import matplotlib.pyplot as plt
+from diffdrr.drr import DRR
+from tqdm import tqdm
+
+
+
+
+
+
+
+
+calibration
+Rigid transforms with camera calibration matrices
+An X-ray C-arm can be modeled as a pinhole camera with its own extrinsic and intrinsic matrices. This module provides utilities for parsing these matrices and working with rigid transforms.
+Rigid transformations
+We represent rigid transforms as \(4 \times 4\) matrices (following the right-handed convention of PyTorch3D),
\[\begin{equation} +\begin{bmatrix} + \mathbf R^T & \mathbf 0 \\ + \mathbf t^T & 1 +\end{bmatrix} +\in \mathbf{SE}(3) \,, +\end{equation}\]
+where \(\mathbf R \in \mathbf{SO}(3)\) is a rotation matrix and \(\mathbf t\in \mathbb R^3\) represents a translation.
+Note that since rotation matrices are orthogonal, we have a simple closed-form equation for the inverse: \[\begin{equation} +\begin{bmatrix} + \mathbf R^T & \mathbf 0 \\ + \mathbf t^T & 1 +\end{bmatrix}^{-1} = +\begin{bmatrix} + \mathbf R & \mathbf 0 \\ + -\mathbf R \mathbf t & 1 +\end{bmatrix} \,. +\end{equation}\]
+For convenience, we add a wrapper of pytorch3d.transforms.Transform3d that can be construced from a (batched) rotation matrix and translation vector. This module also includes the closed-form inverse specific to rigid transforms.
+ +
RigidTransform
++++RigidTransform (R:jaxtyping.Float[Tensor,'...'], + t:jaxtyping.Float[Tensor,'...3'], + parameterization:str='matrix', + convention:Optional[str]=None, device=None, + dtype=torch.float32)
Wrapper of pytorch3d.transforms.Transform3d with extra functionalities.
++ +
convert
++++convert (transform, input_parameterization, output_parameterization, + input_convention=None, output_convention=None)
Convert between representations of SE(3).
+Computing a perspective projection
+Given an extrinsic and intrinsic camera matrix, we can compute the perspective projection of a batch of points. This is used for computing where fiducials in world coordinates get mapped onto the image plane.
+ +
perspective_projection
++++perspective_projection (extrinsic:__main__.RigidTransform, + intrinsic:jaxtyping.Float[Tensor,'33'], + x:jaxtyping.Float[Tensor,'bn3'])
| + | Type | +Details | +
|---|---|---|
| extrinsic | +RigidTransform | +Extrinsic camera matrix (world to camera) | +
| intrinsic | +Float[Tensor, ‘3 3’] | +Intrinsic camera matrix (camera to image) | +
| x | +Float[Tensor, ‘b n 3’] | +World coordinates | +
| Returns | +Float[Tensor, ‘b n 2’] | ++ |
