DOI: https://doi.org/10.15588/1607-3274-2020-3-7

STUDY OF STATISTICAL PROPERTIES OF THE BLOCK SUPPLY MODEL FOR A NUMBER OF DECORATORS OF KEY POINTS OF IMAGES

S. V. Gadetska, V. A. Gorokhovatsky, N. I. Stiahlyk

Abstract


Context. Effective classification solutions in modern computer vision systems require an in-depth study of the nature of the processed data. The cluster representation for the basic system of structural features as a set of descriptors of key image points helps to reduce dimensionality and significantly simplify data analysis tools. The main tool is a statistical study of these descriptions as part of a cluster presentation, which reflects the generalized properties of a visual object. The implementation of the tree apparatus is based on a statistical analysis of data components to make a decision on assigning a visual object to the corresponding class. The construction of trees is based on indicators of informativeness of data that provide the logical processing process when dividing in tree branches. Having a single probabilistic nature, these indicators measure and evaluate information that is significantly different in content. It is important to study both the general properties of these criteria in the classification problem and the assessment of their individual characteristics.

Objective. The solution of the problem of classifying visual objects according to the cluster representation of data for the structural description of the image using the apparatus of decision trees.

Method. A method for classifying images based on a cluster representation of data using the apparatus of decision trees and tools of information theory is proposed.

Results. The efficiency and effectiveness of the classification method is confirmed by applying the tree apparatus to the cluster representation of the structural image description data. Using examples of various informational content criteria for real experimental image data, the effectiveness of the created trees is estimated. The features of the introduction of various criteria for information content in the construction of a decision tree are analyzed comparatively.

Conclusions. The application of the considered informational criteria in various ways sets the sequence for introducing independent variables in the classification tree, which are quantitative indicators of the cluster representation of the image description. The calculations show that the Shannon entropy and the Gini coefficient are quite powerful informational criteria that provide practical construction of a classification decision tree. The similarity of the joint informational function of the root node for different criteria confirms the objectivity of the study, and their difference reflects the individual nature of sensitivity to the analyzed data.

The scientific novelty of the study is the improvement and statistical justification of the procedures for making classification decisions for cluster presentation data of image descriptions based on the introduction of tree models.

The practical significance of the work is to confirm the effectiveness of the implementation of the tree apparatus for classifying data using examples of images in computer vision systems. 


Keywords


Computer vision, structural image recognition methods, many key points, BRISK descriptor, cluster representation, description relevance, information growth criterion, Shannon entropy, Renyi entropy, Gini coefficient.

References


Hadetska S. V., Horokhovatskyi V. O. Zastosuvannia statystychnykh mir relevantnosti dlia vektornykh strukturnykh opysiv obiektiv u zadachi klasyfikatsii zobrazhen, Systemy upravlinnia, navihatsii ta zviazku, 2018, No. 4 (50), pp. 62– 68.

Horokhovatskyi V. O., Hadetska S. V., Stiahlyk N. I. Vyvchennia statystychnykh vlastyvostei modeli blochnoho podannia dlia mnozhyny deskryptoriv kliuchovykh tochok zobrazhen, Radio Electronics, Computer Science, Control, 2019, No. 2, pp. 100–107. DOI: 10.15588/1607-3274-20192-11.

Gorokhovatsky V. O. and Gadetska S. V. Determination of Relevance of Visual Object Images by Application of Statistical Analysis of Regarding Fragment Representation of their Descriptions, Telecommunications and Radio Engineering, 2019, No. 78 (3), pp. 211–220. DOI: 10.1615/TelecomRadEng.v78.i3.20.

Leutenegger S., Chli M., and Siegwart R.Y. BRISK: Binary Robust Invariant Scalable Keypoints. Computer Vision (ICCV), 2011, pp. 2548–2555.

Aggarwal C. C. and Reddy C. K. Data Clustering. Algorithms and Application. Boca Raton: CRC Press, 2014.

Gorokhovatskyi O., Gorokhovatskyi V., Peredrii O. Analysis of Application of Cluster Descriptions in Space of Characteristic Image Features, Data, 2018, No. 3(4), P. 52. DOI: 10.3390/data3040052. Available online: https://www.mdpi.com/2306-5729/3/4/52

Gorohovatskij V. A., Putyatin E. P., Stolyarov V. S. Issledovanie rezul’tativnosti strukturnyh metodov klassifikacii izobrazhenij s primeneniem klasternoj modeli dannyh, Radio Electronics, Computer Science, Control, 2017, No. 3 (42), pp. 78–85.

Nong Ye. Data Mining, Theories, Algorithms, and Examples (1st. ed.). CRC Press, Inc., USA, 2013.

Paklin N. B., Oreshkov V. I. Biznes-analitika: ot dannyh k znaniyam: ucheb. posob., SPb., Piter, 2013, 704 p.

Subbotin, S. A. Metody sinteza modelej kolichestvennyh zavisimostej v bazise derev’ev regressii, realizuyushchih klaster-regressionnuyu approksimaciyu po precedentam, Radio Electronics, Computer Science, Control, 2019, No. 3, pp. 76–85.

