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Published in: Pattern Analysis and Applications 2/2009

01-06-2009 | Theoretical Advances

Semi-supervised discriminative classification with application to tumorous tissues segmentation of MR brain images

Authors: Yangqiu Song, Changshui Zhang, Jianguo Lee, Fei Wang, Shiming Xiang, Dan Zhang

Published in: Pattern Analysis and Applications | Issue 2/2009

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Abstract

Due to the large data size of 3D MR brain images and the blurry boundary of the pathological tissues, tumor segmentation work is difficult. This paper introduces a discriminative classification algorithm for semi-automated segmentation of brain tumorous tissues. The classifier uses interactive hints to obtain models to classify normal and tumor tissues. A non-parametric Bayesian Gaussian random field in the semi-supervised mode is implemented. Our approach uses both labeled data and a subset of unlabeled data sampling from 2D/3D images for training the model. Fast algorithm is also developed. Experiments show that our approach produces satisfactory segmentation results comparing to the manually labeled results by experts.

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Appendix
Available only for authorised users
Footnotes
1
Semi-supervised methods could be either transductive or inductive [32, 33]. While a transductive method only works on the observed labeled and unlabeled training data, the inductive methods can naturally handle the unseen data that are not in training set [33].
 
2
For the positive semi-definite case, we can add extra regularization as the jitter noise [59].
 
3
Namely, if we want to induce \({\varvec{\Updelta}}_{N+1}\) from \({\varvec{\Updelta}}_N\) directly, it need compute D ii of each new give point. This is very time consuming.
 
4
The weight matrix is near semi-positive definite, so we use the pseudo-inverse or add the extra regularization to find the square root of A in practice.
 
Literature
1.
go back to reference Song Y, Zhang C, Lee J, Wang F (2006) A discriminative method for semi-automated tumorous tissues segmentation of MR brain images. In: Proceedings of CVPR workshop on mathematical methods in biomedical image analysis (MMBIA). p 79 Song Y, Zhang C, Lee J, Wang F (2006) A discriminative method for semi-automated tumorous tissues segmentation of MR brain images. In: Proceedings of CVPR workshop on mathematical methods in biomedical image analysis (MMBIA). p 79
2.
go back to reference Pham DL, Xu C, Prince JL (2000) Current methods in medical image segmentation. Annu Rev Biomed Eng 2:315–337CrossRef Pham DL, Xu C, Prince JL (2000) Current methods in medical image segmentation. Annu Rev Biomed Eng 2:315–337CrossRef
3.
go back to reference Liew AWC, Yan H (2006) Current methods in the automatic tissue segmentation of 3D magnetic resonance brain images. Curr Med Imaging Rev 2(1):91–103CrossRef Liew AWC, Yan H (2006) Current methods in the automatic tissue segmentation of 3D magnetic resonance brain images. Curr Med Imaging Rev 2(1):91–103CrossRef
4.
go back to reference Leemput KV, Maes F, Vandermeulen D, Suetens P (1999) Automated model-based tissue classification of MR images of the brain. IEEE Trans Med Imaging 18(10):897–908CrossRef Leemput KV, Maes F, Vandermeulen D, Suetens P (1999) Automated model-based tissue classification of MR images of the brain. IEEE Trans Med Imaging 18(10):897–908CrossRef
5.
go back to reference Pham D, Prince J (1999) Adaptive fuzzy segmentation of magnetic resonance images. IEEE Trans Med Imaging 18(9):737–752CrossRef Pham D, Prince J (1999) Adaptive fuzzy segmentation of magnetic resonance images. IEEE Trans Med Imaging 18(9):737–752CrossRef
6.
go back to reference Zhang Y, Brady M, Smith SM (2001) Segmentation of brain MR images through a hidden Markov random field model and the expectation maximization algorithm. IEEE Trans Med Imaging 20(1):45–57CrossRef Zhang Y, Brady M, Smith SM (2001) Segmentation of brain MR images through a hidden Markov random field model and the expectation maximization algorithm. IEEE Trans Med Imaging 20(1):45–57CrossRef
7.
