Abstract
In this paper we present a stochastic relaxation method based on Bayesian decision theory for voxel classification in medical images. The labels are continuous (as opposed to discrete) values representing the degree of belief that a voxel belongs to a certain object class.
In the Bayesian Decision approach, the solution to the labeling problem is constrained by specifying an a priori model for the underlying scene and by specifying the camera model. The model for the underlying scene reflects in this case a priori knowledge on anatomy and morphology. The camera model relates observed MR-image intensities to objects in the scene. Both models are described using the concept of Markov Random Fields (MRF). The optimal labeling, here defined to minimize the percentage of misclassified voxels, can then be approximated asymptotically by a stochastic sampling of the associated Gibbs posterior joint probability distribution.
The method is applied to brain tissue classification in MRI and blood vessel classification in MR angiograms.
Directors: A. Oosterlinck & A.L. Baert
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Leclerc Y.G.: “Constructing simple stable descriptions for image partitioning.”, International journal of computer vision, 3(1): 73–102, 1989.
Low K-C., Coggins J.M.: “Biomedical image segmentation using multiscale orientation fields.”, Proc. of the first conference on visualization in biomedical computing, Atlanta, Georgia, may 1990.
Evans A.C., Dai W., Collins L., Neelin P., Marrett S.: “Warping of a computerized 3-D atlas to match brain image volumes for quantitative neuroanatomical and functional analysis.”, SPIE vol. 1445 image processing, 1991.
Marrett S., Evans A.C., Collins L., Peters T.M.: “A volume of interest (VOI) atlas for the analysis of neurophysiological image data.”, SPIE vol. 1092 medical imaging III — image processing, 1989.
Gerig G., Martin J., Kikinis R., Kubler O., Shenton M., Jolesz F.A.: “Unsupervised tissue type segmentation of 3D dual-echo MR head data.”, Image and vision computing, 10(6): 349–360, 1992.
Drebin R., Carpenter R., Hanrahan P.: “Volume rendering.”, Computer Graphics, 22(4): 65–74, 1988.
Levoy M.: “Display of surfaces from volume data.”, IEEE Transactions on Computer Graphics and Applications, 8(3): 29–37, 1988.
Besag J.: “On the statistical analysis of dirty pictures.”, J. R. Statist. Soc. B., 48(3):259–302, 1986.
Kindermann R., Snell J.: “Markov random fields and their applications.”, American Methematical Society, Providence, RI, 1980.
Besag J.: “Spatial interaction and the spatial analysis of lattice systems.”, Journal of the R. Statist. Soc. B., vol. 36, 1974.
Metropolis N., Rosenbluth M. et al.: “Equation of state calculations by fast computing machines.”, Journal of chemical physics, 21: 1087–1092, 1953
Geman S., Geman D.: “Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images.”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6): 721–741, 1984.
Marroquin J., Mitter S., Poggio T.: “Probabilistic solution of ill-posed problems in computational vision.”, J. Am. Statist. Ass., 82(397): 76–89, 1987.
Tanner M., Wong W.H.: ”Calculation of posterior distributions by data augmentation”, Journal of the American Statistical Society, 82: 528–540, 1987.
Lin W.-J.: Boundary Estimation in Ultrasound Images”, Phd thesis, University of North Carolina at Chapel Hill, august 1991. Also available as Technical Report TR91-037.
Gerig G., Kübler O., Kikinis R., Jolesz F.A.: “Nonlinear anisotropic filtering of MRI data.”, IEEE transactions on medical imaging, 11(2): 221–232, 1992.
Geiger D., Yuille A.: “A common framework for image segmentation.”, Int. Journal of Computer Vision, 6(3): 227–243, 1991.
Snyder W., Logenthiran A., Santago P., Link K., Bilbro G., Rajala S.: “Segmentation of magnetic resonance images using mean field annealing.”, Image and vision computing, 10(6): 361–368, 1992.
Chalmond B.: “An iterative Gibbsian technique for reconstruction of m-ary images.”, Pattern Recognition, 22(6): 747–761, 1989.
Derin H., Elliot H.: “Modeling and segmentation of noisy and textured images using Gibbs Random Fields.”, IEEE transactions on Pattern Analysis and Machine Intelligence, 9(1): 39–55, 1987.
Lakshmanan S., Derin H.: “Simultaneous parameter estimation and segmentation of Gibbs Random Fields using Simulated Annealing.”, IEEE transactions on Pattern Analysis and Machine Intelligence, 11(8): 799–813, 1989.
Verbeeck R., Vandermeulen D., Berben L., Suetens P., Marchal G., “Magnetic Resonance Voxel Labeling based on Bayesian Decision Theory.”, accepted for publication in SPIE vol. 1898 Image Processing, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vandermeulen, D., Verbeeck, R., Berben, L., Suetens, P., Marchal, G. (1993). Continuous voxel classification by stochastic relaxation: Theory and application to MR imaging and MR angiography. In: Barrett, H.H., Gmitro, A.F. (eds) Information Processing in Medical Imaging. IPMI 1993. Lecture Notes in Computer Science, vol 687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013807
Download citation
DOI: https://doi.org/10.1007/BFb0013807
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56800-1
Online ISBN: 978-3-540-47742-6
eBook Packages: Springer Book Archive