Exercise · ZW-MINIMUM-ENERGY-011 · ★★★ Advanced
Let \(E(\varphi_k)=(k-3)^2+2\) for \(k=1,\dots,5\), with \(\mathcal{A}=\{\varphi_1,\varphi_4,\varphi_5\}\). What is \(E_{\min}\)?
Choose one option.
Show answer
- A. \(3\)
Explanation
Evaluate \(E\) at \(k=1\), \(4\) and \(5\), giving values \(6\), \(3\) and \(6\); the smallest is \(3\). The value \(2\) of \(\varphi_3\) does not count because that deformation is not in \(\mathcal{A}\).
Review the concept: Minimum energy
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
- ZW-MINIMUM-ENERGY-001 If A is the set of admissible deformations, what does E_min=min_φinAE(φ) express?
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- ZW-MINIMUM-ENERGY-005 What directly determines the value of the energy of a flow in LDDMM?
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- ZW-MINIMUM-ENERGY-007 What is the name of the smallest value of E over the admissible set?
- ZW-MINIMUM-ENERGY-008 What does the field v_t represent in LDDMM?