Exercise · ZW-MINIMUM-ENERGY-003 · ★★☆ Intermediate
If the norm used to measure \(v_t\) is changed, what can change even if the endpoints are the same?
Choose one option.
Show answer
- A. The energy and, potentially, the minimizing trajectory
Explanation
The energy depends on the norm used to measure \(v_t\), so changing it can alter the minimum value and the optimal trajectory even if the endpoints stay the same.
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?
- ZW-MINIMUM-ENERGY-002 Two transformations reach the same target: E(φ_A)=2 and E(φ_B)=5. If both are admissible, what can…
- ZW-MINIMUM-ENERGY-004 A very low-energy deformation does not satisfy the condition of reaching the target. Why can it not…
- ZW-MINIMUM-ENERGY-005 What directly determines the value of the energy of a flow in LDDMM?
- ZW-MINIMUM-ENERGY-006 What does it mean for a deformation to be admissible in LDDMM?
- 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?
- ZW-MINIMUM-ENERGY-009 What does a lower energy between two admissible deformations indicate?