SymmetryA two-dimensional object is symmetrical if you can rotate
or reflect it so that it perfectly overlays the original.
For example, this pattern is rotationally symmetric When it is rotated by 120 degrees, it lays on top of itself.
A. Type 1 asymmetry - structures that show consistency in topology and in a number of landmarks
B. Type 2 asymmetry - structures that show consistency in topology
but vary in number of corresponding landmarksC. Type 3 asymmetry - variable structures having no
consistent topology, no quantitative consistency, and sometimes
no matching points
Three types of objects for quantifying metric asymmetry
A B C
(J. H. Graham*, S. Raz*, H. Hel-Or, and E. Nevo. 2010. Symmetry)
The leaf-venation hypothesis
New model for quantifying
asymmetry in vein formation
Using anchor points for quantifying leaf asymmetry
(R. Aloni, 2001. Plant Physiology)
Original Symmetrized
Quantifying symmetry in Leaves
Asymmetry of leaves is evaluated as the “distance” from perfect symmetry.Cost of “symmetrization” represents the asymmetry value.
Original Translation ElongationInsertion
Elementary deformations
lIlCOI
dlTdlCOT
llEllCOE newnew
*)(
**),(
||*),(
0
0
0
The order of the secondary veins on either side of the main vein is preserved
We use cost functions which are according tothe bilogical growth model
Local approach – cost functions(D. Milner, S. Raz, H. Hel-Or, D. Keren, E. Nevo. 2007. Pattern Recognition)
Translation
Elongation
Insertion
Consistency of
performance
Distinguish between leaves that were sampled on
the opposing slopes of the Evolution Canyon