Witten I. H., Frank E. and Hall M. A. Data Mining: Practical Machine Learning Tools and Techniques. 3rd Edition, Morgan Kaufmann Publishers, Burlington, 2011.

CHumak O. V. Entropii i fraktaly v analize dannyah, Moskva-Izhevsk: NIC «Regulyarnaya i haoticheskaya dinamika», Institut komp’yuternyh issledovanij, 2011,164 p.

Bashkirov A. G., Entropiya Ren’i kak statisticheskaya entropiya dlya slozhnyh sistem, TMF, 2006, Vol. 149, No. 2, pp. 299–317. DOI: http://dx.doi.org/10.4213/tmf4235

Kacprzyk J., Pedrycz W. Springer Handbook of Computational Intelligence. Springer-Verlag, Berlin Heidelberg, 2015.

Kruse R., Borgelt C., Klawonn F. et. al. Computational intelligence: a methodological introduction. London, SpringerVerlag, 2013, 488 p.

Clarke B., Fokoue E., Zhang H. H. Principles and theory for data mining and machine learning. New York, Springer, 2009, 781 p.

Duda R. O., Hart P. E., Stork D.G . Pattern classification, 2ed., Wiley, 2000, 738p.

Gorokhovatskyi V., Gadetska S., Ponomarenko R. Recognition of Visual Objects Based on Statistical Distributions for Blocks of Structural Description of Image. Lecture Notes in Computational Intelligence and Decision Making, Proc. of the XV Int. Scientific Conf. “Intellectual Systems of Decision Making and Problems of Computational Intelligence” (ISDMCI’ 2019). Ukraine, May 21–25, 2019, pp. 501–512. Available online: https://rd.springer.com/chapter/10.1007/978-3-030-264741_35

Podgorelec V., Kokol P., Stiglic B., Rozman I., Decision trees: an overview and their use in medicine, Journal of Medical Systems, Kluwer Academic/Plenum Press, October 2002, Vol. 26, No. 5, pp. 445–463,

Grzymala-Busse J. W. Selected algorithms of machine learning from example, Fundamenta Informaticae, 1993, No. 18, pp. 193–207.

Abe, Sumiyoshi. Axioms and uniqueness theorem for Tsallis entropy. Physics Letters, 2000, A. 271. pp. 74–79.

Renyi A. On measures of entropy and information. [Electronic resource]. Access mode: http://l.academicdirect.org/Horticulture/GAs/Refs/Renyi_19 61.pdf.

Nielsen, F., & Nock, R. On Rényi and Tsallis entropies and divergences for exponential families. CoRR. abs/1105.3259, 2011.

Beck, C., & Schögl, F. Thermodynamics of Chaotic Systems: An Introduction (Cambridge Nonlinear Science Series). Cambridge. Cambridge University Press, 1993. DOI: 10.1017/CBO9780511524585

Kaftannikov I. L., Parasich A. V. Osobennosti prime-neniya derev’ev reshenij v zadachah klassifikacii. Vestnik YUUrGU. Seriya «Komp’yuternye tekhnologii, upravlenie, radioelektronika», 2015, Vol. 15, No. 3, pp. 26–32. DOI: 10.14529/ctcr15030


GOST Style Citations


1. Гадецька С. В. Застосування статистичних мір релевантності для векторних структурних описів об’єктів у задачі класифікації зображень / С. В. Гадецька, В. О. Гороховатський // Системи управління, навігації та зв’язку. – 2018. – №4 (50). – С. 62–68.

2. Гороховатський В. О. Вивчення статистичних властивостей моделі блочного подання для множини дескрипторів ключових точок зображень / В. О. Гороховатський, С. В. Гадецька, Н. І. Стяглик // Радіоелектроніка,  інформатика, управління.–2019. – № 2. – C. 100–107.  DOI: 10.15588/1607-3274-2019-2-11.

3. Gorokhovatsky V. O. Determination of Relevance of Visual Object Images by Application of  Statistical Analysis of Regarding Fragment Representation of their Descriptions / V. O. Gorokhovatsky and S. V. Gadetska // Telecommunications and Radio Engineering. – 2019. – No. 78 (3). – P. 211–220. DOI: 10.1615/TelecomRadEng.v78.i3.20.

4. Leutenegger S. BRISK: Binary Robust Invariant Scalable Keypoints / S. Leutenegger, M. Chli and R. Y. Siegwart // Computer Vision (ICCV). – 2011.– P. 2548–2555.

5. Aggarwal C. C. and Reddy C. K. Data Clustering. Algorithms and Application / C. C. Aggarwal and C. K. Reddy. – Boca Raton : CRC Press, 2014.

6. Gorokhovatskyi O. Analysis of Application of Cluster Descriptions in Space of Characteristic Image Features / O. Gorokhovatskyi, V. Gorokhovatskyi, O. Peredrii // Data. – 2018. – No. 3(4). – P. 52. DOI: 10.3390/data3040052. Available online: https://www.mdpi.com/2306-5729/3/4/52

7. Гороховатский В. А. Исследование результативности структурных методов классификации изображений с применением кластерной модели данных / В. А. Гороховатский,  Е. П. Путятин, В. С. Столяров // Радиоэлектроника,  информатика, управление. – 2017. – №3 (42). – C. 78–85.

