====== Principal Component Analysis (PCA) ======
This module yields so-called eigenimages from a stack of 2D images or 3D structures, thereby facilitating subsequent image classification to resolve heterogeneity. 


===== Usage =====
The PCA((Hall, P. et al. (2000). Merging and splitting eigenspace models.  IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(9), 1042-49.)) is a prerequisite for data complexity reduction in order to perform a subsequent [[eyes:logics:Classification]]; alternatively, it can also be directly performed within the classification logic. The PCA yields eigenimages (volumes in the 3D case) which represent the heterogeneity or covariance within the data. Pre-computing the PCA before classification allows to inspect the resulting eigenimages and to decide how many eigenimages should be used for image classification. In general, the first eigenimages will correspond to actual variations in structure and/or angular orientation, whereas later eigenimages will rather represent variations in the noise. Using an external mask (e.g. a circle) as additional input allows to suppress background noise. Using external eigenimages from a previous PCA as input allows to combine eigenimages from different groups of data. The latter may be useful when working on data with orientation bias.  


===== Process =====
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^ Parameters                 ^ Description     ^
| Dimension     | Number of calculated dimensions (Eigen images) |
| Eigenimages   | Use external eigen images |
| Using mask    | Use an external mask |

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^ Input            ^ Description ^
| Input            | Stack of input images |
| //Eigen Images// | External Eigen images |
| //Mask//         | External mask |

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^ Output   ^ Description ^
| Eigenimages | Stack of generated Eigen images |

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^ New/Changed Header Values ^ Description ^
| eigenValue | Eigenvalue of the corresponding eigenimage (or volume in 3D case) |