A Maximum entropy calculation Under the constraint on the borders, τ and τ

Average pixel displacement magnitude δ We derive here the large-c asymptotic behavior of δ (Eq.3). The asymptotic relations for τ that are reported in the main text are computed in a similar fashion. In Fig.8, we check the agreement between asymptotic prediction and empirical measurements. If δ 1, our results strongly depend on the choice of interpolation method. Condition for diffeomorphism in the (T, c) plane For a given value of c, there exists a temperature scale beyond which the transformation is not injective anymore, affecting the topology of the image and creating spurious boundaries, see Fig.9a-c for an illustration.