Guaranteed improvement? #8
Description
The BlockRegistration framework is not guaranteed to produce improvement, because during the optimization phase it models deformations like this (for a 2x2 grid of nodes and an imagined 8x8 image):
However, when you apply it to the image, the deformation is made more continuous by interpolation:
As a consequence, the achieved mismatch is different from what was modeled.
One thought for how to produce guaranteed improvement would be to add a 1-dimensional minimization step: if ϕ₀ represents the identity deformation (meaning, no change), and ϕ₁ the deformation suggested by BlockRegistration, then one could minimize the mismatch obtained with (1-α)ϕ₀ + αϕ₁ for α between 0 and 1. (Equivalently, if u is the displacement, this is just testing αu.) This essentially corresponds to the notion that BlockRegistration found something useful to do but perhaps it went "too far."