The computation of 3D vector field is done to avoid a voxel-by-voxel comparison (as a subtraction for example).

After the non-rigid registration, we obtain an apparent 3D displacement field u. Therefore there is a 3D vector at each point P (u(P)) that shows its displacement over time. On the other hand there is a deformation fonction phi at each point P:

 

• When focusing on a shrinking lesion, we see that a 2D projection of the field from 1 to 2 (second image) is representative of the apparent motion over time (first animated image):

• We can show the 3D displacement field around this shrinking lesion:

• And finally it is possible to visualize the effect of the field on a 3D regular grid.

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