# AngularReconstitution

This logic determines Euler angles for a given set of input images based on the common line theorem. This is needed in order to correctly place images (2D projections) in 3D space prior to reconstruction.

## Usage

The input of this logic - class averages - should be of high quality with enough visible structural features. Choosing more class averages for this logic is not always a good idea, since similar views will result in worse angular assignment. So ideally class averages chosen should represent all possible distinct views, but without overlapping. If symmetry of the particle is known in advance, it is recommended to try running reconstitution both with and without applying symmetry restraints. Most modes of this logic only require one input (a stack of images) and generate only one output. Therefore, only divergent I/O information is mentioned below.

## Modes

### Euler

This mode is used for de-novo assignment of angles only from the input projections themselves. The output stack of images contains the assigned Euler angles as header values.

Parameters | Description |
---|---|

Sinograms | Gives options to read already generated sinograms or to write down sinograms for the images being processed |

Symmetry | Symmetry of the particle (if known) |

### Anchor set

This logic determines the angles of stack of projections if the set with known angular relations is available (e.g. 3D model from already performed angular reconstitution)

Parameters | Description |
---|---|

Symmetry | Symmetry of the particle (if known) |

Input | Description |
---|---|

In | Image or stack of images (a set of class averages) |

Anchor set | Projection set with known angular relations (mostly projected 3D-model) |

### Add projection

This mode is used to adds projections to a set with known/determined Euler angles

Parameters | Description |
---|---|

Symmetry | Symmetry of the particle (if known) |

Input | Description |
---|---|

In | Image or stack of images (a set of class averages) |

Dataset | Stack of images (projections) with assigned Euler angles |

### Sinograms

This mode is used to create sinograms from the images. These sinograms can be later used in the same logic to reconstitute the angles.

Parameters | Description |
---|---|

Symmetry | Symmetry of the particle (if known) |

## Concept

This logic is needed as an intermediate step to get from 2D images to a 3D volume. In order to reconstruct the full volume we need to know the relationship between the images (projections) we have - how they are located in 3D relative to each other. In case any reference model for the particle is available, it can be used as 'anchor set' that would increase the precision of the output. However, when no prior model is available for the particles of interest, determination of Euler angles should be done de novo. This logic does it based on Common line theorem.