Exercise · ZW-LDDMM-001 · ★★☆ Intermediate

If \(\varphi_0=\operatorname{id}\) and \(\varphi_1\) is fixed, what distinguishes the solution that LDDMM prefers?

Choose one option.

Show answer
  • B. It minimizes \(\int_0^1\|v_t\|_V^2\,dt\) among the admissible flows

Explanation

LDDMM chooses the admissible flow whose energy \(\int_0^1\|v_t\|_V^2\,dt\) is minimal. This is the central rule of the framework, which seeks the minimum-cost geodesic.

Open the ZWMath map →

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-002 →