go back to reference Marroquín JL, Vemuri BC, Botello S, Calderón F, Fernández-Bouzas A (2002) An accurate and efficient Bayesian method for automatic segmentation of brain MRI. IEEE Trans Med Imaging 21(8):934–945CrossRef Marroquín JL, Vemuri BC, Botello S, Calderón F, Fernández-Bouzas A (2002) An accurate and efficient Bayesian method for automatic segmentation of brain MRI. IEEE Trans Med Imaging 21(8):934–945CrossRef
8.
go back to reference Liew AWC, Yan H (2003) An adaptive spatial fuzzy clustering algorithm for 3d MR image segmentation. IEEE Trans Med Imaging 22(9):1063–1075CrossRef Liew AWC, Yan H (2003) An adaptive spatial fuzzy clustering algorithm for 3d MR image segmentation. IEEE Trans Med Imaging 22(9):1063–1075CrossRef
9.
go back to reference Prastawa M, Gilmore JH, Lin W, Gerig G (2004) Automatic segmentation of neonatal brain MRI. In: Proceedings of medical image computing and computer-assisted intervention (MICCAI). pp 10–17 Prastawa M, Gilmore JH, Lin W, Gerig G (2004) Automatic segmentation of neonatal brain MRI. In: Proceedings of medical image computing and computer-assisted intervention (MICCAI). pp 10–17
10.
go back to reference Hall L, Bensaid A, Clarke L, Velthuizen R, Silbiger M, Bezdek J (1992) A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain. IEEE Trans Med Imaging 3(5):672–682 Hall L, Bensaid A, Clarke L, Velthuizen R, Silbiger M, Bezdek J (1992) A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain. IEEE Trans Med Imaging 3(5):672–682
11.
go back to reference Sammouda R, Niki N, Nishitani H (1996) A comparison of Hopfield neural network and Boltzmann machine in segmenting MR images of the brain. IEEE Trans Nucl Sci 43(6):3361–3369CrossRef Sammouda R, Niki N, Nishitani H (1996) A comparison of Hopfield neural network and Boltzmann machine in segmenting MR images of the brain. IEEE Trans Nucl Sci 43(6):3361–3369CrossRef
12.
go back to reference Zhou J, Chan KL, Chongand VFH, Krishnan SM (2005) Extraction of brain tumor from MR images using one-class support vector machine. In: Proceedings of 27th annual international conference of the IEEE Engineering in Medicine and Biology Society (EMBS). pp 6411–6414 Zhou J, Chan KL, Chongand VFH, Krishnan SM (2005) Extraction of brain tumor from MR images using one-class support vector machine. In: Proceedings of 27th annual international conference of the IEEE Engineering in Medicine and Biology Society (EMBS). pp 6411–6414
13.
go back to reference Moon N, Bullitt E, Leemput KV, Gerig G (2002) Automatic brain and tumor segmentation. In: Proceedings of 5th international conference on medical image computing and computer-assisted intervention (MICCAI). pp 372–379 Moon N, Bullitt E, Leemput KV, Gerig G (2002) Automatic brain and tumor segmentation. In: Proceedings of 5th international conference on medical image computing and computer-assisted intervention (MICCAI). pp 372–379
14.
go back to reference Shen S, Sandham W, Granat M, Sterr A (2005) MRI fuzzy segmentation of brain tissue using neighborhood attraction with neural-network optimization. IEEE Trans Med Imaging 9(3):459–467 Shen S, Sandham W, Granat M, Sterr A (2005) MRI fuzzy segmentation of brain tissue using neighborhood attraction with neural-network optimization. IEEE Trans Med Imaging 9(3):459–467
15.
go back to reference Li C, Goldgof D, Hall L (1993) Knowledge-based classification and tissue labeling of MR images of human brain. IEEE Trans Med Imaging 12(4):740–750CrossRef Li C, Goldgof D, Hall L (1993) Knowledge-based classification and tissue labeling of MR images of human brain. IEEE Trans Med Imaging 12(4):740–750CrossRef
16.
