Exercise · ZW-VECTOR-FIELD-004 · ★★☆ Intermediate
A smooth vector field can generate a flow, but that does not mean the flow preserves all distances. What distinguishes the two ideas?
Choose one option.
A Smoothness controls regularity and invertibility; being an isometry would also require preserving distances B Smoothness and distance are exactly the same property C A vector field only exists in discrete spaces D Preserving distances removes the need for an inverse Show answer A. Smoothness controls regularity and invertibility; being an isometry would also require preserving distances← Back to the question
Explanation A smooth field generates a regular, invertible flow, but an isometry must also preserve all distances. These are distinct properties.
A velocity field \(v_t\) is a vector field that changes with time: at each instant \(t\) it assigns to every point the velocity at which it moves. In LDDMM it guides the smooth motion of the deformation.
\[v_t(x)\]
More practice problems: velocity field