Exercise · ZW-LDDMM-009 · ★★☆ Intermediate

What change would directly weaken the interpretation of LDDMM as a geometric problem with a metric?

Choose one option.

Show answer
  • B. Replacing the cost with an arbitrary, asymmetric score with no norm or energy

Explanation

Removing the metric or the energy eliminates the Riemannian structure that gives LDDMM its geometric meaning. The other choices are standard ingredients of the framework.

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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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