Figure 2.

We illustrate two steps in our optimization of a population template through a symmetric diffeomorphic parameterization. The shape of an initial template guess (orange circle) is updated by first estimating the diffeomorphic paths, φ_i. We then change the initial conditions, ψ, to the maps between the template, Ī, and the individual images, J_i, to shorten their total length. The template shape also changes under ψ. We term this approach “symmetric” because it uses symmetric pairwise mapping, symmetrically optimizes the two terms in normalization methods (geometry and appearance) across the population and is unbiased, that is, does not prefer any specific image or require user input.