Abstract
We describe a new approach for estimating the posterior probability of tissue labels. Conventional likelihood models are combined with a curve length prior on boundaries, and an approximate posterior distribution on labels is sought via the Mean Field approach. Optimizing the resulting estimator by gradient descent leads to a level set style algorithm where the level set functions are the logarithm-of-odds encoding of the posterior label probabilities in an unconstrained linear vector space. Applications with more than two labels are easily accommodated. The label assignment is accomplished by the Maximum A Posteriori rule, so there are no problems of “overlap” or “vacuum”. We test the method on synthetic images with additive noise. In addition, we segment a magnetic resonance scan into the major brain compartments and subcortical structures.
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References
Fischl, B., van der Kouwe, A., Destrieux, C., Halgren, E., Segonne, F., Salat, D., Busa, E., Seidman, L., Goldstein, J., Kennedy, D., Caviness, V., Makris, N., Rosen, B., Dale, A.: Automatically parcellating the human cerebral cortex. Cerebral Cortex 14, 11–22 (2004)
Yezzi, A., Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A.: A geometric snake model for segmentation of medical imagery. IEEE Transactions on Medical Imaging 16(2), 199–209 (1997)
Krissian, K., Malandain, G., Ayache, N., Vaillant, R., Trousset, Y.: Model based detection of tubular structures in 3d images. Computer Vision and Image Understanding 80(2), 130–171 (2000)
Leventon, M., Grimson, W., Faugeras, O.: Statistical shape influence in geodesic active contours. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1316–1323. IEEE Computer Society Press, Los Alamitos (2000)
Tsai, A., Yezzi, A., Wells, W., Tempany, C., Tucker, D., Fan, A., Grimson, W., Willsky, A.: A shape-based approach to the segmentation of medical imagery using level sets. IEEE Transactions on Medical Imaging 22(2), 137–154 (2003)
Rousson, M., Paragios, N., Deriche, R.: Active shape models from a level set perspective. Technical Report 4984, Institut National de Recherche en Informatique et en Automatique (2003)
Yang, J., Staib, L.H., Duncan, J.S.: Neighbor-constrained segmentation with level set based 3D deformable models. IEEE Transactions on Medical Imaging 23(8), 940–948 (2004)
Xu, M., Thompson, P., Toga, A.: An adaptive level set segmentation on a triangulated mesh. IEEE Transactions on Medical Imaging 23(2), 191–201 (2004)
Yushkevich, P., Piven, J., Hazlett, H., Smith, R., Ho, S., Gee, J., Gerig, G.: User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability. NeuroImage 31(1), 1116–1128 (2006)
Kapur, T.: Model based three dimensional Medical Imaging Segmentation. PhD thesis, Massachusetts Institute of Technology (1999)
Van Leemput, K., Maes, F., Vandermeulen, D., Suetens, P.: Automated model-based tissue classification of MR images of the brain. IEEE Transactions on Medical Imaging 18(10), 897–908 (1999)
Besag, J.: On the statistical analysis of dirty pictures. Journal of the Royal Society. Series B. 48(3), 259–302 (1986)
Fischl, B., Salat, D., Busa, E., Albert, M., Dieterich, M., Haselgrove, C., van der Kouwe, A., Killiany, R., Kennedy, D., Klaveness, S., Montillo, A., Makris, N., Rosen, B., Dale, A.: Whole brain segmentation: Automated labeling of neuroanatomical structures in the human brain. Neuron 33 (2002)
Zhang, Y., Brady, M., Smith, S.: Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm. IEEE Transactions on Medical Imaging 20(1), 45–57 (2001)
Marroquin, J., Santana, E., Botello, S.: Hidden Markov measure field models for image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 25, 1380–1387 (2003)
Pohl, K., Fisher, J., Shenton, M., McCarley, R.W., Grimson, W., Kikinis, R., Wells, W.: Logarithm odds maps for shape representation. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4191, pp. 955–963. Springer, Heidelberg (2006)
Pohl, K.M., Fisher, J., Grimson, W., Kikinis, R., Wells, W.: A Bayesian model for joint segmentation and registration. NeuroImage 31(1), 228–239 (2006)
Kendall, M.G., Buckland, W.R.: A Dictionary of Statistical Terms. Longman Group (1976)
Evans, M., Hastings, N., Peacock, B.: 4: Bernoulli Distribution. In: Statistical Distributions, 3rd edn. pp. 31–33. Wiley, Chichester (2000)
Taron, M., Paragios, N., Jolly, M.P.: Modelling shapes with uncertainties: Higher order polynomials, variable bandwidth kernels and non-parametric density estimation. In: IEEE International Conference on Computer Vision, IEEE Computer Society Press, Los Alamitos (2005)
Grayson, M.: The heat equation shrinks embedded plane curves to round points. Journal of Differential Geometry 26(2), 285–314 (1987)
Krissian, K., Westin, C.: Fast sub-voxel re-initialization of the distance map for level set methods. Pattern Recognition Letters 26(10), 1532–1542 (2005)
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Pohl, K.M., Kikinis, R., Wells, W.M. (2007). Active Mean Fields: Solving the Mean Field Approximation in the Level Set Framework. In: Karssemeijer, N., Lelieveldt, B. (eds) Information Processing in Medical Imaging. IPMI 2007. Lecture Notes in Computer Science, vol 4584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73273-0_3
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DOI: https://doi.org/10.1007/978-3-540-73273-0_3
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