INVESTIGATION OF RUPTURE LINES OF THE FUNCTIONS OF TWO VARIABLES OR THEIR DERIVATIVES OF SOME ORDER

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J. of Mech. Eng., 2016, vol. 19, no. 1, pp. 37-43

DOI:  https://doi.org/10.15407/pmach2016.01.037

Journal Journal of Mechanical Engineering
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 19, no. 1, 2016 (March)
Pages 37–43

 

Authors

O. M. Lytvyn, Ukrainian Engineering Pedagogics Academy (16, Universitetskaya St., Kharkiv, 61003, Ukraine),
e-mail: academ_mail@ukr.net

O. V. Slavik, Ukrainian Engineering Pedagogics Academy (16, Universitetskaya St., Kharkiv, 61003, Ukraine)

 

Abstract

A review of the existing methods for the automatic detection of ruptures in digital images is conducted. Two methods for detecting surface ruptures defined by a function of two variables are given. A new method for finding the lines of discontinuity of a function of two variables (which describes a surface) or its derivative of some order is proposed.

 

Keywords: image segmentation, ε-continuity, dε -continuity, dkε -continuity

 

References

  1. Gruzman, I. S., Kirichuk, V. S., Kosyih V. P., Peretyagin, G. I., Spektor, A. A. (2000). Digital image processing in information systems.  Novosibirsk State Technical University, 168 p.
  2. Shrivakshan, G. & Chandrasekar, C. (2012). A Comparison of various Edge Detection Techniques used in Image Processing. International Journal of Computer Science Issues, vol. 9, pp. 269–276.
  3. Jähne, B., Scharr, H., & Körkel, S. (1999). Principles of filter design. Handbook of Computer Vision and Applications, pp. 125–152.
  4. Muthukrishman, R. & Radha, M. (2011). Edge Detection Techniques for Image Segmentation. International Journal of Computer Science & Information Technology, vol. 3, pp. 259-267. https://doi.org/10.5121/ijcsit.2011.3620
  5. Maini R. & Aggrwal, H. (2009) Study and Comparison of Various Image Edge Detection Techniques. International Journal of Image Processing, vol. 3, pp. 1–12.
  6. Pershina, Y. I. (2015). Discontinuous splines theory and its application in computed tomography: diss. dr. phys.-math. sci. 385 p.
  7. Nefedova, V. (2014). Choosing the optimal basis functions and components in the finite element method (rectangular elements) in the mathematical modeling of heat distribution: dis. cand. phys.-math. sci. 167 p.

 

Received 28 January 2016