8. Nong Ye. Data Mining: Theories, Algorithms, and Examples (1st. ed.) / Ye. Nong. – CRC Press, Inc., USA, 2013.

9. Паклин Н. Б. Бизнес-аналитика: от данных к знаниям: учеб. пособ. / Н. Б. Паклин, В. И.  Орешков. – СПб. : Питер,  2013. – 704 с.

10. Субботин С. А. Методы синтеза моделей количественных зависимостей в базисе деревьев регрессии, реализующих кластер-регрессионную аппроксимацию по прецедентам / С. А. Субботин// Радіоелектроніка, інформатика, управління. – 2019. – № 3. – С. 76–85.

11. Witten I. H. Data Mining: Practical Machine Learning Tools and Techniques. 3rd Edition / I. H. Witten, E. Frank, and M. A. Hall. – Morgan Kaufmann Publishers, Burlington. – 2011.

12. Чумак О. В. Энтропии и фракталы в анализе даннях / О. В. Чумак. – Москва-Ижевск : НИЦ «Регулярная и хаотическая динамика», Институт компьютерных исследований, 2011. – 164 с.

13. Башкиров А. Г. Энтропия Реньи как статистическая энтропия для сложных систем / А. Г. Башкиров // ТМФ. – 2006. – Т. 149, № 2. – С. 299–317. DOI: http://dx.doi.org/10.4213/tmf4235

14. Kacprzyk, J. Springer Handbook of Computational Intelligence / J. Kacprzyk, W. Pedrycz. – Springer-Verlag, Berlin Heidelberg, 2015.

15. Computational intelligence: a methodological introduction / [R. Kruse, C. Borgelt, F.Klawonn et. al.]. – London : Springer-Verlag, 2013. – 488 p.

16. Clarke B. Principles and theory for data mining and machine learning / B. Clarke, E. Fokoue, H. H. Zhang. – New York : Springer, 2009. – 781 p.

17. Duda R. O. Pattern classification, 2ed. / R. O. Duda, P. E. Hart, D. G. Stork. – Wiley, 2000. – 738 p.

18. Gorokhovatskyi V. Recognition of Visual Objects Based on Statistical Distributions for Blocks of Structural Description of Image. Lecture Notes in Computational Intelligence and Decision Making / V. Gorokhovatskyi, S. Gadetska, R. Ponomarenko // Proc. of the XV Int. Scientific Conf. “Intellectual Systems of Decision Making and Problems of Computational Intelligence” (ISDMCI’ 2019). – Ukraine, May 21– 25, 2019. – P. 501–512. Available online: https://rd.springer.com/chapter/10.1007/978-3-030-264741_35

19. Decision trees: an overview and their use in medicine / [V. Podgorelec, P. Kokol, B. Stiglic, I. Rozman] // Journal of Medical Systems, Kluwer Academic/Plenum Press. – October 2002. – Vol. 26, No. 5. – P. 445–463.

20. Grzymala-Busse J. W. Selected algorithms of machine learning from example / J. W. Grzymala-Busse // Fundamenta Informaticae. – 1993. – No. 18. –P. 193–207

21. Sumiyoshi Abe. Axioms and uniqueness theorem for Tsallis entropy / Abe Sumiyoshi // Physics Letters. – 2000. – A. 271. – P. 74–79.

22. Renyi A. On measures of entropy and information.[Електронний ресурс] / A. Renyi. – Режим доступу: http://l.academicdirect.org/Horticulture/GAs/Refs/Renyi_19 61.pdf.

23. Nielsen F. On Rényi and Tsallis entropies and divergences for exponential families / F. Nielsen & R. Nock, CoRR. abs/1105.3259, 2011.

24. Beck C. Thermodynamics of Chaotic Systems: An Introduction (Cambridge Nonlinear Science Series) / C. Beck & F. Schögl. – Cambridge : Cambridge University Press, 1993. DOI:10.1017/CBO9780511524585

25. Кафтанников И. Л. Особенности применения деревьев решений в задачах классификации / И. Л. Кафтанников, А. В. Парасич // Вестник ЮУрГУ. Серия «Компьютерные технологии, управление, радиоэлектроника». – 2015. – Т. 15, № 3. – С. 26–32.DOI: 10.14529/ctcr150304







Copyright (c) 2020 S. V. Gadetska, V. A. Gorokhovatsky, N. I. Stiahlyk

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Address of the journal editorial office:
Editorial office of the journal «Radio Electronics, Computer Science, Control»,
National University "Zaporizhzhia Polytechnic", 
Zhukovskogo street, 64, Zaporizhzhia, 69063, Ukraine. 
Telephone: +38-061-769-82-96 – the Editing and Publishing Department.
E-mail: rvv@zntu.edu.ua

The reference to the journal is obligatory in the cases of complete or partial use of its materials.