Patent ID: 7616836

Claim:
A method for motion compensation in first and second images in a temporal sequence by computing a deformation function, said method comprising: using a computer to performing a conjugate gradient maximization of a similarity measure between said first and second images; and deriving said deformation function by utilizing said gradient maximization in conjunction with composition of a plurality of regularized gradients of said similarity measure such that said deformation function exhibits essentially no singularities, wherein said step of deriving said deformation function comprises applying an algorithm to update a displacement field between said images, comprising: field between said images, comprising: { Let ⁢ ⁢ U 0 = id For ⁢ ⁢ k = 1 ⁢ ⁢ ⋯ ⁢ ⁢ n ⁢ : ⁢ v k = G σ * ∇ S ⁡ ( I 1 , I 2 ⁢ ∘ ⁢ ϕ k ) ⁢ ϕ k + 1 = ϕ k ⁢ ∘ ⁢ ( id + ɛ k ⁢ v k ) End wherein U 0 denotes a current estimation of said displacement field, id denotes an identity function, k denotes an index, V k denotes a regularized gradient of said similarity measure, operator G σ * denotes convolution by a Gaussian kernel, S denotes the similarity measure, ∇S denotes the gradient of S with respect to φ, I 1 :→R denotes said first image, I 2 :→R denotes said second image, φ:Ω→R 3 denotes said deformation such that said similarity measure is maximized, ∘ denotes composition of functions, and ε k is the step size, which is made sufficiently small to ensure invertibility.