Classification of binary spatial textures using stochastic geometry, nonlinear deterministic analysis and artificial neural networks

International Journal of Pattern Recognition and Artificial Intelligence

Volumn 17, Issue 2, 2003, Pages 275-300

  Mattfeldt, Torsten ^a  

^a Department of Pathology ^*  (Germany)

Author keywords

Artificial neural networks; Learning vector quantization; Mammary carcinoma; Pancreatic cancer; Pathology; Pattern recognition; Prostate cancer; Stereology; Stochastic geometry; Support vector machine

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; CORRELATION METHODS; VECTOR QUANTIZATION;

BINARY SPATIAL TEXTURES; NONLINEAR DETERMINISTIC ANALYSIS; STOCHASTIC GEOMETRY; SUPPORT VECTOR MACHINE;

NEURAL NETWORKS;

EID: 0038060616     PISSN: 02180014     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218001403002332     Document Type: Article

References (55)

1. A. D. Barbour and V. Schmidt, "On Laslett's transform for the Boolean model," Adv. Appl. Prob. 33 (2001) 1-5.
2. U. Bindrich and D. Stoyan, "Stereology of the pore structure in bread," J. Microsc. 162 (1991) 231-239.
3. J. C. Burges, "A tutorial on support vector machines for pattern recognition," Data Mining Knowl. Discov. 2 (1998) 121-167.
4. P. Coullet, C. Elphick and D. Repaux, "Nature of spatial chaos," Phys. Rev. Lett. 58, (1987) 431-434.
5. N. A. C. Cressie, Statistics for Spatial Data, Wiley, NY, 1991.
6. L. M. Cruz-Orive, "Second-order stereology: estimation of second moment volume measures," Acta Stereol. 8 (1989) 641-646.
7. J.-P. Eckmann and D. Ruelle, "Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems," Physica D56 (1992) 185-187.
8. T. Elbert, W. J. Ray, Z. J. Kowalik, J. E. Skinner, K. E. Graf and N. Birbaumer, "Chaos and physiology: deterministic chaos in excitable cell assemblies," Physiol. Rev. 74 (1994) 1-47.
9. J. Fell and J. Röschke, "Nonlinear dynamical aspects of the human sleep EEG," Int. J. Neurosci. 76 (1994) 109-129.
10. K. Fukunaga, Introduction to Statistical Pattern Recognition, 2nd edition, Academic Press, San Diego, 1990.
11. W. Gerlach and D. Stoyan, "Determination of the covariance of random sets from thin sections," Biometr. J. 4 (1986) 427-432.
12. P. Grassberger, "An optimized box-assisted algorithm for fractal dimension," Phys. Lett. A148 (1990) 63-68.
13. P. Grassberger and I. Procaccia, "Characterization of strange attractors," Phys. Rev. Lett. 50 (1983) 346-349.
14. P. Grassberger and I. Procaccia, "Measuring the strangeness of strange attractors," Physica 9D (1983) 189-208.
15. C. V. Howard and M. G. Reed, Unbiased Stereology. Three-Dimensional Measurement in Microscopy, Bios Scientific Publishers, Oxford, 1998.
16. V. Isham, "Statistical aspects of chaos: a review," Networks and Chaos - Statistical and Probabilistic Aspects, eds. O. E. Barndorff-Nielsen, J. L. Jensen and W. S. Kendall, Chapman Hall, London, 1993, pp. 124-200.
17. T. Kohonen, J. Hynninen, J. Kangas, J. Laaksonen and K. Torkkola, "LVQ_PAK: the learning vector quantization program package," Technical Report A30, Helsinki University of Technology, Laboratory of Computer and Information Science, Otaniemi, Finland, 1996.
18. T. Kohonen, J. Hynninen, J. Kangas and J. Laaksonen, "SOM_PAK: the self-organizing map program package," Technical Report A31, Helsinki University of Technology, Laboratory of Computer and Information Science, Espoo, Finland, 1996.
19. T. Kohonen, Self-Organizing Maps, 2nd edition, Springer, Heidelberg, 1997.
20. G. M. Laslett, N. Cressie and S. Liow "Intensity estimation in a spatial model of overlapping particles," unpublished manuscript, Division of Mathematics and Statistics, CSIRO, Melbourne, (quoted from Cressie (1991)). (1991).
21. C. Markopoulos, P. Karakitsos, E. Botsoli-Stergiou, A. Pouliakis, A. Iokim-Liossi, L. Kyrkou and J. Gogas, "Application of the learning vector quantizer to the classification of breast lesions," Anal. Quant. Cytol. Histol. 19 (1997) 453-460.
22. T. Mattfeldt, H. Frey and C. Rose, "Second-order stereology of benign and malignant alterations of the human mammary gland," J. Microsc. 171 (1993) 143-151.
23. T. Mattfeldt, V. Schmidt, D. Reepschläger, C. Rose and H. Frey, "Centred contact density functions for the statistical analysis of random sets," J. Microsc. 183 (1996) 158-169.
24. T. Mattfeldt, "Nonlinear deterministic analysis of tissue texture: a stereological study on mastophatic and mammary cancer tissue using chaos theory," J. Microsc. 185 (1997) 47-66.
