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11 - Segmentation: statistical approach

from Part V - Image analysis tools

Published online by Cambridge University Press:  05 November 2014

Aly A. Farag
Aly A. Farag
Affiliation:
University of Louisville, Kentucky
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Summary

Introduction

Segmentation is a fundamental step in understanding images. As image formation involves various sensor types, and objects vary in complexities of shape, spatial support, texture, and color, and the circumstances of the scenes may not be fully understood in advance, various approaches and algorithms for image segmentation have evolved over the years. In this book we address the basic issues in image segmentation: this chapter and the next will consider statistical and variational calculus approaches for segmentation. The focus will be on general frameworks which can be altered according to the specifics of the objects in the image, and the models used.

This chapter describes an unsupervised maximum-a-posteriori (MAP) based segmentation framework of N-dimensional multimodal images, in which objects occupy distinct, albeit overlapping, domains in the intensity histogram. The input image and its desired map (labeled image) are described by a joint Markov–Gibbs random field (MGRF) model of independent image signals and interdependent region labels. These models were discussed in Chapter 6. We deploy the kernel approach of Chapter 7 to model the joint and marginal probability densities of objects from the gray-level histogram, which incorporates a generalized linear combination of Gaussians (LCG), where the weights of the kernels may take positive and negative values, while maintaining the positivity and integrability constraints. The number of classes is estimated using a maximum likelihood approach applied to the LCG model. An approach is devised for MGRF model identification based on region characteristics. The segmentation process is conducted by using the LCG-model to provide an initial segmentation (pre-labeled image), and then a subsequent algorithm iteratively refines the labeled image using the MGRF. The convergence of the algorithm is examined, and a sensitivity analysis is performed to quantify its robustness with respect to initialization, improper estimation of the number of classes, and discontinuities in the objects. We illustrate the effectiveness of this approach for modeling and segmentation of objects (structures) in synthetic and biomedical images.

Type
Chapter
Information
Biomedical Image Analysis
Statistical and Variational Methods
 , pp. 297 - 315
Publisher: Cambridge University Press
Print publication year: 2014

