Geodesic
Mathematical methods of modeling of image processing and analysis in the modified descriptive algebras of images
Journal of computational and engineering mathematics, Tome 3 (2016) no. 1, pp. 3-9.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article is devoted to the development of the method of mathematical modeling of image processing and analysis in an apparatus of the modified descriptive algebras of images. A brief chronology of the formation of an algebraic approach in the studies of foreign and domestic scientists is given in materials. The present state of an mathematical apparatus of the modified descriptive algebras of images is described. The results of the latest researches are presented as a technique of the organization of a computing experiment. The combinatorial evaluation of the initial images, which are randomly selected among all the possible variants, is carried at the first step of the computing experiment . At the second step the initial images are used in the development of an algorithm and a mathematical method of their processing and analysis modeling. The second step is to develop an objective function to optimize and select the variable parameters of a mathematical model. At the third step a genetic algorithm should be applied to find the optimal values of variable parameters of the mathematical model.
Keywords: image processing and analysis; modified descriptive algebra of images; mathematical modeling method; combinatorial evaluation sampling; objective function; genetic algorithm; technique of computing experiment. 
@article{JCEM_2016_3_1_a0,
     author = {A. R. Iskhakov},
     title = {Mathematical methods of modeling of image processing and analysis in the modified descriptive algebras of images},
     journal = {Journal of computational and engineering mathematics},
     pages = {3--9},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2016_3_1_a0/}
}
TY  - JOUR
AU  - A. R. Iskhakov
TI  - Mathematical methods of modeling of image processing and analysis in the modified descriptive algebras of images
JO  - Journal of computational and engineering mathematics
PY  - 2016
SP  - 3
EP  - 9
VL  - 3
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCEM_2016_3_1_a0/
LA  - en
ID  - JCEM_2016_3_1_a0
ER  - 
%0 Journal Article
%A A. R. Iskhakov
%T Mathematical methods of modeling of image processing and analysis in the modified descriptive algebras of images
%J Journal of computational and engineering mathematics
%D 2016
%P 3-9
%V 3
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCEM_2016_3_1_a0/
%G en
%F JCEM_2016_3_1_a0
A. R. Iskhakov. Mathematical methods of modeling of image processing and analysis in the modified descriptive algebras of images. Journal of computational and engineering mathematics, Tome 3 (2016) no. 1, pp. 3-9. http://geodesic.mathdoc.fr/item/JCEM_2016_3_1_a0/

[1] G. Matheron, Random Sets and Integral Geometry, Wiley, New York, 1975 | MR | Zbl

[2] J. Serra, Image Analysis and Mathematical Morphology, Academic Press, London, 1982 | MR | Zbl

[3] W. Grenander, Lectures on the Theory of Images: Synthesis of Images, Mir, Moscow, 1979 | MR

[4] W. Grenander, Lectures on the Theory of Images:Analysis of Images, Mir, Moscow, 1981 | MR

[5] W. Grenander, Lectures on the Theory of Images:Regular Structures, Mir, Moscow, 1983 | MR

[6] Yu. I. Zhuravlev, “Algebraic Methods for Designing Algorithms for Pattern Recognition and Forecasting”, Pattern Recognition and Image Analysis. Advances in Mathematical Theory and Applications, 9:4 (1999), 790–791

[7] E.V. Djukova, Yu. I. Zhuravlev, “Discrete Methods of Information Analysis in Recognition and Algorithm Synthesis”, Pattern Recognition and Image Analysis. Advances in Mathematical Theory and Applications, 7:2 (2003), 192–205

[8] M. Pavel, Fundamentals of Pattern Recognition, Marcel Dekker. Inc., New York, 1989 | MR | Zbl

[9] S. R. Sternberg, An Overview of Image Algebra and Related Architectures, Integrated Technology for Parallel Image Processing, Academic Press, London, 1985

[10] G. X. Ritter, Image Algebra, Center for Computer Vision and Visualization. Department of Computer and Information Science and Engineering, University of Florida, Gainesville, 2001

[11] I. B. Gurevich, “Descriptive Technique for Image Description, Representation and Recognition”, Pattern Recognition and Image Analysis. Advances in Mathematical Theory and Applications in the USSR, 1 (1991), 50–53

[12] I. B. Gurevich, V. V. Yashina, “Descriptive Image Algebras with One Ring”, Pattern Recognition and Image Analysis. Advances in Mathematical Theory and Applications, 13:4 (2004), 579–599

[13] A. R. Iskhakov, R. F. Malikov, Modeling of Vision Systems in the Modified Descriptive Image Algebras, BSPU Publ, Ufa, 2015

[14] A. R. Iskhakov, “Parametric Synthesis of Vision Systems in the Modified Descriptive Image Algebras”, Science City Research – Issledovanija Naukograda, 12:2 (2015)

[15] M. V. Burakov, Genetic Algorithm: Theory and Practice, SUAE, St. Petersburg, 2008