Exercise · ZW-LDDMM-002 · ★★☆ Intermediate

In \(\dot{\varphi}_t=v_t\circ\varphi_t\), what does evaluating the right-hand side at a point \(x\) mean?

Choose one option.

Show answer
  • A. Taking the velocity \(v_t\) at the current position \(\varphi_t(x)\)

Explanation

Evaluating \(v_t\circ\varphi_t\) at \(x\) means using the velocity at the already transported position \(\varphi_t(x)\). The field thus follows the point as it moves.

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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

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