Diffeomorphic Registration of Images with Variable Contrast Enhancement

Table 1

Multiscale nonparametric procedure.

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Inputs and parameters:

 (i) Images 𝑓 and 𝑚 defined on 1D4A2.

 (ii) Number of scales 𝐽.

 (iii) A stopping criterion 𝒮.

 (iv) Gaussian kernel variance 𝜎^2Ψ of Ψ.

Output: The displacement field 𝐷_𝑎.

Algorithm:

 (4)  Initialization:

  Set scale to 𝑗=𝐽 and initialize 𝐷_𝑎=0 on 𝒢_𝐽+1.

  (5)  Transfer on grid 𝒢_𝑗:

  Compute 𝑚_𝑗 =Down_j (𝑚), 𝑓_𝑗=Down_j (𝑓),

  and assign 𝐷_𝑎←  Up(𝐷_𝑎).

  (6) While 𝒮 is false, do:

  (i) Warping: 𝑤=𝑚_𝑗∘Δ_𝑎

  (ii) Field computation: 𝐷_𝑢←Θ(𝑓_𝑗,𝑤)

  (iii) Accumulation: 𝐷_𝑎←Φ(𝐷_𝑎,𝐷_𝑢)

  (iv) Regularization: 𝐷_𝑎←Ψ(𝐷_𝑎)

  (7) If 𝑗=0, stop and return 𝐷_𝑎,

  else, set 𝑗←𝑗−1 and return to step (5).

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