Another Bias Correction Method John Ashburner


Re-estimating  makes use of the histogram and its gradient w.r.t. intensity - therefore zeroeth degree splines can not be used



Yüklə 0,75 Mb.
səhifə6/6
tarix28.12.2021
ölçüsü0,75 Mb.
#17120
1   2   3   4   5   6

Re-estimating makes use of the histogram and its gradient w.r.t. intensity - therefore zeroeth degree splines can not be used.



Regularisation + Optimisation

  • Distinction between intensity variations due to:

    • bias artefact due to MR physics
    • different tissue properties.
  • Don’t want to over-fit the data, so regularisation is used.

  • Maximise the joint probability of y and , assuming independence of and :

  • P(y,|) = P(y|,) P()

    • where P() is assumed to be a d dimensional multi-normal distribution:
  • P() = N (0,C0) = ((2)d|C0|)-1/2 exp{ -1/2 (-0)TC0 -1 (-0)}

  • A Newton-Raphson optimisation scheme can be derived from this:

  • First and second derivatives of E can be efficiently computed by parameterising the bias field in terms of separable basis functions.



A Quick Evaluation



Discussion

  • Optimising the current objective function is equivalent to optimising the entropy of the probability distribution of log-transformed intensities.

    • Entropy of log-transformed data is:
      • H = -I-1i log{i() yi k k k(i()yi)} = I-1 E - I-1 i log{yi}
      • where I is the number of voxels.
  • Histograms are produced from intensities that are not log-transformed.

    • Same method can be applied to images containing low or negative image intensities.
  • Resolves a problem pointed out by Arnold et al (2001), with the SPM99 bias correction approach (Ashburner, 2000):

    • The entropy of non-transformed intensity distribution is maximised when the estimated bias field is uniformly zero.
    • Resulted in side effects because average bias (rather than average corrected image intensity) was constrained to one.
  • Accuracy of the results depends on form and magnitude of regularisation.



References

  • J.B. Arnold, J.S. Liow, K.A. Schaper, J.J. Stern, J.G. Sled, D.W. Shattuck, A.J. Worth, M.S. Cohen, R.M. Leahy, J.C. Mazziotta & D.A. Rottenberg. Qualitative and quantitative evaluation of six algorithms for correcting intensity nonuniformity effect. NeuroImage 3(15):931-943, 2001.

  • J. Ashburner & K.J. Friston. Voxel-based morphometry - the methods. NeuroImage 11:805-821, 2000.

  • R.K.-S. Kwan, A.C. Evans & G.B. Pike. An Extensible MRI Simulator for Post-Processing Evaluation. Visualization in Biomedical Computing (VBC'96). Lecture Notes in Computer Science, vol. 1131. Springer-Verlag, 1996. 135-140

  • J.-F. Mangin. Entropy minimisation for automatic correction of intensity nonuniformity. In Proc. IEEE Workshop on Mathematical Methods in Biomedical Image Analysis, 2000.

  • J.G. Sled, A.P. Zijdenbos & A.C. Evans. A non-parametric method for automatic correction of intensity nonuniformity in MRI data. IEEE Transactions on Medical Imaging 17(1):87-97, 1998.

  • K. Van Leemput, F. Maes, D. Vandermeulen & P. Seutens. Automated model-based bias field correction of MR images of the brain. IEEE Transactions on Medical Imaging 18(10):885-896, 1999.

  • W.M Wells III, W.E.L Grimson, R. Kikinis & F.A. Jolesz. Adaptive segmentation of MRI data. IEEE Transactions on Medical Imaging 15(4):429-442, 1996.



Yüklə 0,75 Mb.

Dostları ilə paylaş:
1   2   3   4   5   6




Verilənlər bazası müəlliflik hüququ ilə müdafiə olunur ©azkurs.org 2024
rəhbərliyinə müraciət

gir | qeydiyyatdan keç
    Ana səhifə


yükləyin