go back to reference Clark M, Hall L, Goldgof D, Velthuizen R, Murtagh F, Silbiger M (1998) Automatic tumor segmentation using knowledge-based techniques. IEEE Trans Med Imaging 17(2):187–201CrossRef Clark M, Hall L, Goldgof D, Velthuizen R, Murtagh F, Silbiger M (1998) Automatic tumor segmentation using knowledge-based techniques. IEEE Trans Med Imaging 17(2):187–201CrossRef
17.
go back to reference Cuadra M, Pollo C, Bardera A, Cuisenaire O, Villemure JG, Thiran JP (2004) Atlas-based segmentation of pathological MR brain images using a model of lesion growth. IEEE Trans Med Imaging 23(10):1301–1314CrossRef Cuadra M, Pollo C, Bardera A, Cuisenaire O, Villemure JG, Thiran JP (2004) Atlas-based segmentation of pathological MR brain images using a model of lesion growth. IEEE Trans Med Imaging 23(10):1301–1314CrossRef
18.
go back to reference Zhu Y, Yan Z (1997) Computerized tumor boundary detection using a hopfield neural network. IEEE Trans Med Imaging 16(1):55–67CrossRef Zhu Y, Yan Z (1997) Computerized tumor boundary detection using a hopfield neural network. IEEE Trans Med Imaging 16(1):55–67CrossRef
19.
go back to reference Droske M, Meyer B, Rumpf M, Schaller C (2001) An adaptive level set method for medical image segmentation. In: Proceedings of 17th international conference information processing in medical imaging (IPMI). Davis, CA, USA, pp 416–422 Droske M, Meyer B, Rumpf M, Schaller C (2001) An adaptive level set method for medical image segmentation. In: Proceedings of 17th international conference information processing in medical imaging (IPMI). Davis, CA, USA, pp 416–422
20.
go back to reference Lefohn AE, Cates JE, Whitaker RT (2003) Interactive, GPU-based level sets for 3D segmentation. In: Proceedings of medical image computing and computer-assisted intervention (MICCAI). Springer, Montreal, QC, Canada, pp 564–572 Lefohn AE, Cates JE, Whitaker RT (2003) Interactive, GPU-based level sets for 3D segmentation. In: Proceedings of medical image computing and computer-assisted intervention (MICCAI). Springer, Montreal, QC, Canada, pp 564–572
21.
go back to reference Prastawa M, Bullitt E, Ho S, Gerig G (2004) Robust estimation for brain tumor segmentation. In: Proceedings of medical image computing and computer-assisted intervention (MICCAI), pp 10–17 Prastawa M, Bullitt E, Ho S, Gerig G (2004) Robust estimation for brain tumor segmentation. In: Proceedings of medical image computing and computer-assisted intervention (MICCAI), pp 10–17
23.
go back to reference Tortorella F (2004) Reducing the classification cost of support vector classifiers through an ROC-based reject rule. Pattern Anal Appl 7(2):128–143MathSciNet Tortorella F (2004) Reducing the classification cost of support vector classifiers through an ROC-based reject rule. Pattern Anal Appl 7(2):128–143MathSciNet
24.
go back to reference Debnath R, Takahide N, Takahashi H (2004) A decision based one-against-one method for multi-class support vector machine. Pattern Anal Appl 7(2):164–175MathSciNet Debnath R, Takahide N, Takahashi H (2004) A decision based one-against-one method for multi-class support vector machine. Pattern Anal Appl 7(2):164–175MathSciNet
25.
go back to reference Sánchez JS, Mollineda RA, Sotoca JM (2007) An analysis of how training data complexity affects the nearest neighbor classifiers. Pattern Anal Appl 10(3):189–201CrossRefMathSciNet Sánchez JS, Mollineda RA, Sotoca JM (2007) An analysis of how training data complexity affects the nearest neighbor classifiers. Pattern Anal Appl 10(3):189–201CrossRefMathSciNet
26.
