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Abstract

Due to the absolute value involved, the first absolute central moment can be divided into two complementary filters: a positive deviation e p and a negative deviation e n . Both e p and e n can be used separately to highlight edges, lines, line endings, corners and junctions in images. Furthermore, the recovered edge information can be usefully combined to obtain additional information that would not be obtained by varying the parameters of the original filter. The mass center of the first absolute central moment can be also defined and an iterative localization procedure can be developed by exploiting its properties. Mathematical operators derived from the first absolute central moment were used on a video processing device based on a DSP board and they proved to be robust and suitable for real-time implementations.

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References

  1. Papoulis, A.: Probability, Random Variables, and Stochastic Process. Mc Graw-Hill, New York (1965)

    Google Scholar 

  2. Bevington, P.R.: Data reduction and error analysis for the Physical Sciences. McGraw-Hill, New York (1969)

    Google Scholar 

  3. Jain, A.K.: Fundamentals of digital image processing. Prentice-Hall, Englewood Cliffs (1989)

    MATH  Google Scholar 

  4. Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes. Cambridge University Press, Cambridge (1991)

    Google Scholar 

  5. Pratt, W.K.: Digital image processing. Wiley, New York (1991)

    MATH  Google Scholar 

  6. Huber, P.J.: Robust Statistics. Wiley, New York (1981)

    MATH  Google Scholar 

  7. Chellappa, R.: Digital image processing. Computer Society press, Los Alamitos (1992)

    Google Scholar 

  8. Demi, M.: Contour Tracking by Enhancing Corners and Junctions. Computer Vision and Image Understanding 63, 118–134 (1996)

    Article  Google Scholar 

  9. Demi, M., Paterni, M., Benassi, A.: The First Absolute Central Moment in Low-Level Image Processing, Comput. Vision Image Understanding 80, 57–87 (2000)

    Article  MATH  Google Scholar 

  10. Demi, M.: An Artificial Vision Model Based on Statistical Filters. In: Proc. of the Brain-Machine Workshop, pp. 37–44 (2000)

    Google Scholar 

  11. Marr, D.: Vision. W.H.Freeman, San Francisco (1982)

    Google Scholar 

  12. Torre, V., Poggio, T.: On edge detection. IEEE Trans. Pattern Anal. Machine Intell. PAMI-8, 147–163 (1986)

    Article  Google Scholar 

  13. Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Machine Intell. PAMI-8, 679–698 (1986)

    Google Scholar 

  14. Marr, D.C., Hildreth, E.C.: Theory of edge detection. In: Proc. Roy. Soc. London B, vol. 207, pp. 187–217 (1980)

    Google Scholar 

  15. Demi, M.: The First Absolute Central Moment as an Edge Detector. Journal of Nonlinear Analysis 47(9), 5815–5826 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  16. Witkin, A.P.: Scale-space filtering. In: Proc. Int. Joint Conf. Artificial Intelligence, pp. 1019–1022 (1983)

    Google Scholar 

  17. Koenderink, J.J.: The structures of images. Biological Cybernetics 50, 363–370 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  18. Babaud, J., Witkin, A.P., Baudin, M., Duda, R.O.: Uniqueness of the Gaussian kernel for scale-space filtering. IEEE Trans. Pattern Anal. Machine Intell. 8(1), 26–33 (1986)

    MATH  Google Scholar 

  19. Yuille, A.L., Poggio, T.: Scaling theorems for zero-crossings. IEEE Trans. Pattern Anal. Machine Intell. 8(1), 15–25 (1986)

    MATH  Google Scholar 

  20. Watt, R.J., Morgan, M.J.: A theory of the primitive spatial code in human vision. Vision Research 25, 1661–1674 (1985)

    Article  Google Scholar 

  21. Heal, K.M., Hansen, M.L., Richard, K.M.: MapleV Learning Guide. Springer, Heidelberg (1998)

    Google Scholar 

  22. Demi, M., Gemignani, V., Paterni, M., Benassi, A.: Real Time Contour Tracking of Cardiovascular Structures with Statistical Filters. In: 5th International Workshop on Nonlinear Signal and Image Processing, pp. 1–5 (2001)

    Google Scholar 

  23. Faita, F., Gemignani, V., Giannoni, M., Benassi, A.: A Fully Customizable DSP Based System for Real-Time Imaging. In: Proc. of International Signal Processing Conference - GSPx, pp. 1–5 (2003)

    Google Scholar 

  24. Corretti, M.C., Anderson, T.J., Benjamin, E.J., Celermajer, D., Charbonneau, F., Creager, M.A., Deanfield, J., Drexler, H., Gerhard-Herman, M., Herrington, D., Vallance, P., Vita, J., Vogel, R.: Guidelines for the ultrasound assessment of endothelial-dependent flow-mediated vasodilation of the brachial artery: a report of the International Brachial Artery Reactivity Task Force. J. Am. Coll. Cardiol. 39(2), 257–265 (2002)

    Article  Google Scholar 

  25. Bots, M.L., Evans, G.W., Riley, W.A., Grobbee, D.E.: Carotid intima-media thickness measurements in intervention studies: design options, progression rates, and sample size considerations: a point of view. Stroke 34(12), 2985–2994 (2003)

    Article  Google Scholar 

  26. Wang, J.G., Staessen, J.A., Li, Y., Van Bortel, L.M., Nawrot, T., Fagard, R., Messerli, F.H., Safar, M.: Carotid intima-media thickness and antihypertensive treatment: a meta-analysis of randomized controlled trials. Stroke 37(7), 1933–1940 (2006)

    Article  Google Scholar 

  27. De Micheli, E., Caprile, B., Ottonello, P., Torre, V.: Localization and Noise In Edge Detection. IEEE Trans. Pattern Anal. Machine Intell. 11, 1106–1117 (1989)

    Article  Google Scholar 

  28. Fleck, M.M.: Some Defects in Finite-Difference Edge Finders. IEEE Trans. Pattern Anal. Machine Intell. 14, 337–345 (1992)

    Article  Google Scholar 

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Petra Perner Ovidio Salvetti

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Demi, M., Bianchini, E., Faita, F., Gemignani, V. (2008). A Mathematical Operator for Automatic and Real Time Analysis of Sequences of Vascular Images. In: Perner, P., Salvetti, O. (eds) Advances in Mass Data Analysis of Images and Signals in Medicine, Biotechnology, Chemistry and Food Industry. MDA 2008. Lecture Notes in Computer Science(), vol 5108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70715-8_9

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  • DOI: https://doi.org/10.1007/978-3-540-70715-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

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  • Online ISBN: 978-3-540-70715-8

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