B* = affine_transform(B)

f(θ,tx,ty) = σ(A-B*)

[U V 1] = [X Y 1]*[cos(θ) -sin(θ) 0; sin(θ) cos(θ) 0; tx ty 1]

[sin(θ) -cos(θ) 0; cos(θ) -sin(θ) 0; 0 0 0]

[0 0 0; 0 0 0; 1 0 1]

[0 0 0; 0 0 0; 0 1 1]