go back to reference Abe S (2007) Sparse least squares support vector training in the reduced empirical feature space. Pattern Anal Appl 10(3):203–214CrossRefMathSciNet Abe S (2007) Sparse least squares support vector training in the reduced empirical feature space. Pattern Anal Appl 10(3):203–214CrossRefMathSciNet
27.
go back to reference Herrero JR, Navarro JJ (2007) Exploiting computer resources for fast nearest neighbor classification. Pattern Anal Appl 10(4):265–275CrossRefMathSciNet Herrero JR, Navarro JJ (2007) Exploiting computer resources for fast nearest neighbor classification. Pattern Anal Appl 10(4):265–275CrossRefMathSciNet
28.
go back to reference Tyree EW, Long JA (1998) A monte carlo evaluation of the moving method, k-means and two self-organising neural networks. Pattern Anal Appl 1(2):79–90MATHCrossRef Tyree EW, Long JA (1998) A monte carlo evaluation of the moving method, k-means and two self-organising neural networks. Pattern Anal Appl 1(2):79–90MATHCrossRef
29.
go back to reference Chou CH, Su MC, Lai E (2004) A new cluster validity measure and its application to image compression. Pattern Anal Appl 7(2):205–220MathSciNet Chou CH, Su MC, Lai E (2004) A new cluster validity measure and its application to image compression. Pattern Anal Appl 7(2):205–220MathSciNet
30.
go back to reference Frigui H (2005) Unsupervised learning of arbitrarily shaped clusters using ensembles of gaussian models. Pattern Anal Appl 8(1-2):32–49CrossRefMathSciNet Frigui H (2005) Unsupervised learning of arbitrarily shaped clusters using ensembles of gaussian models. Pattern Anal Appl 8(1-2):32–49CrossRefMathSciNet
31.
go back to reference Omran MGH, Salman A, Engelbrecht AP (2006) Dynamic clustering using particle swarm optimization with application in image segmentation. Pattern Anal Appl 8(4):332–344CrossRefMathSciNet Omran MGH, Salman A, Engelbrecht AP (2006) Dynamic clustering using particle swarm optimization with application in image segmentation. Pattern Anal Appl 8(4):332–344CrossRefMathSciNet
34.
go back to reference Belkin M, Niyogi P (2003) Using manifold structure for partially labeled classification. In: Proceedings of advances in neural information processing systems (NIPS). MIT Press, Cambridge, pp 929–936 Belkin M, Niyogi P (2003) Using manifold structure for partially labeled classification. In: Proceedings of advances in neural information processing systems (NIPS). MIT Press, Cambridge, pp 929–936
35.
go back to reference Belkin M, Niyogi P, Sindhwani V (2006) Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J Mach Learn Res 1(1):1–48MathSciNet Belkin M, Niyogi P, Sindhwani V (2006) Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J Mach Learn Res 1(1):1–48MathSciNet
36.
go back to reference Krishnapuram B, Williams D, Xue Y, Hartemink A, Carin L, Figueiredo M (2005) On semi-supervised classification. In: Proceedings of advances in neural information processing systems (NIPS). MIT Press, Cambridge, pp 721–728 Krishnapuram B, Williams D, Xue Y, Hartemink A, Carin L, Figueiredo M (2005) On semi-supervised classification. In: Proceedings of advances in neural information processing systems (NIPS). MIT Press, Cambridge, pp 721–728
37.
go back to reference Zhou D, Bousquet O, Lal TN, Weston J, Schölkopf B (2003) Learning with local and global consistency. In: Proceedings of advances in neural information processing systems (NIPS). MIT Press, Cambridge, pp 321–328 Zhou D, Bousquet O, Lal TN, Weston J, Schölkopf B (2003) Learning with local and global consistency. In: Proceedings of advances in neural information processing systems (NIPS). MIT Press, Cambridge, pp 321–328
38.
