# Coordinate Systems

Written by Andrew Taylor

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* **Image Spaces (associated with distinct coordinate system)**
  * Native space – coordinates unique to subject’s head placement in MRI scanner
  * Standard space – standard defined world coordinates across all images in this space define anatomy location (images in this space can have differ resolutions)
* **Coordinate Systems**
  * Voxel coordinates
    * no units; integers
    * voxel count in each dimension reflecting matrix size
    * Origin: corner of image (e.g., 0,0,0 or 1,1,1)
    * Origin and axes naming conventions differ in programs
  * World coordinates
    * Have units in mm; floating values
    * Denote anatomy
      * Handedness system
        * Right-handed (RAS) system
          * x+ Left-Right
          * y+ Posterior-Anterior
          * z+ Inferior-Superior
          * Default for: MNI152 space, NifTi
        * LPS system
          * Default for: Dicom
    * Origin: can differ in programs, standard space (e.g., MNI152 space origin at anterior commissure)
*   **qform and sform Matrices**

    PURPOSE: Used to convert voxel coordinates into world coordinates

    o   qform & sform stored in the Nifti File

    o   Historically, both matrices in a file to keep track of scanner coordinate system (qform) and standard space coordinates (sform); in practice not used; one matrix usually set to 0)

    o   Meaningful only if have a NON-ZERO code (0=unknown)