25. T. Mattfeldt, H. A. Kestler, R. Hautmann and H.-W. Gottfried, "Prediction of prostatic cancer progression after radical prostatectomy using artificial neural networks: a feasibility study," BJU Int. 84 (1999) 316-323.
26. T. Mattfeldt, H.-W. Gottfried, V. Schmidt and H. A. Kestler, "Classification of spatial textures in benign and cancerous glandular tissues by stereology and stochastic geometry using artificial neural networks," J. Micros. 198 (2000) 143-158.
27. T. Mattfeldt and D. Stoyan, "Improved estimation of the pair correlation function," J. Microsc. 200 (2000), 158-173.
28. T. Mattfeldt, H. A. Kesler, R. Hautmann and H.-W. Gottfried, "Prediction of post-operative prostatic cancer stage on the basis of systematic biopsies using two types of artificial neural networks," Eur. Urol. 39 (2001) 530-537.
29. T. M. Mayhew, "Second-order stereology and ultrastructural examination of the spatial arrangements of tissue compartments within glomeruli of normal and diabetic kidneys," J. Microsc. 195 (1999) 87-95.
30. I. Molchanov, Statistics of the Boolean Model for Practitioners and Mathematicians, Wiley, Chichester, 1997.
31. J. Ohser, "On statistical analysis of the Boolean model," Elektron. Informationsverarb. Kybern. 16 (1980) 651-653.
32. J. Ohser, "On estimation of pair correlation functions," Res. Inform. 4 (1991) 147-152.
33. J. Ohser and F. Mücklich, Statistical Analysis of Microstructures in Materials Sciences, Wiley, Chichester, 2000.
34. D. Pantazopoulos, P. Karakitsos, A. Iokim-Liossi, A. Pouliakis and K. Dimopoulos, "Comparing neural networks in the discrimination of benign from malignant lower urinary tract lesions," Br. J. Urol. 81 (1998) 574-579.
35. D. Pantazopoulos, P. Karakitsos, A. Pouliakis, A. Iokim-Liossi and M.A. Dimopoulos, "Static cytometry and neural networks in the discrimination of lower urinary system lesions," Urol. 51 (1998) 946-950.
36. H. O. Peitgen, H. Jürgens and D. Saupe, Chaos and Fractals. New Frontiers of Science, Springer, NY, 1992.
37. W. S. Pritchard and D. W. Duke, "Measuring 'chaos' in the brain: tutorial review of EEG dimension estimation," Brain Cogn. 27 (1995) 353-397.
38. M. G. Reed and C. V. Howard, "Stereological estimation of covariance using linear dipole probes," J. Microsc. 195 (1999) 96-103.
39. M. T. Rosenstein, J. J. Collins and C. J. DeLuca, "Reconstruction expansion as a geometry-based framework for choosing proper delay times," Physica D73 (1994) 82-98.
40. SAS Institute, SAS/STAT User's Guide: Release 6.03 Edition, SAS Institute Inc., Cary (NC), 1988.
41. R. Saunders, M. O. Stitson, J. Weston, L. Bottou, B. Schölkopf and A. Smola, "Support vector machine reference manual," Technical Report, Royal Holloway, University of London, 1998.
42. H.-G. Schuster, Deterministisches Chaos, VCH Verlagsgesellschaft, Weinheim, 1994.
43. J. Serra, "The Boolean model and random sets," Comput. Graph. Imag. Process. 12 (1980) 99-126.
44. J. Serra, Image Analysis and Mathematical Morphology, Academic Press, London, 1982.
45. G. Sherlock, "Analysis of large-scale expression data," Curr. Opin. Immunol. 12 (2000) 201-205.
46. D. Stoyan, W. S. Kendall and J. Mecke, Stochastic Geometry and its Applications, 2nd edition, Wiley, Chichester, 1995.
47. F. Takens, "Detecting strange attractors in turbulence," Lecture Notes Math. 898 (1981) 366-381.
48. P. Tamayo, D. Slonim, J. Mesirov, Q. Zhu, S. Kitareewan, E. Dmitrovsky, E. S. Lander and T. R. Golub, "Interpreting patterns of gene expression with self-organizing maps: methods and application to hemopoietic differentiation," Proc. Natl. Acad. Sci. 96 (1999) 2907-2912.
49. A. Tewari, "Artificial intelligence and neural networks: concept, applications and future in oncology," Br. J. Urol. 80 Suppl. 3 (1997) 53-58.
50. G. D. Tourassi and C. E. Floyd, "The effect of data sampling on the performance evaluation of artificial neural networks in medical diagnosis," Med. Decis. Making 17 (1997) 186-192.
51. V. N. Vapnik, Statistical Learning Theory, Wiley, NY, 1998.
52. J. T. Wei, Z. Zhang, S. D. Barnhill, K. R. Madyastha, H. Zhang and J. E. Oesterling, "Understanding artificial neural networks and exploring their potential applications for the practicing urologist," Urol. 52 (1998) 161-172.
53. E. R. Weibel, Stereological Methods. I. Practical Methods for Biological Morphometry, Academic Press, London, 1979.
54. A. Zell, Simulation neuronaler Netze, Bonn, Addison-Wesley, 1994.
55. D. Zimmerman, "A bivariate Cramér-von Mises type of test for spatial randomness," Appl. Statist. 42 (1993) 43-54.