go back to reference Zhou D, Schölkopf B (2005) Regularization on discrete spaces. In: Proceedings of pattern recognition, 27th DAGM symposium (DAGM-symposium). Lecture notes in computer science. Springer, Vienna, pp 361–368 Zhou D, Schölkopf B (2005) Regularization on discrete spaces. In: Proceedings of pattern recognition, 27th DAGM symposium (DAGM-symposium). Lecture notes in computer science. Springer, Vienna, pp 361–368
39.
go back to reference Zhu X, Ghahramani Z, Lafferty JD (2003) Semi-supervised learning using Gaussian fields and harmonic functions. In: Proceedings of twentieth international conference of machine learning (ICML). AAAI Press, Washington, DC, USA, pp 912–919 Zhu X, Ghahramani Z, Lafferty JD (2003) Semi-supervised learning using Gaussian fields and harmonic functions. In: Proceedings of twentieth international conference of machine learning (ICML). AAAI Press, Washington, DC, USA, pp 912–919
41.
go back to reference Sindhwani V, Chu W, Keerthi SS (2007) Semi-supervised Gaussian process classifiers. In: Proceedings of international joint conferences on artificial intelligence (IJCAI), pp 1059–1064 Sindhwani V, Chu W, Keerthi SS (2007) Semi-supervised Gaussian process classifiers. In: Proceedings of international joint conferences on artificial intelligence (IJCAI), pp 1059–1064
42.
go back to reference Fowlkes C, Belongie S, Chung F, Malik J (2004) Spectral grouping using the Nyström method. IEEE Trans Pattern Anal Mach Intell 26(2):214–225CrossRef Fowlkes C, Belongie S, Chung F, Malik J (2004) Spectral grouping using the Nyström method. IEEE Trans Pattern Anal Mach Intell 26(2):214–225CrossRef
43.
go back to reference Grady L, Funka-Lea G (2004) Multi-label image segmentation for medical applications based on graph-theoretic electrical potentials. In: Proceedings of ECCV workshops on CVAMIA and MMBIA, pp 230–245 Grady L, Funka-Lea G (2004) Multi-label image segmentation for medical applications based on graph-theoretic electrical potentials. In: Proceedings of ECCV workshops on CVAMIA and MMBIA, pp 230–245
44.
go back to reference Suri JS, Singh S, Reden L (2002) Computer vision and pattern recognition techniques for 2-D and 3-D MR cerebral cortical segmentation (part i): a state-of-the-art review. Pattern Anal Appl 5(1):46–76CrossRefMathSciNet Suri JS, Singh S, Reden L (2002) Computer vision and pattern recognition techniques for 2-D and 3-D MR cerebral cortical segmentation (part i): a state-of-the-art review. Pattern Anal Appl 5(1):46–76CrossRefMathSciNet
45.
go back to reference Suri JS, Singh S, Reden L (2002) Computer vision and pattern recognition techniques for 2-D and 3-D MR cerebral cortical segmentation (part i): a state-of-the-art review. Pattern Anal Appl 5(1):77–98CrossRefMathSciNet Suri JS, Singh S, Reden L (2002) Computer vision and pattern recognition techniques for 2-D and 3-D MR cerebral cortical segmentation (part i): a state-of-the-art review. Pattern Anal Appl 5(1):77–98CrossRefMathSciNet
46.
go back to reference Liang F, Mukherjee S, West M (2007) The use of unlabeled data in predictive modeling. Stat Sci 22(2):189–205 Liang F, Mukherjee S, West M (2007) The use of unlabeled data in predictive modeling. Stat Sci 22(2):189–205
47.
go back to reference Zhu S (2003) Statistical modeling and conceptualization of visual patterns. IEEE Trans Pattern Anal Mach Intell 25(6):691–712CrossRef Zhu S (2003) Statistical modeling and conceptualization of visual patterns. IEEE Trans Pattern Anal Mach Intell 25(6):691–712CrossRef
48.
go back to reference German S, German D (1984) Stochastic relaxation, gibbs distributions, and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 6(6):721–742CrossRef German S, German D (1984) Stochastic relaxation, gibbs distributions, and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 6(6):721–742CrossRef
49.
