FIGURE 3.

Matching and object symmetry for shape analysis of flowers with any type of symmetry. (A) Analysis of a flower with matching symmetry. First, the whole flower is divided into individual repeated parts or modules that generate the symmetry. Second, an individual configuration of landmarks is considered for each repeated part. A configuration is selected as a reference and reflections are applied to the rest of the images as needed so that all subsequently digitised configurations from the transformed pictures match the orientation of the chosen reference. Note that rotations are not needed here since the GPA automatically carries this step during the superimposition procedure. Finally, all individual configurations are superimposed simultaneously in a single GPA. (B) Analysis of a flower with object symmetry. First, an original configuration of landmarks is digitised for the whole flower. Second, n copies of this original configuration are generated and each of them is transformed according to one of the symmetry transformations in the symmetry group of the flower (here, n = 4). Finally, all original configurations and their transformed relabelled copies are superimposed simultaneously in a single GPA. The resulting mean shape (consensus) is symmetric.