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Improving Landmark Positions for Evolutionary Morphing

Improving Landmark Positions for Evolutionary Morphing. Dan Alcantara Nina Amenta. Outline. What is evolutionary morphing? Blending process Improving the results Problems encountered & future directions. What is evolutionary morphing?. Method of visualizing an evolutionary tree.

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Improving Landmark Positions for Evolutionary Morphing

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  1. Improving Landmark Positions for Evolutionary Morphing Dan Alcantara Nina Amenta

  2. Outline • What is evolutionary morphing? • Blending process • Improving the results • Problems encountered & future directions

  3. What is evolutionary morphing? • Method of visualizing an evolutionary tree. • Relies on shape analysis theory from Geometric Morphometrics.

  4. Theory basics

  5. 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.

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

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

  8. Bookstein’s minimization method • 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.

  9. Observations about semi-landmark sliding • Calculated minimums don’t 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

  10. Sliding results

  11. 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.

  12. 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.

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

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