evolutionary morphing and shape distance
DESCRIPTION
Evolutionary Morphing and Shape Distance. Nina Amenta Computer Science, UC Davis. Collaborators. Physical Anthropology Eric Delson, Steve Frost, Lissa Tallman, Will Harcourt-Smith Morphometrics F. James Rohlf Computer Science and Math - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/1.jpg)
Evolutionary Morphing and Shape Distance
Nina Amenta
Computer Science, UC Davis
![Page 2: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/2.jpg)
Collaborators
Physical AnthropologyEric Delson, Steve Frost, Lissa Tallman, Will
Harcourt-Smith
MorphometricsF. James Rohlf
Computer Science and MathKatherine St. John, David Wiley, Deboshmita Ghosh,
Misha Kazhdan, Owen Carmichael, Joel Hass, David Coeurjolly
![Page 3: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/3.jpg)
Outline
• Application of 3D Procrustes tangent space analysis in primate evolution
• Some issues with the shape space
• An idea
![Page 4: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/4.jpg)
Evolutionary Trees
![Page 5: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/5.jpg)
Computing Trees
Tree inference method
Papio
Macaca
Cercocebus
Cercopithecus
Allenopithecus
Trees on extant species come from genomic data.
![Page 6: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/6.jpg)
Estimating morphology
Using 3D data for extant species, and tree, estimate cranial shapes for the hypothetical ancestors.
3D input data
![Page 7: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/7.jpg)
Estimating morphology
Generalized least-squares, covariance matrix derived from weighted tree edges.
![Page 8: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/8.jpg)
Evolutionary Morphing
![Page 9: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/9.jpg)
Fossils
Genomic trees don’t include fossils.
Primates: ~200 extinct genera, ~60 extant.
Fossils have to be added based on shape and meta-data.
![Page 10: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/10.jpg)
Fossil Restoration
fossil symmetrization reflection
![Page 11: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/11.jpg)
Sahelanthropos
![Page 12: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/12.jpg)
Fossil Restoration
restored fossil
template surface
reconstructed specimen
TPS
![Page 13: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/13.jpg)
Improve Estimated Morphology
synthetic basal node
repairedVictoriapithecus
![Page 14: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/14.jpg)
Improve Estimated Morphology
improved basal node
repairedVictoriapithecus
![Page 15: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/15.jpg)
Parapapio, a more recent fossil
Template is root of subtree where we believe it falls
![Page 16: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/16.jpg)
Placement of Parapaio
![Page 17: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/17.jpg)
User-defined landmarks
Our users want to specify or edit landmarks, but more automation is clearly needed.
We optimize for correspondence only within surface patches (Bookstein sliding, does not work well).
![Page 18: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/18.jpg)
Procrustes Distance
DEuc(A,B) = Euclidean distance in R3n
Choose transformation T (scale, trans, rot) producing minimum DEuc
DProc(A,B) = min DEuc(T(A), B)
T
We work in Euclidean tangent space.
![Page 19: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/19.jpg)
Example
![Page 20: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/20.jpg)
Features are not aligned
..even starting with optimal correspondence. Procrustes distance emphasizes big change, misses similarity of parts.
![Page 21: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/21.jpg)
Features are not aligned
Changing the details might even reduce DProc.
![Page 22: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/22.jpg)
Features are not aligned
Optimizing correspondence under DProc will not lead to intuitively better correspondence.
![Page 23: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/23.jpg)
Complex Shapes
All parts cannot be simultaneously aligned by linear deformations. Deformation really is non-linear.
![Page 24: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/24.jpg)
Edge-length Distance
Proposal: represent correspondence as corresponding triangle meshes instead of corresponding point samples.
![Page 25: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/25.jpg)
Edge-length Distance
Li is Euclidean length of edge ei
Shape feature vector v is (L1 … Lk)
DEL = DEuc(v(A), v(B))
This represents a mesh as a discrete metric – set of lengths on a triangulated graph, respecting the triangle inequality
![Page 26: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/26.jpg)
Information Loss
In 2D, this does not make much sense.
But in 3D, almost all triangulated polyhedra are rigid. So a discrete metric has a finite number of rigid realizations.
![Page 27: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/27.jpg)
Not a New Idea
Euclidean Distance Matrix Analysis, Lele and Richtmeier, 2001 – use the complete distance matrix as shape rep.
“Truss metrics” – include only enough edges to get rigidity.
![Page 28: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/28.jpg)
Quote
“…the arbitrary choice of a subset of linear distances could accentuate the influence of certain linear distances in the comparison of forms, while masking the influence of others.” - Richtsmeier, Deleon, and Lele, 2002.
Not an issue in R3!
![Page 29: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/29.jpg)
Nice Properties
• Rotation and translation invariant
• Invariant to rotations and translations of parts (isometries).
• Any convex combination of specimens gives another vector of Li obeying triangle inequalities. So we can do statistics in a convex region of Euclidean space.
![Page 30: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/30.jpg)
Scale
Can normalize to produce scale invariance, as with Procrustes distance.
Choosing scale so that Li = 1 keeps all specimens in a linear subspace.
![Page 31: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/31.jpg)
Degrees of Freedom
Dimension of Kendall shape space is 3n-7
Number of edges for a triangulated object homeomorphic to a sphere is 3n-6 (Euler+triangulation constraints), -1 for scale = 3n-7
![Page 32: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/32.jpg)
Scale
But this does not solve the problem of matching parts getting different scales.
What if we apply local scale factors at each vertex?
![Page 33: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/33.jpg)
Local Scale?
We could add a scale factor at each vertex, producing a discrete conformal representation (Springborn, Schoeder, Bobenko, Pinkall)…but this has way too many degrees of freedom.
Q1: How to incorporate the right amount of local scale?
![Page 34: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/34.jpg)
Drawback
Isometric surfaces have distance zero.
Complicates reconstruction of interpolated shapes. Q2.
![Page 35: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/35.jpg)
More Questions
Q3: Given a discrete metric formed as a convex combination of specimens, how to choose the right 3D realization for visualization?
Q4: How to optimize correspondence so as to minimize DEL? How to weight by area?
![Page 36: Evolutionary Morphing and Shape Distance](https://reader035.vdocuments.site/reader035/viewer/2022062301/56814cce550346895db9d5ca/html5/thumbnails/36.jpg)
Thank you!