Automatic alignment and angle refinement in tomography using fiducial markers

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Automatic alignment and angle refinement in
tomography using fiducial markers

• Chao

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Purpose

• Automatically tracking the position of each
  marker, and align each image precisely.
• Using these positions to refine the tilt axis,
  tilt angle and rotation angle of each image.
• Finally, using these refined parameters to do
  the 3D reconstruction

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Basic theory
Assume we have totally v images and s markers in
each image image 1,2,3,,i,v marker1,2,3,
,j,.s
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Classic method
Using center of mass frame
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Shortcomings

• If the markers are not well distributed, i.e. the
  center of mass is not around the center of the
  image, then you can not use the full information
  of the image.
• It requires that the position of each image is
  precisely known, which does not apply to the
  automatic marker picking case.

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Alternative method
Using the zero tilted image as the reference
frame
Build the marker pattern , using cross
correlation to get the image shift.
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Angle refinement
Using brute force way, vary the 3 angles around
their initial values(-5 to 5 degree), find the
values which minimize the chi square.
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Program flow

• Go to the zero tilted image, manually pick some
  good markers( spread, no cluster),
• save to a star file.
• Build a marker pattern image, cross correlate
  with the 1st tilted image, get the shift.
• Build individual marker image, cross correlate
  with the 1st tilted image, search the
• peaks near their theoretical positions.
• 4. Refine the z-coordinate of each marker
• Repeat step23 for the rest of images.
• Refine the 3 angles for each image.
• Go back to step1, repeat this flow until some
  figure of merit has been reached.

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Demonstration
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I am working on this

• Local search will never work in case of the
  cluster, need find a way to use the information
  of the cluster structure
• Find a better algorithm to vary the angles and
  z-coordinates, to increase speed.
• Apply this to dual-axis series