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References

Sahoo, P. K., Farag, A. A. and Yeap, Y. P., Threshold selection based on histogram modeling. IEEE Int. Conf. Systems, Man, and Cybernetics, Chicago, IL (1992) 351–356.Google Scholar
Chen, P. C. and Pavlidis, T., Segmentation by texture using a cooccurrence matrix and a split-and-merge algorithm. Comput. Graph. Image Proc. 10 (1979) 172–182.CrossRefGoogle Scholar
Besag, J. E., Spatial interaction and the statistical analysis of lattice systems. J. Roy. Stat. Soc. B 36 (1974) 192–236.Google Scholar
Besag, J. E., On the statistical analysis of dirty pictures. J. Roy. Stat. Soc. B 48 (1986) 259–302.Google Scholar
Geman, S. and Geman, D., Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intel. 6 (1984) 721–741.CrossRefGoogle ScholarPubMed
Derin, H. and Elliott, H., Modeling and segmentation of noisy and textured images using Gibbs random fields. IEEE Trans. Pattern Anal. Mach. Intel. 9 (1) (1987) 39–55.CrossRefGoogle ScholarPubMed
Zhu, S., Wu, Y. and Mumford, D., Filters, random fields and maximum entropy (FRAME): Towards a unified theory of texture modeling. Int. J. Comp. Vision 27(2) (1998) 107–126.CrossRefGoogle Scholar
Zhang, Y., Brady, M. and Smith, S., Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm. IEEE Trans. Med. Imaging 20(1) (2001) 45–57.CrossRefGoogle ScholarPubMed
Farag, A. A., El-Baz, A. and Gimel’farb, G. L., Precise segmentation of multimodal images. IEEE Trans. Image Processing 15(4) (2006) 952–968.CrossRefGoogle ScholarPubMed
Ali, A. M. and Farag, A. A., Density estimation using a new AIC-type criterion and the EM algorithm for a linear combination of Gaussians. Proc. IEEE Int. Conf. Image Processing (ICIP08) (2008) 3024–3027.Google Scholar
Dubes, R. C. and Jain, A. K., Random field models in image analysis. J. Appl. Stat. 16 (1989) 131–164.CrossRefGoogle Scholar
Gimel’farb, G. L., Texture modeling with multiple pairwise pixel interactions. IEEE Trans. Pattern Anal. Mach. Intel. 18 (11) (1996) 1110–1114.CrossRefGoogle Scholar
Picard, R. W., Gibbs random field: Temperature and parameter analysis. Proc. ICASSP III, San Francisco, March (1992) 45–48.Google Scholar
Ali, A. M., Farag, A. A. and Gimel’farb, G., Analytical method for MGRF Potts model parameters estimation, in Proc. Int. Conf. Pattern Recognition (ICPR-08), Tampa, Florida (2008) 1–4.Google Scholar
Boykov, Y. Y. and Jolly, M. P., Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images. Proc. ICCV 1 (2001) 105–112.Google Scholar
Boykov, Y., Veksler, O. and Zabih, R., Fast approximation energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intel. 23(11) (2001) 1222–1239.CrossRefGoogle Scholar
Boykov, Y. and Kolmogorov, V., An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Trans. Pattern Anal. Mach. Intel. 26(9) (2004) 1124–1137.CrossRefGoogle ScholarPubMed
Comaniciu, D. and Meer, P., Mean shift: A robust approach toward feature space analysis. IEEE Trans. Pattern Anal. Mach. Intel. 24 (5) (2002) 603–619.CrossRefGoogle Scholar
Shi, J. and Malik, J., Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intel. 22(8) (2000) 888–905.Google Scholar
Hu, S., Hoffman, E. A. and Reinhardt, J. M., Automatic lung segmentation for accurate quantitation of volumetric X-ray CT images. IEEE Trans. Med. Imag. 20(6) (2001) 490–498.CrossRefGoogle ScholarPubMed
Farag, Amal, Graham, J. H. and Farag, A. A., Robust segmentation of lung tissue in chest CT scanning. Proc. IEEE Int. Conf. Image Processing (ICIP) (2010) 2249–2252.Google Scholar
Farag, A. A., Modeling small objects under uncertainties: novel algorithms and applications. Unpublished Ph.D. thesis, University of Louisville, Department of Electrical and Computer Engineering, (2012).
Aslan, M. S., Ali, A., Farag, A. A. et al., 3D vertebral body segmentation using shape based graph cuts. 20th Int. Conf. Pattern Recognition, ICPR’10, Istanbul, Turkey (2010) 3951–3954.Google Scholar
Yuksel, S. E., El-Baz, A., Farag, A. A. et al., Automatic detection of renal rejection after kidney transplantation, Proc. Computer Assisted Radiology and Surgery (CARS), Berlin, Germany, June 22–25, (2005) 773–778.Google Scholar
Ali, A., Farag, A. A. and El-Baz, A., Graph cuts framework for kidney segmentation with prior shape constraints, Proc. Int. Conf. Medical Image Computing and Computer-Assisted Intervention (MICCAI’07), Sydney, Australia, October 29 – November 2 (2007) 384–392.Google Scholar
Hassouna, M. S., Farag, A. A., Hushek, S. and Moriarty, T., Cerebrovascular segmentation from TOF using stochastic models, Med. Image Anal. 10 (1) (2006) 2–16.CrossRefGoogle ScholarPubMed
El-Baz, A., Farag, A. A., Gimel’farb, G. L., El-Ghar, M. Abou and Eldiasty, T., A new adaptive probabilistic model of blood vessels for segmenting MRA images, Proc. Int. Conf. Medical Image Computing and Computer-Assisted Intervention (MICCAI’06), Copenhagen, Denmark, October 1–6 (2006) 799–806.Google Scholar
Ali, A., Farag, A., Al-Ajlan, N. and Farag, A. A., Multimodal imaging-modeling and segmentation with biomedical applications. Brit. Comp. Vision J., IET-CV 6 (2012) 524–539.CrossRefGoogle Scholar

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