Exercise · ZW-LDDMM-003 · ★☆☆ Basic
A discretization produces a velocity field that creates folds and stops being invertible. What was lost?
Choose one option.
Show answer
- D. The guarantee of a diffeomorphic deformation
Explanation
A discretized field can create folds and lose invertibility. What is lost is the guarantee that the deformation is diffeomorphic.
Review the concept: LDDMM
LDDMM (Large Deformation Diffeomorphic Metric Mapping) is a registration framework that looks for a smooth diffeomorphic deformation \(\varphi_t\), generated by a vector field \(v_t\), with minimum energy \(E_{\min}\).
\[\begin{gathered}\dot{\varphi}_t=v_t\circ\varphi_t\\\varphi_0=\operatorname{id}\end{gathered}\]
More practice problems: lddmm
- ZW-LDDMM-001 If φ_0=id and φ_1 is fixed, what distinguishes the solution that LDDMM prefers?
- ZW-LDDMM-002 In φ_t=v_t∘φ_t, what does evaluating the right-hand side at a point x mean?
- ZW-LDDMM-004 Two flows reach the same target and have energies E_A=9 and E_B=4. If both are admissible, which cr…
- ZW-LDDMM-005 In geodesic shooting, why can an initial velocity determine the whole trajectory?
- ZW-LDDMM-006 A method chains many pairwise registrations and reaches the target. Which conclusion is NOT justifi…
- ZW-LDDMM-007 If φ_1 takes the template to the target, what does φ_1^-1 naturally represent?
- ZW-LDDMM-008 Which property by itself characterizes an admissible diffeomorphic deformation?
- ZW-LDDMM-009 What change would directly weaken the interpretation of LDDMM as a geometric problem with a metric?