Here the Theory of Size Functions is introduced and joined to some statistical techniques of discriminant analysis, to perform automatic classification of families of random shapes. The method is applied to the classification of normal and malignant tumor cell nuclei, described via their section profiles. The results here reported are compared with other techniques of shape analysis, already applied to the same data, showing some improvements.
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References
M. D'Amico, P. Frosini, C. Landi, Natural pseudo-distance and optimal matching between reduced size functions, Preprint, 2005.
I. L. Dryden, K. V. Mardia, Statistical Shape Analysis, Wiley, New York, 1998.
P. Frosini, C. Landi, Size theory as a topological tool for computer vision, Pattern Recognition and Image Analysis 9, pp. 596-603, 1999.
P. Frosini, C. Landi, Size functions and formal series, AAECC 12, pp. 327-349, 2001.
P. Frosini, M. Pittore, New methods for reducing size graphs, Intern. J. Computer Math. 70, pp. 505-517, 1999.
P.A. Lachenbruch, Discriminant Analysis, Hafner Press, New York, 1975.
G. Landini, J.W. Rippin, Quantification of nuclear pleomorphism using an asymptotic fractal model, Anal. Quant. Cyt. Hist., 18, pp. 167-176, 1996.
A. Micheletti, Statistical shape analysis applied to automatic recognition of tumor cells, Fractals in Biology and Medicine IV, G.A. Losa et al. Editors, Birkhauser Verlag, Basel, pp. 165-174, 2005.
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Micheletti, A., Landini, G. (2008). Size Functions Applied to the Statistical Shape Analysis and Classification of Tumor Cells. In: Bonilla, L.L., Moscoso, M., Platero, G., Vega, J.M. (eds) Progress in Industrial Mathematics at ECMI 2006. Mathematics in Industry, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71992-2_86
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DOI: https://doi.org/10.1007/978-3-540-71992-2_86
Publisher Name: Springer, Berlin, Heidelberg
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