Continuous Gaussian mixture modeling
When the projection of a collection of samples onto a subset of basis feature vectors has a Gaussian distribution, those samples have a generalized projective Gaussian distribution (GPGD). GPGDs arise in a variety of medical images as well as some speech recognition problems. We will demonstrate that GPGDs are better represented by continuous Gaussian mixture models (CGMMs) than finite Gaussian mixture models (FGMMs).
This paper introduces a novel technique for the automated specification of CGMMs, height ridges of goodness-of-fit. For GPGDs, Monte Carlo simulations and ROC analysis demonstrate that classifiers utilizing CGMMs defined via goodness-of-fit height ridges provide consistent labelings and compared to FGMMs provide better true-positive rates (TPRs) at low false-positive rates (FPRs). The CGMM-based classification of gray and white matter in an inhomogeneous magnetic resonance (MR) image of the brain is demonstrated.
KeywordsGaussian Mixture Model Intensity Inhomogeneity Gradient Ascent Height Ridge Maximum Likelihood Expectation Maximization
Unable to display preview. Download preview PDF.
- 1.Aylward, S.R., “Continuous Mixture Modeling via Goodness-of-Fit Cores,” Dissertation, Department of Computer Science, University of North Carolina, Chapel Hill, 1997Google Scholar
- 2.Aylward, S.R. and Coggins, J.M., “Spatially Invariant Classification of Tissues in MR Images.” Visualization in Biomedical Computing, Rochester, MN, 1994Google Scholar
- 3.Bellegarda, J.R. and Nahamoo, D., “Tied Mixture Continuous Parameter Modeling for Speech Recognition.” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 38, no. 12. 1990 p. 2033–2045Google Scholar
- 4.Dawant, B.M., Zijdenbos, A.P. and Margolin, R.A., “Correction of Intensity Variations in MR Images for Computer-Aided Tissue Classification.” IEEE Transactions on Medical Imaging, vol. 12, no. 4. 1993 p. 770–781Google Scholar
- 5.Depmster, A., Laird, N., Rubin, D., “Maximum Likelihood for Incomplete Data via the EM Algorithm.” Royal Statistical Society, vol. 1, no. 1. 1977Google Scholar
- 6.Egan, J.P., Signal detection theory and ROC analysis. Academic Press, Inc., New York, 1975Google Scholar
- 7.Jordan, M.I. and Xu, L., “Convergence Results for the EM Approach to Mixtures of Experts Architectures.” Technical Report, Massachusetts Institute of Technology, Artificial Intelligence Laboratory, November 18, 1994Google Scholar
- 8.Liang, Z., Jaszezak, R.J. and Coleman, R.E., “Parameter Estimation of Finite Mixtures Using the EM Algorithm and Information Criteria with Application to Medical Image Processing.” IEEE Transactions on Nuclear Science, vol. 39, no. 4. 1992 p. 1126–1133Google Scholar
- 9.McLachlan, G.J. and Basford, K.E., Mixture Models. Marcel Dekker, Inc., New York, vol. 84, 1988 p. 253Google Scholar
- 10.Meyer, C.R., Bland, P.H. and Pipe, J., “Retrospective Correction of Intensity Inhomogeneities in MRI.” IEEE Transactions on Medical Imaging, vol. 14, no. 1. 1995 p. 36–41Google Scholar
- 11.Morse, B.S., Pizer, S.M., Puff, D.T. and Gu, C., “Zoom-Invariant Vision of Figural Shape: Effects on Cores of Image Disturbances.” Computer Vision and Image Understanding, Accepted, 1997Google Scholar
- 12.Pizer, S.M., Eberly, D., Morse, B.S. and Fritsch, D.S., “Zoom-invariant Vision of Figural Shape: the Mathematics of Cores.” Computer Vision and Image Understanding, Accepted, 1997Google Scholar
- 13.Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T., Numerical Recipes in C. Cambridge University Press, Cambridge, 1990Google Scholar
- 14.Read, T.R.C. and Cressie, N.A.C., Goodness-of-fit statistics for discrete multivariate data. Springer-Verlag, New York, 1988Google Scholar
- 15.Titterington, D.M., Smith, A.G.M. and Markov, U.E., Statistical Analysis of Finite Mixture Distributions. John Wiley and Sons, Chichester, 1985Google Scholar
- 16.Wells III, W.M., Grimson, W.E.L., Kikinis, R. and Jolesz, F.A., “Adaptive Segmentation of MRI Data.” IEEE Transactions on Medical Imaging, vol. 15, no. 4. 1996 p. 429–442Google Scholar
- 17.Yoo, T. “Image Geometry Through Multiscale Statistics,” Dissertation, Department of Computer Science, University of North Carolina, Chapel Hill, 1996Google Scholar
- 18.Zhuang, X., Huang, Y., Palaniappan, K. and Zhao, Y., “Gaussian Mixture Density Modeling, Decomposition, and Applications.” IEEE Transactions on Image Processing, vol. 5, no. 9. 1996 p. 1293–1302Google Scholar