# 2D Projectors

Projectors determine the (implicit) weight matrix of the geometries. All CPU reconstruction algorithms require a projector.

Each projector is only suitable for specific projection geometries.

## Creation

```
id = astra_create_projector(...);
```

Create a projector object. Projectors determine the (implicit) weight matrix of the geometries. All CPU reconstruction algorithms require a projector.

This script is a wrapper around astra_mex_projector(‘create’, …) with a more convenient interface. See below for specifics.

The allocated object must be freed after use with a call to

```
astra_mex_projector('delete', id)
```

## Parallel beam

The projectors in this section can be used with the parallel projection geometry.

**line**

```
proj_id = astra_create_projector('line', proj_geom, vol_geom);
```

The weight of a ray/pixel pair is given by the length of the intersection of the pixel and the ray, considered as a zero-thickness line.

**strip**

```
proj_id = astra_create_projector('strip', proj_geom, vol_geom);
```

The weight of a ray/pixel pair is given by the area of the intersection of the pixel and the ray, considered as a strip with the same width as a detector pixel.

**linear**

```
proj_id = astra_create_projector('linear', proj_geom, vol_geom);
```

A ray is traced through successive columns or rows (depending on which are most orthogonal to the ray). The contribution of this column/row to this ray is then given by linearly interpolating between the two nearest volume pixels of the intersection of the ray and the column/row.

This is also known as the Joseph kernel, or a slice-interpolated kernel.

## Fan beam

**line_fanflat**

```
proj_id = astra_create_projector('line_fanflat', proj_geom, vol_geom);
```

The weight of a ray/pixel pair is given by the length of the intersection of the pixel and the ray, considered as a zero-thickness line. This projector can be used with the fanflat and fanflat_vec geometries.

**strip_fanflat**

```
proj_id = astra_create_projector('strip_fanflat', proj_geom, vol_geom);
```

The weight of a ray/pixel pair is given by the area of the intersection of the pixel and the ray. The ray is considered as a 2D cone from the source to the full width of the detector pixel. The projector can only be used with the fanflat geometry.

NB: This mathematical model does not properly take into account the fan beam magnification effect.

## Miscellaneous

**sparse_matrix**

```
proj_id = astra_create_projector('sparse_matrix', proj_geom, vol_geom);
```

This projector uses a sparse matrix projection geometry. See the documentation for that geometry for details.

**cuda**

```
proj_id = astra_create_projector('cuda', proj_geom, vol_geom);
```

This projector does not directly specify a weight matrix, but instead is intended to let algorithms use GPU/CUDA code. It can be used with parallel, fanflat and fanflat_vec projection geometries.

NB: This functionality has not yet been implemented everywhere. This projector is currently only usable in astra_create_sino and astra_create_backprojection.

## astra_mex_projector

astra_mex_projector is used to manage projector objects.

It is a wrapper around the MEX file astra_mex_projector_c.

astra_mex_projector contains the following commands.

create

matrix

volume_geometry

projection_geometry

is_cuda

delete

clear

info

**create**

```
id = astra_mex_projector('create', cfg);
```

Create a projector from a config object. This is called internally by the script [[astra_create_projector]], which is the recommended way to create most projectors.

**matrix**

```
matrix_id = astra_mex_projector('matrix', projector_id);
```

Create an explicit sparse matrix for the weight matrix encoded by this projector.

This is only implemented for 2D CPU projectors.

The returned matrix_id can be further manipulated with [astra_mex_matrix]. In particular, it can be retrieved as a Matlab sparse matrix with

```
S = astra_mex_matrix('get', matrix_id);
```

It has to be freed after use with

```
astra_mex_matrix('delete', matrix_id);
```

NB: Such a matrix can be very large for large geometries.

**volume_geometry**

```
vol_geom = astra_mex_projector('volume_geometry', id);
```

Get the volume geometry attached to the given projector object.

NB: This is not fully implemented yet and the return value may not accurately represent the geometry.

**projection_geometry**

```
proj_geom = astra_mex_projector('projection_geometry', id);
```

Get the projection geometry attached to the given projector object.

NB: This is not fully implemented yet and the return value may not accurately represent the geometry.

**is_cuda**

```
c = astra_mex_projector('is_cuda', id);
```

Return if the the projector is a CUDA projector.

**delete**

```
astra_mex_projector('delete', id)
astra_mex_projector('delete', id1, id2, ...)
```

Free a single or multiple projector(s).

**clear**

```
astra_mex_projector('clear')
```

Free all projectors.

**info**

```
astra_mex_projector('info')
```

Print basic information about all allocated projector objects.