Exercise · ZW-MINIMUM-ENERGY-001 · ★☆☆ Basic
If \(\mathcal{A}\) is the set of admissible deformations, what does \(E_{\min}=\min_{\varphi\in\mathcal{A}}E(\varphi)\) express?
Choose one option.
A The deformation with the most steps B The energy of the identity only C The lowest cost among the deformations that satisfy the constraints D The value of \(E\) for any deformation Show answer C. The lowest cost among the deformations that satisfy the constraints← Back to the question
Explanation The definition takes the smallest value of \(E\) over the admissible set , so it is the lowest cost among deformations that satisfy the constraints.
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