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."
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
ϕ₀represents the identity deformation (meaning, no change), andϕ₁the deformation suggested by BlockRegistration, then one could minimize the mismatch obtained with(1-α)ϕ₀ + αϕ₁forαbetween 0 and 1. (Equivalently, ifuis the displacement, this is just testingαu.) This essentially corresponds to the notion that BlockRegistration found something useful to do but perhaps it went "too far."CC @ChantalJuntao