Exercise · ZW-MINIMUM-ENERGY-002 · ★★☆ Intermediate
Two transformations reach the same target: \(E(\varphi_A)=2\) and \(E(\varphi_B)=5\). If both are admissible, what can be stated?
Choose one option.
A The one with lower energy cannot reach the target B \(\varphi_A\) is preferable according to the minimum-energy criterion C \(\varphi_B\) is preferable because it moves more D Costs of the same functional cannot be compared Show answer B. \(\varphi_A\) is preferable according to the minimum-energy criterion← Back to the question
Explanation Under the minimum-energy criterion the lower-cost admissible deformation is preferred. Since \(2<5\), \(\varphi_A\) is the preferable one.
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