Exercise · ZW-LDDMM-004 · ★★☆ Intermediate

Two flows reach the same target and have energies \(E_A=9\) and \(E_B=4\). If both are admissible, which criterion does LDDMM favor?

Choose one option.

Show answer

C. Choosing flow \(B\), because it satisfies the same endpoint with lower energy

Explanation

Both flows reach the same endpoint, so LDDMM compares energies. Since \(E_B=4<9=E_A\), flow \(B\) is preferred.

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 \(E_{\min}\).

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