go back to reference McInerney T, Terzopoulos D (1996) Deformable models in medical image analysis: a survey. Med Image Anal 1(2):91–108CrossRef McInerney T, Terzopoulos D (1996) Deformable models in medical image analysis: a survey. Med Image Anal 1(2):91–108CrossRef
51.
go back to reference Malladi R, Sethian J, Vemuri B (1995) Shape modeling with front propagation: a level set approach. IEEE Trans Pattern Anal Mach Intell 17(2):158–175CrossRef Malladi R, Sethian J, Vemuri B (1995) Shape modeling with front propagation: a level set approach. IEEE Trans Pattern Anal Mach Intell 17(2):158–175CrossRef
52.
go back to reference Boykov Y, Jolly MP (2001) Interactive graph cuts for optimal boundary and region segmentation of objects in n-d images. In: Proceedings of IEEE international conference on computer vision (ICCV), vol I. IEEE Computer Society, Vancouver, B.C., Canada, pp 105–112 Boykov Y, Jolly MP (2001) Interactive graph cuts for optimal boundary and region segmentation of objects in n-d images. In: Proceedings of IEEE international conference on computer vision (ICCV), vol I. IEEE Computer Society, Vancouver, B.C., Canada, pp 105–112
53.
go back to reference Boykov Y, Veksler O, Zabih R (2001) Fast approximate energy minimization via graph cuts. IEEE Trans Pattern Anal Mach Intell 23(11):1222–1239CrossRef Boykov Y, Veksler O, Zabih R (2001) Fast approximate energy minimization via graph cuts. IEEE Trans Pattern Anal Mach Intell 23(11):1222–1239CrossRef
54.
go back to reference Li Y, Sun J, Tang CK, Shum HY (2004) Lazy snapping. ACM Trans Graph 23(3):303–308CrossRef Li Y, Sun J, Tang CK, Shum HY (2004) Lazy snapping. ACM Trans Graph 23(3):303–308CrossRef
55.
go back to reference Rother C, Kolmogorov V, Blake A (2004) “Grab cut”: interactive foreground extraction using iterated graph cuts. ACM Trans Graph 23(3):309–314CrossRef Rother C, Kolmogorov V, Blake A (2004) “Grab cut”: interactive foreground extraction using iterated graph cuts. ACM Trans Graph 23(3):309–314CrossRef
56.
go back to reference WU Q, Dou W, Chen Y, Constans J (2005) Fuzzy segementaion of cerebral tumorous tissues in MR images via support vector machine and fuzzy clustering. In: Proceedings of world congress of International Fuzzy Systems Association (IFSA). Tsinghua University Press, Beijing WU Q, Dou W, Chen Y, Constans J (2005) Fuzzy segementaion of cerebral tumorous tissues in MR images via support vector machine and fuzzy clustering. In: Proceedings of world congress of International Fuzzy Systems Association (IFSA). Tsinghua University Press, Beijing
57.
go back to reference Ulusoy I, Bishop C (2005) Generative versus discriminative methods for object recognition. In: Proceedings of computer vision and pattern recognition (CVPR), vol 2, pp 258–265 Ulusoy I, Bishop C (2005) Generative versus discriminative methods for object recognition. In: Proceedings of computer vision and pattern recognition (CVPR), vol 2, pp 258–265
58.
go back to reference Abrahamsen P (1997) A review of Gaussian random fields and correlation functions, 2nd edn. Technical report 917, Norwegian Computing Center Abrahamsen P (1997) A review of Gaussian random fields and correlation functions, 2nd edn. Technical report 917, Norwegian Computing Center
60.
go back to reference Williams C, Barber D (1998) Bayesian classification with Gaussian processes. IEEE Trans Pattern Anal Mach Intell 20(12):1342–1351CrossRef Williams C, Barber D (1998) Bayesian classification with Gaussian processes. IEEE Trans Pattern Anal Mach Intell 20(12):1342–1351CrossRef
61.
