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affine.transformation.md

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Atlas coordinates

  1. Structures from 3 reference brains (MD589, MD594, and MD585) are outlined by anatomists.
  2. The coordinates from those structures are used to created a set of averaged structures which is the Atlas.
  3. Yuncong used a virtual 3D space with units in 10microns. For example, the origin Yuncong derived for structure 3N_L is: [-165.58293065 -127.18518508 -38.94194041]
  4. That origin gets transformed into the COM in the Atlas box space with:
 center = (origin + ndimage.measurements.center_of_mass(volume))
 com = atlas_box_center + center * atlas_raw_scale / atlas_box_scales
  1. Where:
    1. atlas_box_size=(1000, 1000, 300) # Arbitrary size of the box we are using
    2. atlas_box_scales=(10, 10, 20) # scales for Neuroglancer of the box
    3. atlas_raw_scale=10 # raw Yuncong scale of 10microns
    4. atlas_box_center = atlas_box_size / 2 # The center of our "Atlas Box"
  2. resulting in: [-135.44472549 -108.49438786 -13.52838526] and this is placed in the database as the center of mass for the Atlas structure 3N_L
  3. All the remaining structure COMs are computed with the same procedure.

Goal

  • make atlas coordinate units be microns
    • Longer term: make coordinates conform to the Allen Atlas.
  • make brain coordinate units be micrones.
  • Process: origin -> center -> com, com is the point that is saved in the database.
  • Fixing the database: multiply x and y by 10, multiply z by 20
  • Fixing Neuroglancer: translate from the transformed coordinates, which are in microns, to section/pixel coordinates.

Coordinate systems:

  • atlas coordinate system: in microns from center of brain.
  • stack coordinate system: in microns from top left, first section
  • Neuroglancer coordinate system: in pixels within a section, section number.

Brain coordinates

  1. Brain stack COMs are derived from Neuroglancer. For NTB brains, the resolution is 0.325 in the x and y directions and 20um in the z direction.

  2. We get the Atlas and the brain coordinates into 1um space to make a common reference.

    1. Use atlas_box_scales = [10, 10, 20]
    2. Use brain reference_scales of [0.325, 0.325, 20]

  3. With python we do:

        common_keys = atlas_centers.keys() & reference_centers.keys() # get common structures
        atlas_point_set = np.array([atlas_centers[s] for s in structures if s in common_keys]).T
        atlas_point_set = np.diag(atlas_box_scales) @ atlas_point_set
        brain_point_set = np.array([reference_centers[s] for s in structures if s in common_keys]).T
        brain_point_set = np.diag(reference_scales) @ brain_point_set
  1. Then we send those two sets to the align_atlas method