortion parameters, with shape (...)."""
return self.k1 / (self.f[..., 1] / self.size[..., 1]) ** 2
def update_dist(self, delta: torch.Tensor, dist_range: Tuple[float, float] = (-0.7, 0.7)):
"""Update the self parameters after changing the k1 distortion parameter."""
delta_dist = self.new_ones(self.dist.shape) * delta
dist = (self.dist + delta_dist).clamp(*dist_range)
data = torch.cat([self.size, self.f, self.c, dist], -1)
return self.__class__(data)
@autocast
def check_valid(self, p2d: torch.Tensor) -> torch.Tensor:
"""Check if the distorted points are valid."""
return p2d.new_ones(p2d.shape[:-1]).bool()
def distort(self, p2d: torch.Tensor, return_scale: bool = False) -> Tuple[torch.Tensor]:
"""Distort normalized 2D coordinates and check for validity of the distortion model."""
r2 = torch.sum(p2d**2, -1, keepdim=True)
radial = 1 + self.k1[..., None, None] * r2
if return_scale:
return radial, None
return p2d * radial, self.check_valid(p2d)
def J_distort(self, p2d: torch.Tensor, wrt: str = "pts"):
"""Jacobian of the distortion function."""
k1 = self.k1[..., None, None]
r2 = torch.sum(p2d**2, -1, keepdim=True)
if wrt == "pts": # (..., 2, 2)
radial = 1 + k1 * r2
ppT = torch.einsum("...i,...j->...ij", p2d, p2d) # (..., 2, 2)
return (2 * k1 * ppT) + torch.diag_embed(radial.expand(radial.shape[:-1] + (2,)))
elif wrt == "dist": # (..., 2)
return r2 * p2d
elif wrt == "scale2dist": # (..., 1)
return r2
elif wrt == "scale2pts": # (..., 2)
return 2 * k1 * p2d
else:
return super().J_distort(p2d, wrt)
@autocast
def undistort(self, p2d: torch.Tensor) -> Tuple[torch.Tensor]:
"""Undistort normalized 2D coordinates and check for validity of the distortion model."""
b1 = -self.k1[..., None, None]
r2 = torch.sum(p2d**2, -1, keepdim=True)
radial = 1 + b1 * r2
return p2d * radial, self.check_valid(p2d)
@autocast
def J_undistort(self, p2d: torch.Tensor, wrt: str = "pts") -> torch.Tensor:
"""Jacobian of the undistortion function."""
b1 = -self.k1[..., None, None]
r2 = torch.sum(p2d**2, -1, keepdim=True)
if wrt == "dist":
return -r2 * p2d
elif wrt == "pts":
radial = 1 + b1 * r2
ppT = torch.einsum("...i,...j->...ij", p2d, p2d) # (..., 2, 2)
return (2 * b1[..., None] * ppT) + torch.diag_embed(
radial.expand(radial.shape[:-1] + (2,))
)
else:
return super().J_undistort(p2d, wrt)
def J_up_projection_offset(self, p2d: torch.Tensor, wrt: str = "uv") -> torch.Tensor:
"""Jacobian of the up-projection offset."""
if wrt == "uv": # (..., 2, 2)
return torch.diag_embed((2 * self.k1[..., None, None]).expand(p2d.shape[:-1] + (2,)))
elif wrt == "dist":
return 2 * p2d # (..., 2)
else:
return super().J_up_projection_offset(p2d, wrt)
class SimpleDivisional(BaseCamera):
"""Implementation of the simple divisional camera model."""
@property
def dist(self) -> torch.Tensor:
"""Distortion parameters, with shape (..., 1)."""
return self._data[..., 6:]
@property
def k1(self) -> torch.Tensor:
"""Distortion parameters, with shape (...)."""
return self._data[..., 6]
def update_dist(self, delta: torch.Tensor, dist_range: Tuple[float, float] = (-3.0, 3.0)):
"""Update the self parameters after changing the k1 distortion parameter."""
delta_dist = self.new_ones(self.dist.shape) * delta
dist = (self.dist + delta_dist).clamp(*dist_range)
data = torch.cat([self.size, self.f, self.c, dist], -1)
return self.__class__(data)
@autocast
def check_valid(self, p2d: torch.Tensor) -> torch.Tensor:
"""Check if the distorted points are valid."""
return p2d.new_ones(p2d.shape[:-1]).bool()
def distort(self, p2d: torch.Tensor, return_scale: bool = False) -> Tuple[torch.Tensor]:
"""Distort normalized 2D coordinates and check for validity of the distortion model."""
r2 = torch.sum(p2d**2, -1, keepdim=True)
radial = 1 - torch.sqrt((1 - 4 * self.k1[..., None, None] * r2).clamp(min=0))
denom = 2 * self.k1[..., None, None] * r2
ones = radial.new_ones(radial.shape)
radial = torch.where(denom == 0, ones, radial / denom.masked_fill(denom == 0, 1e6))
if return_scale:
return radial, None
return p2d * radial, self.check_valid(p2d)
def J_distort(self, p2d: torch.Tensor, wrt: str = "pts"):
"""Jacobian of the distortion function."""