go back to reference MacKay DJC (1998). In: Introduction to Gaussian processes. NATO ASI, vol 168. Springer, Berlin, pp 133–165 MacKay DJC (1998). In: Introduction to Gaussian processes. NATO ASI, vol 168. Springer, Berlin, pp 133–165
62.
go back to reference Chung F (1997) Spectral graph theory. Number 92 in CBMS regional conference series in mathematics. American Mathematical Society, Providence Chung F (1997) Spectral graph theory. Number 92 in CBMS regional conference series in mathematics. American Mathematical Society, Providence
64.
go back to reference Williams CKI, Seeger M (2001) Using the Nyström method to speed up kernel machines. In: Proceedings of advances in neural information processing systems (NIPS). MIT Press, Cambridge, pp 682–688 Williams CKI, Seeger M (2001) Using the Nyström method to speed up kernel machines. In: Proceedings of advances in neural information processing systems (NIPS). MIT Press, Cambridge, pp 682–688
65.
go back to reference Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905CrossRef Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905CrossRef
66.
go back to reference Press W, Teukolsky S, Vetterling W, Flannery B (1992) Numerical Recipes in C, 2nd edn. Cambridge University Press, CambridgeMATH Press W, Teukolsky S, Vetterling W, Flannery B (1992) Numerical Recipes in C, 2nd edn. Cambridge University Press, CambridgeMATH
67.
go back to reference Dou W, Ruan S, Chen Y, Bloyet D, Constans JM (2007) A framework of fuzzy information fusion for the segmentation of brain tumor tissues on mr images. Image Vis Comput 25(2):164–171CrossRef Dou W, Ruan S, Chen Y, Bloyet D, Constans JM (2007) A framework of fuzzy information fusion for the segmentation of brain tumor tissues on mr images. Image Vis Comput 25(2):164–171CrossRef
68.
go back to reference Dou W, Ren Y, Wu Q, Ruan S, Chen Y, Bloyet D, Constans JM (2007) Fuzzy kappa for the agreement measure of fuzzy classifications. Neurocomputing 70(4-6):726–734 Dou W, Ren Y, Wu Q, Ruan S, Chen Y, Bloyet D, Constans JM (2007) Fuzzy kappa for the agreement measure of fuzzy classifications. Neurocomputing 70(4-6):726–734
69.
go back to reference Tao D, Li X, Wu X, Maybank SJ (2007) General tensor discriminant analysis and gabor features for gait recognition. IEEE Trans Pattern Anal Mach Intell 29(10):1700–1715CrossRef Tao D, Li X, Wu X, Maybank SJ (2007) General tensor discriminant analysis and gabor features for gait recognition. IEEE Trans Pattern Anal Mach Intell 29(10):1700–1715CrossRef
70.
go back to reference Tao D, Li X, Hu W, Maybank SJ, Wu X (2007) Supervised tensor learning. Knowl Inf Syst 13(1):1–42 Tao D, Li X, Hu W, Maybank SJ, Wu X (2007) Supervised tensor learning. Knowl Inf Syst 13(1):1–42
71.
go back to reference Lawrence ND, Jordan MI (2005) Semi-supervised learning via Gaussian processes. In: Proceedings of advances in neural information processing systems (NIPS 17). MIT Press, Cambridge, pp 753–760 Lawrence ND, Jordan MI (2005) Semi-supervised learning via Gaussian processes. In: Proceedings of advances in neural information processing systems (NIPS 17). MIT Press, Cambridge, pp 753–760
Metadata
Title
Semi-supervised discriminative classification with application to tumorous tissues segmentation of MR brain images
Authors
Yangqiu Song
Changshui Zhang
Jianguo Lee
Fei Wang
Shiming Xiang
Dan Zhang
Publication date
01-06-2009
Publisher
Springer-Verlag
Published in
Pattern Analysis and Applications / Issue 2/2009
Print ISSN: 1433-7541
Electronic ISSN: 1433-755X
DOI
https://doi.org/10.1007/s10044-008-0104-3

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