Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2020. No. 11

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DOI  https://doi.org/10.30898/1684-1719.2020.11.14

UDC 004.852+004.855.5


new machine learning based method for identifying objects in biomedical images obtained by photon counting detectors


V. E. Antsiperov

Kotelnikov Institute of Radioengineering and Electronics of the Russian Academy of Sciences, Mokhovaya 11-7, Moscow, 125009, Russia.


The paper is received on November 15, 2020 


Abstract. The article discusses a new approach to the problem of recognition, or rather the identification of objects by the shape of their intensity in images formed by photon counting detectors or those close to them. The main problem analyzed within the framework of the approach proposed is related to the quantitative estimation of similarity between the form of radiation intensity of the object in the image and the forms of intensity of previously observed objects (precedents), providing that all of them are given by the registered sets of discrete photocounts (~ photons). It is shown that when the intensity shape is approximated by a mixture of components of an exponential family, for the implementation of the approach proposed in this work a recurrent PM algorithm for estimating the parameters of the intensity shape from a finite sample of counts associated with radiation can be synthesized. The PM algorithm turns out to be a close analogue of the well-known K-means algorithm, which is one of the most popular in the field of machine (statistical) learning. The main features of the method and its implementation are illustrated by the example of applying the method to the problem of image fragments identification for the COVID ‒ CT ‒ Dataset database.

Key words: machine learning by precedents, pattern recognition, object identification in images, computer tomography (CT), K-means segmentation method, frame theory, Poisson point processes.


1.     Darby M.J., Barron D., Hyland R.E., editors. Oxford Handbook of Medical Imaging. Oxford, Oxford University Press. 2011.

2.     Leng S., et. al. Photon-counting Detector CT: System Design and Clinical Applications of an Emerging Technology. RadioGraphics. 2019. Vol.39. No.3. P.729-743.

3.     Willemink M.J., et. al. Photon-counting CT: technical principles and clinical prospects. Radiology. 2018. Vol.289. No.2. P.293-312.

4.     Gonzalez R.C., Woods R.E. Digital Image Processing, 3rd ed. Prentice Hall. 2010.

5.     Goodman J.W. Statistical Optics. 2nd ed. New York. Wiley. 2015.

6.    Pal N.R., Pal S.K. Image model, poisson distribution and object extraction. J. Patt. Recogn. Artif. Intell. 1991. Vol. 5. No.3. P.459–483.

7.    Yang F., Lu Y. M., Sbaiz L., Vetterli M. Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics. IEEE Transactions on Image Processing. 2012. Vol.21. No.4. P.1421-1436.

8.     Fossum E.R., Teranishi N., et. al., editors. Photon–Counting Image Sensors.  MDPI Books under CC BY–NC–ND license. 2017.

9.     Streit R. L. Poisson Point Processes. Imaging, Tracking and Sensing. New Yor. Springer. 2010.

10.   Antsiperov V. Machine Learning Approach to the Synthesis of Identification Procedures for Modern Photon-Counting Sensors. 8th International Conference on Pattern Recognition Applications and Methods ICPRAM Proceedings. 2019. Vol.1. P.19–21.

11.   Bertero M., Boccacci P., Desidera G., Vicidomini G. TOPICAL REVIEW: Image deblurring with Poisson data: from cells to galaxies. Inverse Problems. 2009. Vol.25. No.12. P.123006. https://doi.org/10.1088/0266-5611/25/12/123006

12.   Barber D. Bayesian Reasoning and Machine Learning. Cambridge: Cambridge Univ. Press. 2012.

13.   MacKay D.J.C. Information Theory, Inference, and Learning Algorithms. Cambridge. Cambridge Univ. Press. 2003.

14.   Szirmay-Kalos L., Szecsi L., Penzov A.A. Importance Sampling with Floyd-Steinberg Halftoning. Eurographics Short Papers. 2009. P. 69–72.

15.   Floyd R., Steinberg L. An adaptive algorithm for spatial gray scale. Proceedings of the Society of Information Display. 1976. Vol.17. No.2. P.75–77.

16.   Gooran S., Yang L. Basics of Tone Reproduction. In: Kriss M., editor. Handbook of Digital Imaging.  2015.

17.   Jebara T. Machine Learning: Discriminative and Generative. Dordrecht. Kluwer. 2004.

18.   Wasserman L. All of statistics: a concise course in statistical inference. New York. Springer. 2004.

19.   Efron B. Maximum likelihood and decision theory. Ann. Statist. 1982. Vol.10. P.340–356.

20.   Gröchenig K. Foundations of Time-Frequency Analysis. Boston. Birkhäuser. 2001.

21.   Murphy K.P. Machine learning: a probabilistic perspective. Cambridge, MA. MIT Press. 2012.

22.   Du D, Ko K. Theory of Computational Complexity, 2nd ed. John Wiley & Sons. 2014.

23.   Bregman L.M. The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics. 1967. Vol.7. No.3. P.200–217.

24.   Sun S., Cao Z., Zhu H., Zhao J. A Survey of Optimization Methods from a Machine Learning Perspective. IEEE Transactions on Cybernetics. 2020. Vol.50. No.8. P.3668-3681.

25.   Nguyen H.D., Forbes F., McLachlan G.J. Mini-batch learning of exponential family finite mixture models. Statistics and Computing. 2020. Vol.30. P.731–748.

26.   Yang X., He X., Zhao J., Zhang Y., Zhang S. COVID-CT-Dataset: A CT san dataset about COVID-19. arXiv:2003.13865, 2020.


For citation:

Antsiperov  V.E. New machine learning based method for identifying objects in biomedical images obtained by photon counting detectors. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2020. No.11. https://doi.org/10.30898/1684-1719.2020.11.14  (In Russian)