If φ_1 takes the template to the target, what does φ_1^-1 naturally represent?

The map that takes the target back to the template

The same map applied a second time

The minimum energy without units

Exercise · ZW-LDDMM-007 · ★★☆ Intermediate

If \(\varphi_1\) takes the template to the target, what does \(\varphi_1^{-1}\) naturally represent?

Choose one option.

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If \(\varphi_1\) takes the template to the target, its inverse \(\varphi_1^{-1}\) undoes that motion and takes the target back to the template.

LDDMM (Large Deformation Diffeomorphic Metric Mapping) is a registration framework that looks for a smooth diffeomorphic deformation \(\varphi_t\), generated by a vector field \(v_t\), with minimum energy \(E_{\min}\).

\[\begin{gathered}\dot{\varphi}_t=v_t\circ\varphi_t\\\varphi_0=\operatorname{id}\end{gathered}\]