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. Author manuscript; available in PMC: 2014 Dec 1.
Published in final edited form as: Med Image Anal. 2013 Aug 19;17(8):1181–1191. doi: 10.1016/j.media.2013.08.001

Table 3.

Summary of the proposed unified registration / label fusion framework.

  1. Initialize registrations with affine transforms. Initialize Gaussian parameters with sample means and variances. Set bias field coefficients bk = 0, ∀k. Set qx(m) = 1/N, ∀x, m.

  2. For each resolution level, from coarse to fine:
    • a)
      update q with Equation 4 until convergence.
    • b)
      update means and variances with Equations 6 and 7.
    • c)
      update the bias field parameters with the BFGS algorithm, using the expression in Equation 8 for the gradient.
    • d)
      Update the registration by:
      1. computing un(x) with Equation 9.
      2. adding the result to the current estimate of the deformation, i.e., Tn ← Tn + un.
      3. update Tn’s with Equation 12
      4. update T with Equation 13
    • d)
      If parameter estimates not converged, go to (b)

  3. Use the latest estimate of q to obtain the final segmentation with Equation 14.