r2 = torch.sum(p2d**2, -1, keepdim=True)
t0 = torch.sqrt((1 - 4 * self.k1[..., None, None] * r2).clamp(min=1e-6))
if wrt == "scale2pts": # (B, N, 2)
d1 = t0 * 2 * r2
d2 = self.k1[..., None, None] * r2**2
denom = d1 * d2
return p2d * (4 * d2 - (1 - t0) * d1) / denom.masked_fill(denom == 0, 1e6)
elif wrt == "scale2dist":
d1 = 2 * self.k1[..., None, None] * t0
d2 = 2 * r2 * self.k1[..., None, None] ** 2
denom = d1 * d2
return (2 * d2 - (1 - t0) * d1) / denom.masked_fill(denom == 0, 1e6)
else:
return super().J_distort(p2d, wrt)
@autocast
def undistort(self, p2d: torch.Tensor) -> Tuple[torch.Tensor]:
"""Undistort normalized 2D coordinates and check for validity of the distortion model."""
r2 = torch.sum(p2d**2, -1, keepdim=True)
denom = 1 + self.k1[..., None, None] * r2
radial = 1 / denom.masked_fill(denom == 0, 1e6)
return p2d * radial, self.check_valid(p2d)
def J_undistort(self, p2d: torch.Tensor, wrt: str = "pts") -> torch.Tensor:
"""Jacobian of the undistortion function."""
# return super().J_undistort(p2d, wrt)
r2 = torch.sum(p2d**2, -1, keepdim=True)
k1 = self.k1[..., None, None]
if wrt == "dist":
denom = (1 + k1 * r2) ** 2
return -r2 / denom.masked_fill(denom == 0, 1e6) * p2d
elif wrt == "pts":
t0 = 1 + k1 * r2
t0 = t0.masked_fill(t0 == 0, 1e6)
ppT = torch.einsum("...i,...j->...ij", p2d, p2d) # (..., 2, 2)
J = torch.diag_embed((1 / t0).expand(p2d.shape[:-1] + (2,)))
return J - 2 * k1[..., None] * ppT / t0[..., None] ** 2 # (..., N, 2, 2)
else:
return super().J_undistort(p2d, wrt)
def J_up_projection_offset(self, p2d: torch.Tensor, wrt: str = "uv") -> torch.Tensor:
"""Jacobian of the up-projection offset.
func(uv, dist) = 4 / (2 * norm2(uv)^2 * (1-4*k1*norm2(uv)^2)^0.5) * uv
- (1-(1-4*k1*norm2(uv)^2)^0.5) / (k1 * norm2(uv)^4) * uv
"""
k1 = self.k1[..., None, None]
r2 = torch.sum(p2d**2, -1, keepdim=True)
t0 = (1 - 4 * k1 * r2).clamp(min=1e-6)
t1 = torch.sqrt(t0)
if wrt == "dist":
denom = 4 * t0 ** (3 / 2)
denom = denom.masked_fill(denom == 0, 1e6)
J = 16 / denom
denom = r2 * t1 * k1
denom = denom.masked_fill(denom == 0, 1e6)
J = J - 2 / denom
denom = (r2 * k1) ** 2
denom = denom.masked_fill(denom == 0, 1e6)
J = J + (1 - t1) / denom
return J * p2d
elif wrt == "uv":
# ! unstable (gradient checker might fail), rewrite to use single division (by denom)
ppT = torch.einsum("...i,...j->...ij", p2d, p2d) # (..., 2, 2)
denom = 2 * r2 * t1
denom = denom.masked_fill(denom == 0, 1e6)
J = torch.diag_embed((4 / denom).expand(p2d.shape[:-1] + (2,)))
denom = 4 * t1 * r2**2
denom = denom.masked_fill(denom == 0, 1e6)
J = J - 16 / denom[..., None] * ppT
denom = 4 * r2 * t0 ** (3 / 2)
denom = denom.masked_fill(denom == 0, 1e6)
J = J + (32 * k1[..., None]) / denom[..., None] * ppT
denom = r2**2 * t1
denom = denom.masked_fill(denom == 0, 1e6)
J = J - 4 / denom[..., None] * ppT
denom = k1 * r2**3
denom = denom.masked_fill(denom == 0, 1e6)
J = J + (4 * (1 - t1) / denom)[..., None] * ppT
denom = k1 * r2**2
denom = denom.masked_fill(denom == 0, 1e6)
J = J - torch.diag_embed(((1 - t1) / denom).expand(p2d.shape[:-1] + (2,)))
return J
else:
return super().J_up_projection_offset(p2d, wrt)
camera_models = {
"pinhole": Pinhole,
"simple_radial": SimpleRadial,
"simple_divisional": SimpleDivisional,
}
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