Improving Landmark Positions for Evolutionary Morphing

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Improving Landmark Positions for Evolutionary
Morphing

• Dan Alcantara
• Nina Amenta

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Outline

• What is evolutionary morphing?
• Blending process
• Improving the results
• Problems encountered future directions

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What is evolutionary morphing?

• Method of visualizing an evolutionary tree.
• Relies on shape analysis theory from Geometric
  Morphometrics.

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Theory basics
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Overview of the morphing process
1) Important points on the models are hand-marked
as landmarks. Curves are approximated by
semi-landmarks.
2) Models are aligned so that corresponding
landmarks are close to each other using a
Generalized Procrustes Alignment.

3) A thin-plate spline warps the models so that
corresponding landmarks lie on top of each other.
4) The models are blended together using weights
calculated from the tree.
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Associated metrics

• Generalized Procrustes Alignment minimizes
  squared distances between corresponding
  landmarks.
• Thin-plate spline minimizes distortion created
  when warping from one model to another.

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Distortion created by the thin-plate spline
Bending energy increases as the plane gets more
distorted.
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Booksteins minimization method

1. Find all of the tangent lines at the
   semi-landmarks.

2) Slide semi-landmarks along their tangent lines
to minimize the bending energy.
3) Reproject the landmarks back onto their
respective curves.
4) Re-align using the new landmark points and
repeat the method until convergence.
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Observations about semi-landmark sliding

• Calculated minimums dont lie on the skull.
• Bending energy may increase once reprojected.
• Semi-landmarks tend to spread out evenly.

Actual minimum not on skull
Reprojection location on skull
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Sliding results
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Future plans

• Completely extend the method to 3D features.
• Utilize the metric from the Generalized
  Procrustes Alignment.
• May be more correct according to some
  morphologists.

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References

• Fred L. Bookstein. Landmark Methods for Forms
  Without Landmarks Localizing Group Differences
  in Outline Shape. Proceedings of the Workshop on
  Mathematical Methods in Biomedical Image
  Analysis, June 1996, pp 279-289.
• W.D.K. Green. The thin-plate spline and images
  with curving features. Proceedings in Image
  Fusion and Shape Variability Techniques, pp
  79-87.
• David F. Wiley, et al. Evolutionary Morphing.
  To appear in IEEE Visualization 2005.

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Acknowledgements

• Nina Amenta for letting me work with her the past
  year.
• Lab mates for helping me with various problems
  Ive come across.
• Stephen Frost for providing more insight into the
  sliding process.
• AGEP program