Exercise · ZW-TIME-DERIVATIVE-009 · ★☆☆ Basic
What is the flow \(\varphi_t\) in LDDMM?
Choose one option.
Show answer
- B. A family of deformations depending on \(t\)
Explanation
The flow \(\varphi_t\) is a family of deformations indexed by time. The other options describe objects that are not deformations.
Review the concept: Time derivative
The time derivative \(\dot{\varphi}_t\) describes how a deformation changes as the time parameter \(t\) varies.
\[\dot{\varphi}_t=\frac{d\varphi_t}{dt}\]
More practice problems: time derivative
- ZW-TIME-DERIVATIVE-001 In the LDDMM equation, what does φ_t represent?
- ZW-TIME-DERIVATIVE-002 If φ_t=0 for all t, what happens to the flow?
- ZW-TIME-DERIVATIVE-003 The equality φ_t=v_t∘φ_t is a form of...
- ZW-TIME-DERIVATIVE-004 What is the difference between φ_t and an acceleration?
- ZW-TIME-DERIVATIVE-005 What is the initial condition of the flow φ_t in an initial value problem?
- ZW-TIME-DERIVATIVE-006 What is the time derivative of φ_t?
- ZW-TIME-DERIVATIVE-007 How is the time derivative of φ_t written?
- ZW-TIME-DERIVATIVE-008 What does the order of a time derivative indicate?