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Skin lesion feature vectors classification in models of a Riemannian manifold

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Abstract

This study is a continuation of a work published by Mete, Ou, and Sirakov (2012), where a model of a 4D manifold of feature vectors was developed. The present paper introduces an improved metric in the 4D manifold first and then extends both the size of the sample space and the dimension (to 6D) of the manifold model in which the sample space lies. As a result, we not only overcame the issue of one single vector representing multiple skin lesions, which occurred in the work of Mete, Ou, and Sirakov (2012), but also improved the accuracy of classification. Furthermore, a statistical evaluation of our support vector machine (SVM) classification method was performed. The intervals of confidence were calculated for the mean of classification of a large sample set in the 6D model. Comparison results of classification with our SVM in 4D and 6D models using 10-fold cross-validation are given at the end of the paper. It is found that the 6D model improves the classification results of the previous study suggesting that two newly introduced features contributed to the increase of the classification accuracy.

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References

  1. Mete, M., Ou, Y.-L., Sirakov, N. M.: Skin Lesion Feature Vector Space With A Metric To Model Geometric Structures Of Malignancy, R.P. Barneva, V. Brimkov, J. Aggarval(Eds.): IWCIA 2012, LNCS 7655, Springer Verlag, pp. 285-297 (2012)

  2. Nachbar, F., Stolz, W., Merkle, T., et al.: The ABCD rule of dermatoscopy: High prospective value in the diagnosis of doubtful melanocytic skin lesions. J.. Am. Acad. Dermatol. 30 (4), 551–559 (1994)

    Article  Google Scholar 

  3. Argenziano, G., Fabbrocini, G., Carli, P., De Giorgi, V., Sammarco, E., Delfino, M.: Epiluminescence microscopy for the diagnosis of doubtful melanocytic skin lesions. Comparison of ABCD rule of dermatoscopy and a new 7-point checklist based on pattern analysis. Arch. Dermatol 134, 1563–1570 (1998)

    Article  Google Scholar 

  4. American Cancer Society: Cancer Facts & Figures 2010, http://www.cancer.org/. Accessed July, 26 (2010)

  5. Argenziano, G., Soyer, H.P., De Giorgi, V., et al.: Interactive atlas of dermoscopy. Milan. EDRA Medical Pub, Italy (2000)

    Google Scholar 

  6. Sirakov, N.M., Ushkala, K.: An integral active contour model for convex hull and bound- ary extraction. In: Bebis, G. et al. (Eds), LNCS, Vol. 5876, Springer, pp. 1031-1040 (2009)

  7. Silveira, M., Marques, J.S.: :Level set segmentation of dermoscopy images, 5th IEEE ISBI: From Nano to Macro, Paris, 14-17 May 2008, pp. 173 - 176, (2008). doi:10.1109/ISBI.2008.4540960

  8. Zhou, H., Schaefer, Celebi, M.E., Lin, F.: : Gradient vector flow with mean shift for skin lesion segmentation. Comp. Med. Imaging Graphics 35 (I.2), 121–127 (2011)

    Article  Google Scholar 

  9. Sadeghi, M., Razmara, M., Atkins, M.S., Lee, T.K.: :A novel method for detection of pigment network in dermoscopic images using graphs. Comput. Med. Imaging Graphics 35 (2), 137–143 (2011)

    Article  Google Scholar 

  10. Xie, F., Bovik, A.: :Automatic segmentation of dermoscopy images using self-generating neural networks seeded by genetic algorithm. Journal of Pattern Recognition 46 (3), 1012–1019 (2013)

    Article  Google Scholar 

  11. Maglogiannis, I.: Doukas, G.N.:Overview of Advanced Computer Vision Systems for Skin Lesions Characterization, IEEE Tran. on Information Technology in Biomedicine, V. 13, NO. 5. SEPTEMBER (2009)

  12. Gilmore, S., Hofmann-Wellenhof, R., Soyer, P. H.: A support vector machine for decision support in melanoma recognition. Exp Dermatol 830-5 (2010), 19 (2010)

    Google Scholar 

  13. Alcon, J.F, Ciuhu, C., Kate, W., Heinrich, A., Uzunbajakava, N., Krekels, G., Siem, D., Haan, G.: :Automatic Imaging System With Decision Support for Inspection of Pigmented Skin Lesions and Melanoma Diagnosis. IEEE J. Sel. Top Signal Proc. 3 (1) (2009)

  14. Mete, M., Sirakov, N.M.: Application of active contour and density based models for lesion detection in dermoscopy images. In: BMC Bioinformatics 2010, 11(Suppl 6):S23 (2010). doi:10.1186/1471-2105-11-S6-S23

  15. Mete, M., Sirakov, N.M.: Dermoscopic diagnosis of melanoma in a 4D feature space constructed by active contour extracted features. Journal of Medical Imaging and Graphics 2012 (36), 572–579 (2012)

    Article  Google Scholar 

  16. Nara, C.: : Active contour on the exact solution of the active convex hull model working with noise, Master Degree Thesis, Texas A and M Univ. Commer 07, 01 (2011)

    Google Scholar 

  17. Mulchrone, K., Choudhury, K.: Fitting an ellipse to an arbitrary shape: implications for strain analysis. J. Struct Geol. 26 (1), 143–153 (2004)

    Article  Google Scholar 

  18. O’Neill, B.: Semi-Riemannian geometry with applications to relativity. Academic Press, New York (1983)

    MATH  Google Scholar 

  19. Petersen, P.: Riemannian geometry, Vol. 171. Springer-Verlag, New York (1998)

    Book  Google Scholar 

  20. Scholkopf, B., Smola, A.J., Williamson, R. C., Bartlett, P. L.: New Support Vector Algorithms. Neural Comput. 12, 1207–1245 (2000)

    Article  Google Scholar 

  21. Sirakov, N.M., Mete, M., Nara, S.C.: Automatic boundary detection and symmetry calculation in dermoscopy images of skin lesions, IEEE ICIP2011, Brussels, pp. 1637-1640 (2011)

  22. Thieu, Q.T., Luong, M., Rocchisani, J.M., Vienne, E.: A convex active contour region-based model for image segmentation. Proc. CAIP’11, Part I, LNCS, Vol. 6854, Springer-Verlag Berlin, Heidelberg, pp. 135-143 (2011)

  23. Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995)

    Book  MATH  Google Scholar 

  24. Chang, C.C., Lin, C.-J.: LIBSVM: a library for support vector machines, Vol. 2 (2011). http://www.csie.ntu.edu.tw/~cjlin/libsvm

  25. Devore, J., Berk, K.: Modern mathematical statistics with applications. International Student Edition ed. Belmont, CA: Thomson Higher Education (2007)

  26. Blackledge, J.M., Dubovitskiy, D.A.: Object Detection and Classification with Applications to Skin Cancer Screening. ISAST Tran. Intiligent Syst. 1 (2) (2008)

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Correspondence to Nikolay Metodiev Sirakov.

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Sirakov, N.M., Ou, YL. & Mete, M. Skin lesion feature vectors classification in models of a Riemannian manifold. Ann Math Artif Intell 75, 217–229 (2015). https://doi.org/10.1007/s10472-014-9424-8

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  • DOI: https://doi.org/10.1007/s10472-014-9424-8

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