Figure 1.

The template J is to be estimated given hypertemplate J₀ and observed images I₁, I₂, …, I_N. We model the template as $J=J_0\circ g_{\mu }^{-1}$, where μ is the random initial momentum. In the following EM algorithm, μ is computed iteratively, with random initial momenta θ₁, θ₂, …, θ_N being hidden variables.