Naming

Classes, structs, types and functions are PascalCase.
- ..with the exception of functions that have different implementations for different hardware. In this case, the hardware type is appended in PascalCase after an underscore, e.g. FunctionName_HardwareType.
- Classes that are specific to one type of hardware have the hardware type appended in PascalCase without an underscore, e.g. ClassNameHardwareType.
Variables and namespaces are camelCase.
File names have the same rules as classes. When a file contains the implementation of a class, it should generally have the same name as that class.

Implementation conventions

Wherever possible, all functions and methods are:

made constexpr,
annotated with __host__ and __device__ for potential use in CUDA kernels (these macros are given empty definitions in include/Global.h when compiling as C++).

Cartesian coordinates

2D

In image data, the dimensions from largest to smallest are (Y, X), so the 1D index in a 2D array is given by width * Y + X.

3D

(X, Y, Z) is always right-handed.

In volume data, the origin is placed at the centre, and the dimensions from largest to smallest are (Z, Y, X), so the 1D index in a 3D array is given by width * height * Z + width * Y + X.

Polar coordinates

In 2D sinograms, lines in 2D space defined in polar coordinates are done so as follows:

The vector from the origin to the closest point on the line (which is therefor normal to the line) defines the line, and is parametrised by the following 2-vector:

(r, phi)

where

r is the signed length of the vector (the signed shortest distance between the line and the origin),
phi in (-pi/2, pi/2) is the angle anti-clockwise from the positive x-direction to the vector.

Spherical coordinates

In 3D sinograms, planes in 3D space defined in spherical coordinates are done so as follows:

The vector from the origin to the closest point on the plane (which is therefore normal to the plane) defines the plane, and is parametrised by the following 3-vector:

(r, theta, phi)

where

r is the signed length of the vector (the signed shortest distance between the plane and the origin),
theta in (-pi/2, pi/2) is the angle of an initial rotation of the vector, left-hand-rule about the y-axis, taking the vector's initial position to be from the origin to the point (r, 0, 0),
phi in (-pi/2, pi/2) is the angle of a second rotation of the vector, right-hand-rule about the z-axis.

Transformations and spaces

In a 2D/3D radiographic image registration problem, we define 'world' space as a 3D space containing:

the 2D fixed image, which exists on a 2D, finite plane
the moving 3D volume, and
the X-ray source, which is a single point.

The world coordinate system:

is Cartesian,
is centred on the centre of the fixed image, in the plane of the fixed image,
has axes in the following directions:
- $x$ is to the right in the fixed image, as viewed from the X-ray source,
- $y$ is up in the fixed image, as viewed from the X-ray source, and
- $z$ points towards the X-ray source.
is, as a result, right-handed in chirality,
has a scale 1mm in all directions.

Assuming no offset between the X-ray source and the centre of the fixed image, the position of the X-ray source will be $$ (0, \, 0, \, \mathrm{source}\ \mathrm{distance}) $$ or, for a centre-offset of $(s_x, \, s_y)$: $$ (s_x, \, s_y, \, \mathrm{source}\ \mathrm{distance}) $$

An affine transformation $T$ of the moving image is expressed using the reg23_experiments.data.structs.Transformation struct, which stores a 3D rotation in axis-angle form, and a 3D translation. This represents the transformation of the CT volume within world space, where a transformation of (0, 0, 0); (0, 0, 0) would leave the CT volume centred on the origin, with axes aligned to those of the world coordinate system.

As such, mapping from the coordinate system of world space to that of the CT volume involves applying the inverse of the transformation to the coordinates. This is why all DRR projection functions take as an argument an 'inverse homography matrix'.