Total Variation Filtered Demons for Improved Registration of Sliding Organs

Algorithm 1

Reset deformation field: 𝑣=𝟎

Set 𝑛 to a total of num iterations

Compute ∇𝑆_𝑖 for each pixel 𝑖

for 𝑖𝑡=1 to number of iterations 𝑛

 for each pixel 𝑖

  Compute intensity value in deformed image:

  𝐷(𝑖)=𝑀(𝐼_𝑑) where 𝑖_𝑑=𝑖−𝑣_𝑖

  Compute additional displacement vector:

  𝐯_𝑖=(𝑚−𝑠)𝛁𝑠(𝛁𝑠)²+𝛼₁(𝑚−𝑠)²+(𝑚−𝑠)𝛁𝑚(𝛁𝑚)²+𝛼₂(𝑠−𝑚)²

  Compute total displacement vector 𝑣=𝑣+𝑣_𝑖

 end

 Smooth v with a Total Variation filter

end