Diffeomorphic Registration of Images with Variable Contrast Enhancement

Figure 2

The diffeomorphic flow exp(𝐷) associated to the vector field 𝐷 is the solution at time 𝑡=1 on the trajectory tangent to 𝐷 at each point (here represented in 2D). We see that the motion of 𝑥 induced by exp(𝐷)(𝑥) is more compatible with 𝑉 than this produced by Δ(𝑥)=𝑥+𝐷(𝑥).