Abstract
Nonuniformity in the pixel intensity in homogeneous regions of an observed image is modeled as a multiplicative smooth bias field. The multiplicative bias field tends to increase the entropy of the original image. Thus, the entropy of the observed image is minimized to estimate the original image. The entropy minimization should be constrained such that the estimated image is close to the observed image and the estimated bias field is smooth. To enforce these constraints, the bias field is modeled as a thin–plate deforming elastically. Mathematically, the elastic deformation is described using the partial differential equation (PDE) with the body force evaluated at each pixel. In our formulation, the body force is evaluated such that the overall entropy of the image decreases. In addition, modeling the bias field as an elastic deformation ensures that the estimated image is close to the observed image and that the bias field is smooth. This provides a mathematical formulation which is simple and devoid of weighting parameters for various constraints of interest. The performance of our proposed algorithm is evaluated using both 2D and 3D simulated and real subject brain MR images.
Chapter PDF
Similar content being viewed by others
References
Ahmed, M., Yamany, S., Mohamed, N., Farag, A.: A modified fuzzy Cmeans algorithm for MRI bias field estimation and adaptive segmentation. In: Taylor, C., Colchester, A. (eds.) MICCAI 1999. LNCS, vol. 1679, pp. 72–81. Springer, Heidelberg (1999)
Arnold, J., Liow, J., Schaper, K., Stern, J., Sled, J., Shattuck, D., Worth, A., Cohen, M., Leahy, R., Mazziotta, J., Rottenberg, D.: Qualitative and quantitative evaluation of six algorithms for correcting intensity nonuniformity effects. NeuroImage 13, 931–943 (2001)
Cohen, M., DuBois, R., Zeineh, M.: Rapid and effective correction of RF inhomogeneity for high field magnetic resonance imaging. Human Brain Mapping 10, 204–211 (2000)
Davatzikos, C., et al.: A computerized method for morphological analysis of the corpus callosum. J. Comp. Assis. Tomo. 20, 88–97 (1996)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via EM algorithm. J. Royal Statistical Soc. Ser. B 39, 1–38 (1977)
Mangin, J.: Entropy minimization for automatic correction of intensity nonuniformity. In: IEEE Workshop on Math. Methods in Bio. Image Analysis (MMBIA), pp. 162–169 (2000)
McVeigh, E., Bronskill, M., Henkelman, R.: Phase and sensitivity of receiver coils in magnetic resonance imaging. Med. Phys. 13, 806–814 (1986)
Papoulis, A.: Probability, Random Variable, and Stochastic Processes, 3rd edn. McGraw–Hill, Inc. New York (1991)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C. The Art of Scientific Computing. Cambridge University Press, Cambridge (1992)
Prima, S., Ayache, N., Barrick, T., Roberts, N.: Maximum likelihood estimation of the bias field in mr brain images: Investigating different modelings of the imaging process. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 811–819. Springer, Heidelberg (2001)
Simmons, A., Tofts, P., Barker, G., Arridge, S.: Sources of intensity nonuniformity in spin echo images. Magn. Reson. Med. 32, 121–128 (1994)
Sled, G., Zijdenbos, A., Evans, A.: A nonparametric method for automatic correction of intensity nonuniformity in MRI data. IEEE Trans. of Medical Imaging 17(1), 87–97 (1998)
Viola, P., Wells, W.M.: Alignment by maximization of mutual information. In: Fifth Int. Conf. on Computer Vision, pp. 16–23 (1995)
Wells, W., Grimson, W., Kikinis, R.: Adaptive segmentation of MRI data. IEEE Trans. on Medical Imaging 15(4), 429–442 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bansal, R., Staib, L.H., Peterson, B.S. (2004). Correcting Nonuniformities in MRI Intensities Using Entropy Minimization Based on an Elastic Model. In: Barillot, C., Haynor, D.R., Hellier, P. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2004. MICCAI 2004. Lecture Notes in Computer Science, vol 3216. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30135-6_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-30135-6_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22976-6
Online ISBN: 978-3-540-30135-6
eBook Packages: Springer Book Archive