Improving Landmark Improving Landmark Positions for Positions for

Evolutionary MorphingEvolutionary MorphingDan AlcantaraDan Alcantara

Nina AmentaNina Amenta

OutlineOutline

• What is evolutionary morphing?What is evolutionary morphing?• Blending processBlending process• Improving the resultsImproving the results• Problems encountered & future Problems encountered & future

directionsdirections

What is evolutionary What is evolutionary morphing?morphing?

• Method of Method of visualizing an visualizing an evolutionary tree.evolutionary tree.

• Relies on shape Relies on shape analysis theory analysis theory from Geometric from Geometric Morphometrics.Morphometrics.

Theory basicsTheory basics

Overview of the morphing Overview of the morphing processprocess

1)1) Important points on the Important points on the models are hand-models are hand-marked as marked as landmarkslandmarks. . Curves are Curves are approximated by approximated by semi-semi-landmarkslandmarks..2)2)Models are aligned so Models are aligned so that corresponding that corresponding landmarks are close to landmarks are close to each other using a each other using a Generalized Procrustes Generalized Procrustes AlignmentAlignment..3)3)A A thin-plate splinethin-plate spline warps the models so warps the models so that corresponding that corresponding landmarks lie on top of landmarks lie on top of each other.each other.4)4)The models are The models are blended together using blended together using weights calculated weights calculated from the tree.from the tree.

Associated metricsAssociated metrics

• Generalized Generalized Procrustes Alignment Procrustes Alignment minimizes squared minimizes squared distances between distances between corresponding corresponding landmarks.landmarks.

• Thin-plate spline Thin-plate spline minimizes distortion minimizes distortion created when created when warping from one warping from one model to another.model to another.

Distortion created by the Distortion created by the thin-plate splinethin-plate spline

Bending energy increases as the plane gets more distorted.Bending energy increases as the plane gets more distorted.

Bookstein’s minimization Bookstein’s minimization methodmethod

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

2)2) Slide semi-Slide semi-landmarks along landmarks along their tangent their tangent lines to minimize lines to minimize the bending the bending energy.energy.3)3) Reproject the Reproject the landmarks back landmarks back onto their onto their respective curves.respective curves.

4)4) Re-align using the Re-align using the new landmark new landmark points and repeat points and repeat the method until the method until convergence.convergence.

Observations about semi-Observations about semi-landmark slidinglandmark sliding

• Calculated Calculated minimums don’t minimums don’t lie on the skull.lie on the skull.

• Bending energy Bending energy may increase may increase once reprojected.once reprojected.

• Semi-landmarks Semi-landmarks tend to spread tend to spread out evenly.out evenly.

Actual minimum; not on skullActual minimum; not on skull

Reprojection location on skullReprojection location on skull

Sliding resultsSliding results

Future plansFuture plans

• Completely extend the method to 3D Completely extend the method to 3D features.features.

• Utilize the metric from the Utilize the metric from the Generalized Procrustes Alignment.Generalized Procrustes Alignment.• May be “more correct” according to May be “more correct” according to

some morphologists.some morphologists.

ReferencesReferences• Fred L. Bookstein. Landmark Methods for Fred L. Bookstein. Landmark Methods for

Forms Without Landmarks: Localizing Group Forms Without Landmarks: Localizing Group Differences in Outline Shape. Differences in Outline Shape. Proceedings of Proceedings of the Workshop on Mathematical Methods in the Workshop on Mathematical Methods in Biomedical Image Analysis, June 1996, pp Biomedical Image Analysis, June 1996, pp 279-289.279-289.

• W.D.K. Green. The thin-plate spline and W.D.K. Green. The thin-plate spline and images with curving featuresimages with curving features.. Proceedings in Proceedings in Image Fusion and Shape Variability Image Fusion and Shape Variability Techniques, pp 79-87.Techniques, pp 79-87.

• David F. Wiley, et al. Evolutionary Morphing. David F. Wiley, et al. Evolutionary Morphing. To appear in IEEE Visualization 2005. To appear in IEEE Visualization 2005.

AcknowledgementsAcknowledgements

• Nina Amenta for letting me work Nina Amenta for letting me work with her the past year.with her the past year.

• Lab mates for helping me with Lab mates for helping me with various problems I’ve come across.various problems I’ve come across.

• Stephen Frost for providing more Stephen Frost for providing more insight into the sliding process.insight into the sliding process.

• AGEP programAGEP program