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