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Symmetry

Symmetry. A 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.

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Symmetry

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  1. Symmetry A 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.

  2. Three types of objects for quantifying metric asymmetry (J. H. Graham*, S. Raz*, H. Hel-Or, and E. Nevo. 2010. Symmetry) A B C 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 landmarks C. Type 3 asymmetry - variable structures having no consistent topology, no quantitative consistency, and sometimes no matching points

  3. The leaf-venation hypothesis Using anchor points for quantifying leaf asymmetry (R. Aloni, 2001. Plant Physiology) New model for quantifying asymmetry in vein formation

  4. Quantifying symmetry in Leaves Asymmetry of leaves is evaluated as the “distance” from perfect symmetry. Cost of “symmetrization” represents the asymmetry value. Original Symmetrized

  5. Translation Elongation Insertion Original Local approach – cost functions (D. Milner, S. Raz, H. Hel-Or, D. Keren, E. Nevo. 2007. Pattern Recognition) We use cost functions which are according to the bilogical growth model Elementary deformations The order of the secondary veins on either side of the main vein is preserved

  6. Translation Elongation Consistency of performance Insertion

  7. Distinguish between leaves that were sampled on the opposing slopes of the Evolution Canyon

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