Symmetric and inverse-consistent deformable registration

A method for symmetric and inverse-consistent registration of a pair of digital images, comprising the steps of:

• calculating a first update of a forward transformation of a first digital image to a second digital image from a previous update of the forward transformation and a gradient of a cost function of the first and second digital images;
• calculating a first update of a backward transformation of the second digital image to the first digital image from an inverse of the first update of the forward transformation;
• initializing an error correction to the forward transformation, and
• calculating the error correction for the forward transformation according to
• φj+1−1=ν(−φj(id·φj−1(x)))+(1−ν)φj−1(x)
• j=1, . . . , K,
• νε[0,1],
• wherein φj, φj−1 are the to-be-corrected forward and backward transformations, K is the number of iterations for which the error correction is calculated, id is an identity transformation, x is an image point, and ν is a weighting factor that trades off convergence speed and robustness.

A non-transitory program storage device readable by a computer, tangibly embodying a program of instructions executed by the computer to perform the method steps for symmetric and inverse-consistent registration of a pair of digital images, the method comprising the steps of:

• calculating a first update of a forward transformation of a first digital image to a second digital image from a previous update of the forward transformation and a gradient of a cost function of the first and second digital images;
• calculating a first update of a backward transformation of the second digital image to the first digital image from an inverse of the first update of the forward transformation;
• calculating a second update of the backward transformation from first update of the backward transformation and the gradient of a cost function of the second and first digital images;
• and
• calculating a second update of the forward transformation from an inverse of the second update of the backward transformation.