pyxu-xrt 0.5

Pyxu X-Ray Transform Operators.

Pyxu X-Ray Transform Operators

pyxu_xrt provides Pyxu operators to compute samples of the X-Ray Transform in 2D and 3D.

The X-Ray Transform (XRT) of a function \(f: \mathbb{R}^{D} \to \mathbb{R}\) is defined as

\begin{equation*} \mathcal{P}[f](\mathbf{n}, \mathbf{t}) = \int_{\mathbb{R}} f(\mathbf{t} + \mathbf{n} \alpha) d\alpha, \end{equation*}

where \(\mathbf{n}\in \mathbb{S}^{D-1}\) and \(\mathbf{t} \in \mathbf{n}^{\perp}\). \(\mathcal{P}[f]\) hence denotes the set of line integrals of \(f\).

Two class of algorithms exist to evaluate the XRT:

• Fourier methods leverage the Fourier Slice Theorem (FST) to efficiently evaluate the XRT when multiple values of \(\mathbf{t}\) are desired for each \(\mathbf{n}\).

• Ray methods compute estimates of the XRT via quadrature rules by assuming \(f\) is piecewise constant on short intervals.

The operators in pyxu_xrt allow one to efficiently evaluate samples of the XRT assuming \(f\) is a pixelized image/volume where:

• the lower-left element of \(f\) is located at \(\mathbf{o} \in \mathbb{R}^{D}\),

• pixel dimensions are \(\mathbf{\Delta} \in \mathbb{R}_{+}^{D}\), i.e.

\begin{equation*} f(\mathbf{r}) = \sum_{\{\mathbf{q}\} \subset \mathbb{N}^{D}} \alpha_{\mathbf{q}} 1_{[\mathbf{0}, \mathbf{\Delta}]}(\mathbf{r} - \mathbf{q} \odot \mathbf{\Delta} - \mathbf{o}), \quad \alpha_{\mathbf{q}} \in \mathbb{R}. \end{equation*}

In the 2D case, the parametrization is best explained by the figure below:

Installation

You can install pyxu_xrt via pip:

pip install pyxu_xrt

The host system must have CUDA 11.x or 12.x installed to use the GPU. Similarly, using drjit-backed operators on the CPU requires LLVM. If problems arise, we provide Docker receipes to easily create Pyxu developer environments.

License

Distributed under the terms of the MIT license, pyxu_xrt is free and open source software.

Issues

If you encounter any problems, please file an issue along with a detailed description.