Exercise · ZW-MINIMUM-ENERGY-004 · ★★☆ Intermediate
A very low-energy deformation does not satisfy the condition of reaching the target. Why can it not be the LDDMM solution?
Choose one option.
A Because every low energy is impossible B Because the target never takes part in the problem C Because an admissible deformation must have maximum energy D Because minimizing is done within the admissible set, which includes the endpoint constraint Show answer D. Because minimizing is done within the admissible set, which includes the endpoint constraint← Back to the question
Explanation Only admissible deformations compete for the minimum, and that class includes reaching the target. A low energy outside it does not count.
The minimum energy \(E_{\min}\) is the lowest cost among admissible deformations; in LDDMM it measures how much effort the field generating the transformation requires.
\[E_{\min}=\min_{\varphi\in\mathcal{A}}E(\varphi)\]
More practice problems: minimum energy